---
_id: '14243'
abstract:
- lang: eng
text: 'Two-player zero-sum "graph games" are central in logic, verification, and
multi-agent systems. The game proceeds by placing a token on a vertex of a graph,
and allowing the players to move it to produce an infinite path, which determines
the winner or payoff of the game. Traditionally, the players alternate turns in
moving the token. In "bidding games", however, the players have budgets and in
each turn, an auction (bidding) determines which player moves the token. So far,
bidding games have only been studied as full-information games. In this work we
initiate the study of partial-information bidding games: we study bidding games
in which a player''s initial budget is drawn from a known probability distribution.
We show that while for some bidding mechanisms and objectives, it is straightforward
to adapt the results from the full-information setting to the partial-information
setting, for others, the analysis is significantly more challenging, requires
new techniques, and gives rise to interesting results. Specifically, we study
games with "mean-payoff" objectives in combination with "poorman" bidding. We
construct optimal strategies for a partially-informed player who plays against
a fully-informed adversary. We show that, somewhat surprisingly, the "value" under
pure strategies does not necessarily exist in such games.'
acknowledgement: This research was supported in part by ISF grant no.1679/21, by the
ERC CoG 863818 (ForM-SMArt), and the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.
article_processing_charge: No
arxiv: 1
author:
- first_name: Guy
full_name: Avni, Guy
id: 463C8BC2-F248-11E8-B48F-1D18A9856A87
last_name: Avni
orcid: 0000-0001-5588-8287
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Dorde
full_name: Zikelic, Dorde
id: 294AA7A6-F248-11E8-B48F-1D18A9856A87
last_name: Zikelic
orcid: 0000-0002-4681-1699
citation:
ama: 'Avni G, Jecker IR, Zikelic D. Bidding graph games with partially-observable
budgets. In: Proceedings of the 37th AAAI Conference on Artificial Intelligence.
Vol 37. ; 2023:5464-5471. doi:10.1609/aaai.v37i5.25679'
apa: Avni, G., Jecker, I. R., & Zikelic, D. (2023). Bidding graph games with
partially-observable budgets. In Proceedings of the 37th AAAI Conference on
Artificial Intelligence (Vol. 37, pp. 5464–5471). Washington, DC, United States.
https://doi.org/10.1609/aaai.v37i5.25679
chicago: Avni, Guy, Ismael R Jecker, and Dorde Zikelic. “Bidding Graph Games with
Partially-Observable Budgets.” In Proceedings of the 37th AAAI Conference on
Artificial Intelligence, 37:5464–71, 2023. https://doi.org/10.1609/aaai.v37i5.25679.
ieee: G. Avni, I. R. Jecker, and D. Zikelic, “Bidding graph games with partially-observable
budgets,” in Proceedings of the 37th AAAI Conference on Artificial Intelligence,
Washington, DC, United States, 2023, vol. 37, no. 5, pp. 5464–5471.
ista: 'Avni G, Jecker IR, Zikelic D. 2023. Bidding graph games with partially-observable
budgets. Proceedings of the 37th AAAI Conference on Artificial Intelligence. AAAI:
Conference on Artificial Intelligence vol. 37, 5464–5471.'
mla: Avni, Guy, et al. “Bidding Graph Games with Partially-Observable Budgets.”
Proceedings of the 37th AAAI Conference on Artificial Intelligence, vol.
37, no. 5, 2023, pp. 5464–71, doi:10.1609/aaai.v37i5.25679.
short: G. Avni, I.R. Jecker, D. Zikelic, in:, Proceedings of the 37th AAAI Conference
on Artificial Intelligence, 2023, pp. 5464–5471.
conference:
end_date: 2023-02-14
location: Washington, DC, United States
name: 'AAAI: Conference on Artificial Intelligence'
start_date: 2023-02-07
date_created: 2023-08-27T22:01:18Z
date_published: 2023-06-27T00:00:00Z
date_updated: 2025-07-14T09:09:56Z
day: '27'
department:
- _id: ToHe
- _id: KrCh
doi: 10.1609/aaai.v37i5.25679
ec_funded: 1
external_id:
arxiv:
- '2211.13626'
intvolume: ' 37'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1609/aaai.v37i5.25679
month: '06'
oa: 1
oa_version: Published Version
page: 5464-5471
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Proceedings of the 37th AAAI Conference on Artificial Intelligence
publication_identifier:
isbn:
- '9781577358800'
publication_status: published
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bidding graph games with partially-observable budgets
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2023'
...
---
_id: '12101'
abstract:
- lang: eng
text: 'Spatial games form a widely-studied class of games from biology and physics
modeling the evolution of social behavior. Formally, such a game is defined by
a square (d by d) payoff matrix M and an undirected graph G. Each vertex of G
represents an individual, that initially follows some strategy i ∈ {1,2,…,d}.
In each round of the game, every individual plays the matrix game with each of
its neighbors: An individual following strategy i meeting a neighbor following
strategy j receives a payoff equal to the entry (i,j) of M. Then, each individual
updates its strategy to its neighbors'' strategy with the highest sum of payoffs,
and the next round starts. The basic computational problems consist of reachability
between configurations and the average frequency of a strategy. For general spatial
games and graphs, these problems are in PSPACE. In this paper, we examine restricted
setting: the game is a prisoner’s dilemma; and G is a subgraph of grid. We prove
that basic computational problems for spatial games with prisoner’s dilemma on
a subgraph of a grid are PSPACE-hard.'
acknowledgement: "Krishnendu Chatterjee: The research was partially supported by the
ERC CoG 863818\r\n(ForM-SMArt).\r\nIsmaël Jecker: The research was partially supported
by the ERC grant 950398 (INFSYS).\r\nJakub Svoboda: The research was partially supported
by the ERC CoG 863818 (ForM-SMArt)"
article_number: 11:1-11:14
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Jakub
full_name: Svoboda, Jakub
id: 130759D2-D7DD-11E9-87D2-DE0DE6697425
last_name: Svoboda
orcid: 0000-0002-1419-3267
citation:
ama: 'Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. Complexity of spatial
games. In: 42nd IARCS Annual Conference on Foundations of Software Technology
and Theoretical Computer Science. Vol 250. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2022. doi:10.4230/LIPIcs.FSTTCS.2022.11'
apa: 'Chatterjee, K., Ibsen-Jensen, R., Jecker, I. R., & Svoboda, J. (2022).
Complexity of spatial games. In 42nd IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science (Vol. 250). Madras,
India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11'
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Ismael R Jecker, and Jakub
Svoboda. “Complexity of Spatial Games.” In 42nd IARCS Annual Conference on
Foundations of Software Technology and Theoretical Computer Science, Vol.
250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11.
ieee: K. Chatterjee, R. Ibsen-Jensen, I. R. Jecker, and J. Svoboda, “Complexity
of spatial games,” in 42nd IARCS Annual Conference on Foundations of Software
Technology and Theoretical Computer Science, Madras, India, 2022, vol. 250.
ista: 'Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. 2022. Complexity of spatial
games. 42nd IARCS Annual Conference on Foundations of Software Technology and
Theoretical Computer Science. FSTTC: Foundations of Software Technology and Theoretical
Computer Science vol. 250, 11:1-11:14.'
mla: Chatterjee, Krishnendu, et al. “Complexity of Spatial Games.” 42nd IARCS
Annual Conference on Foundations of Software Technology and Theoretical Computer
Science, vol. 250, 11:1-11:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2022, doi:10.4230/LIPIcs.FSTTCS.2022.11.
short: K. Chatterjee, R. Ibsen-Jensen, I.R. Jecker, J. Svoboda, in:, 42nd IARCS
Annual Conference on Foundations of Software Technology and Theoretical Computer
Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.
conference:
end_date: 2022-12-20
location: Madras, India
name: 'FSTTC: Foundations of Software Technology and Theoretical Computer Science'
start_date: 2022-12-18
date_created: 2023-01-01T23:00:50Z
date_published: 2022-12-14T00:00:00Z
date_updated: 2025-07-14T09:09:55Z
day: '14'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.FSTTCS.2022.11
ec_funded: 1
file:
- access_level: open_access
checksum: a21e3ba2421e2c4a06aa2cb6d530ede1
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T10:19:19Z
date_updated: 2023-01-20T10:19:19Z
file_id: '12323'
file_name: 2022_LIPICs_Chatterjee.pdf
file_size: 657396
relation: main_file
success: 1
file_date_updated: 2023-01-20T10:19:19Z
has_accepted_license: '1'
intvolume: ' 250'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: 42nd IARCS Annual Conference on Foundations of Software Technology and
Theoretical Computer Science
publication_identifier:
isbn:
- '9783959772617'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Complexity of spatial games
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 250
year: '2022'
...
---
_id: '10694'
abstract:
- lang: eng
text: 'In a two-player zero-sum graph game the players move a token throughout a
graph to produce an infinite path, which determines the winner or payoff of the
game. Traditionally, the players alternate turns in moving the token. In bidding
games, however, the players have budgets, and in each turn, we hold an “auction”
(bidding) to determine which player moves the token: both players simultaneously
submit bids and the higher bidder moves the token. The bidding mechanisms differ
in their payment schemes. Bidding games were largely studied with variants of
first-price bidding in which only the higher bidder pays his bid. We focus on
all-pay bidding, where both players pay their bids. Finite-duration all-pay bidding
games were studied and shown to be technically more challenging than their first-price
counterparts. We study for the first time, infinite-duration all-pay bidding games.
Our most interesting results are for mean-payoff objectives: we portray a complete
picture for games played on strongly-connected graphs. We study both pure (deterministic)
and mixed (probabilistic) strategies and completely characterize the optimal and
almost-sure (with probability 1) payoffs the players can respectively guarantee.
We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical
properties of their first-price counterparts; namely, an equivalence with random-turn
games in which in each turn, the player who moves is selected according to a (biased)
coin toss. The equivalences for all-pay bidding are more intricate and unexpected
than for first-price bidding.'
acknowledgement: This research was supported in part by the Austrian Science Fund
(FWF) under grant Z211-N23 (Wittgenstein Award), ERC CoG 863818 (FoRM-SMArt), and
by the European Union's Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie Grant Agreement No. 665385.
article_processing_charge: No
arxiv: 1
author:
- first_name: Guy
full_name: Avni, Guy
id: 463C8BC2-F248-11E8-B48F-1D18A9856A87
last_name: Avni
orcid: 0000-0001-5588-8287
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Dorde
full_name: Zikelic, Dorde
id: 294AA7A6-F248-11E8-B48F-1D18A9856A87
last_name: Zikelic
orcid: 0000-0002-4681-1699
citation:
ama: 'Avni G, Jecker IR, Zikelic D. Infinite-duration all-pay bidding games. In:
Marx D, ed. Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms.
Society for Industrial and Applied Mathematics; 2021:617-636. doi:10.1137/1.9781611976465.38'
apa: 'Avni, G., Jecker, I. R., & Zikelic, D. (2021). Infinite-duration all-pay
bidding games. In D. Marx (Ed.), Proceedings of the 2021 ACM-SIAM Symposium
on Discrete Algorithms (pp. 617–636). Virtual: Society for Industrial and
Applied Mathematics. https://doi.org/10.1137/1.9781611976465.38'
chicago: Avni, Guy, Ismael R Jecker, and Dorde Zikelic. “Infinite-Duration All-Pay
Bidding Games.” In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms,
edited by Dániel Marx, 617–36. Society for Industrial and Applied Mathematics,
2021. https://doi.org/10.1137/1.9781611976465.38.
ieee: G. Avni, I. R. Jecker, and D. Zikelic, “Infinite-duration all-pay bidding
games,” in Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms,
Virtual, 2021, pp. 617–636.
ista: 'Avni G, Jecker IR, Zikelic D. 2021. Infinite-duration all-pay bidding games.
Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium
on Discrete Algorithms, 617–636.'
mla: Avni, Guy, et al. “Infinite-Duration All-Pay Bidding Games.” Proceedings
of the 2021 ACM-SIAM Symposium on Discrete Algorithms, edited by Dániel Marx,
Society for Industrial and Applied Mathematics, 2021, pp. 617–36, doi:10.1137/1.9781611976465.38.
short: G. Avni, I.R. Jecker, D. Zikelic, in:, D. Marx (Ed.), Proceedings of the
2021 ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied
Mathematics, 2021, pp. 617–636.
conference:
end_date: 2021-01-13
location: Virtual
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2021-01-10
date_created: 2022-01-27T12:11:23Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2025-07-14T09:10:12Z
day: '01'
department:
- _id: GradSch
- _id: KrCh
doi: 10.1137/1.9781611976465.38
ec_funded: 1
editor:
- first_name: Dániel
full_name: Marx, Dániel
last_name: Marx
external_id:
arxiv:
- '2005.06636'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2005.06636
month: '01'
oa: 1
oa_version: Preprint
page: 617-636
project:
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms
publication_identifier:
isbn:
- 978-1-61197-646-5
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Infinite-duration all-pay bidding games
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '10052'
abstract:
- lang: eng
text: "A deterministic finite automaton (DFA) \U0001D49C is composite if its language
L(\U0001D49C) can be decomposed into an intersection ⋂_{i = 1}^k L(\U0001D49C_i)
of languages of smaller DFAs. Otherwise, \U0001D49C is prime. This notion of primality
was introduced by Kupferman and Mosheiff in 2013, and while they proved that we
can decide whether a DFA is composite, the precise complexity of this problem
is still open, with a doubly-exponential gap between the upper and lower bounds.
In this work, we focus on permutation DFAs, i.e., those for which the transition
monoid is a group. We provide an NP algorithm to decide whether a permutation
DFA is composite, and show that the difficulty of this problem comes from the
number of non-accepting states of the instance: we give a fixed-parameter tractable
algorithm with the number of rejecting states as the parameter. Moreover, we investigate
the class of commutative permutation DFAs. Their structural properties allow us
to decide compositionality in NL, and even in LOGSPACE if the alphabet size is
fixed. Despite this low complexity, we show that complex behaviors still arise
in this class: we provide a family of composite DFAs each requiring polynomially
many factors with respect to its size. We also consider the variant of the problem
that asks whether a DFA is k-factor composite, that is, decomposable into k smaller
DFAs, for some given integer k ∈ ℕ. We show that, for commutative permutation
DFAs, restricting the number of factors makes the decision computationally harder,
and yields a problem with tight bounds: it is NP-complete. Finally, we show that
in general, this problem is in PSPACE, and it is in LOGSPACE for DFAs with a singleton
alphabet."
acknowledgement: "Ismaël Jecker: Marie Skłodowska-Curie Grant Agreement No. 754411.
Nicolas Mazzocchi: BOSCO project PGC2018-102210-B-I00 (MCIU/AEI/FEDER, UE), BLOQUESCM
project S2018/TCS-4339, and MINECO grant RYC-2016-20281.\r\nPetra Wolf : DFG project
FE 560/9-1.\r\n"
alternative_title:
- LIPIcs
article_number: '18'
article_processing_charge: No
arxiv: 1
author:
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Nicolas
full_name: Mazzocchi, Nicolas
last_name: Mazzocchi
- first_name: Petra
full_name: Wolf, Petra
last_name: Wolf
citation:
ama: 'Jecker IR, Mazzocchi N, Wolf P. Decomposing permutation automata. In: 32nd
International Conference on Concurrency Theory. Vol 203. Schloss Dagstuhl
- Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.CONCUR.2021.18'
apa: 'Jecker, I. R., Mazzocchi, N., & Wolf, P. (2021). Decomposing permutation
automata. In 32nd International Conference on Concurrency Theory (Vol.
203). Paris, France: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CONCUR.2021.18'
chicago: Jecker, Ismael R, Nicolas Mazzocchi, and Petra Wolf. “Decomposing Permutation
Automata.” In 32nd International Conference on Concurrency Theory, Vol.
203. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.CONCUR.2021.18.
ieee: I. R. Jecker, N. Mazzocchi, and P. Wolf, “Decomposing permutation automata,”
in 32nd International Conference on Concurrency Theory, Paris, France,
2021, vol. 203.
ista: 'Jecker IR, Mazzocchi N, Wolf P. 2021. Decomposing permutation automata. 32nd
International Conference on Concurrency Theory. CONCUR: Conference on Concurrency
Theory, LIPIcs, vol. 203, 18.'
mla: Jecker, Ismael R., et al. “Decomposing Permutation Automata.” 32nd International
Conference on Concurrency Theory, vol. 203, 18, Schloss Dagstuhl - Leibniz
Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.CONCUR.2021.18.
short: I.R. Jecker, N. Mazzocchi, P. Wolf, in:, 32nd International Conference on
Concurrency Theory, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-08-27
location: Paris, France
name: 'CONCUR: Conference on Concurrency Theory'
start_date: 2021-08-23
date_created: 2021-09-27T14:33:14Z
date_published: 2021-08-13T00:00:00Z
date_updated: 2022-05-13T08:12:52Z
day: '13'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.CONCUR.2021.18
ec_funded: 1
external_id:
arxiv:
- '2107.04683'
file:
- access_level: open_access
checksum: 4722c81be82265cf45e78adf9db91250
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-01T11:10:53Z
date_updated: 2021-10-01T11:10:53Z
file_id: '10064'
file_name: 2021_CONCUR_Jecker.pdf
file_size: 1003552
relation: main_file
success: 1
file_date_updated: 2021-10-01T11:10:53Z
has_accepted_license: '1'
intvolume: ' 203'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 32nd International Conference on Concurrency Theory
publication_identifier:
isbn:
- 978-3-9597-7203-7
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Decomposing permutation automata
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 203
year: '2021'
...
---
_id: '10055'
abstract:
- lang: eng
text: "Repeated idempotent elements are commonly used to characterise iterable behaviours
in abstract models of computation. Therefore, given a monoid M, it is natural
to ask how long a sequence of elements of M needs to be to ensure the presence
of consecutive idempotent factors. This question is formalised through the notion
of the Ramsey function R_M associated to M, obtained by mapping every k ∈ ℕ to
the minimal integer R_M(k) such that every word u ∈ M^* of length R_M(k) contains
k consecutive non-empty factors that correspond to the same idempotent element
of M. In this work, we study the behaviour of the Ramsey function R_M by investigating
the regular \U0001D49F-length of M, defined as the largest size L(M) of a submonoid
of M isomorphic to the set of natural numbers {1,2, …, L(M)} equipped with the
max operation. We show that the regular \U0001D49F-length of M determines the
degree of R_M, by proving that k^L(M) ≤ R_M(k) ≤ (k|M|⁴)^L(M). To allow applications
of this result, we provide the value of the regular \U0001D49F-length of diverse
monoids. In particular, we prove that the full monoid of n × n Boolean matrices,
which is used to express transition monoids of non-deterministic automata, has
a regular \U0001D49F-length of (n²+n+2)/2."
acknowledgement: This project has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 754411. I wish to thank Michaël Cadilhac, Emmanuel Filiot and Charles Paperman
for their valuable insights concerning Green’s relations.
alternative_title:
- LIPIcs
article_number: '44'
article_processing_charge: No
author:
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
citation:
ama: 'Jecker IR. A Ramsey theorem for finite monoids. In: 38th International
Symposium on Theoretical Aspects of Computer Science. Vol 187. Schloss Dagstuhl
- Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.STACS.2021.44'
apa: 'Jecker, I. R. (2021). A Ramsey theorem for finite monoids. In 38th International
Symposium on Theoretical Aspects of Computer Science (Vol. 187). Saarbrücken,
Germany: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.STACS.2021.44'
chicago: Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” In 38th International
Symposium on Theoretical Aspects of Computer Science, Vol. 187. Schloss Dagstuhl
- Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.STACS.2021.44.
ieee: I. R. Jecker, “A Ramsey theorem for finite monoids,” in 38th International
Symposium on Theoretical Aspects of Computer Science, Saarbrücken, Germany,
2021, vol. 187.
ista: 'Jecker IR. 2021. A Ramsey theorem for finite monoids. 38th International
Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical
Aspects of Computer Science, LIPIcs, vol. 187, 44.'
mla: Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” 38th International
Symposium on Theoretical Aspects of Computer Science, vol. 187, 44, Schloss
Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.STACS.2021.44.
short: I.R. Jecker, in:, 38th International Symposium on Theoretical Aspects of
Computer Science, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-03-19
location: Saarbrücken, Germany
name: 'STACS: Symposium on Theoretical Aspects of Computer Science'
start_date: 2021-03-16
date_created: 2021-09-27T14:33:15Z
date_published: 2021-03-10T00:00:00Z
date_updated: 2023-08-14T07:03:23Z
day: '10'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.STACS.2021.44
ec_funded: 1
external_id:
isi:
- '000635691700044'
file:
- access_level: open_access
checksum: 17432a05733f408de300e17e390a90e4
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-01T09:55:00Z
date_updated: 2021-10-01T09:55:00Z
file_id: '10063'
file_name: 2021_LIPIcs_Jecker.pdf
file_size: 720250
relation: main_file
success: 1
file_date_updated: 2021-10-01T09:55:00Z
has_accepted_license: '1'
intvolume: ' 187'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 38th International Symposium on Theoretical Aspects of Computer Science
publication_identifier:
isbn:
- 978-3-9597-7180-1
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Ramsey theorem for finite monoids
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 187
year: '2021'
...
---
_id: '10075'
abstract:
- lang: eng
text: We study the expressiveness and succinctness of good-for-games pushdown automata
(GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can
be resolved based on the run constructed so far, but independently of the remainder
of the input word. We prove that GFG-PDA recognise more languages than deterministic
PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal
to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct
than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We
also study GFGness in visibly pushdown automata (VPA), which enjoy better closure
properties than PDA, and for which we show GFGness to be ExpTime-complete. GFG-VPA
can be exponentially more succinct than deterministic VPA, while VPA can be exponentially
more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we
study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has
a positional resolver, a function that resolves nondeterminism and that is only
dependant on the current configuration. Pushdown transducers are sufficient to
implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state
resolvers are determinisable.
acknowledgement: 'Ismaël Jecker: Funded by the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie grant agreement No 754411.
Karoliina Lehtinen: Funded by the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No 892704.'
alternative_title:
- LIPIcs
article_number: '53'
article_processing_charge: No
arxiv: 1
author:
- first_name: Shibashis
full_name: Guha, Shibashis
last_name: Guha
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Karoliina
full_name: Lehtinen, Karoliina
last_name: Lehtinen
- first_name: Martin
full_name: Zimmermann, Martin
last_name: Zimmermann
citation:
ama: 'Guha S, Jecker IR, Lehtinen K, Zimmermann M. A bit of nondeterminism makes
pushdown automata expressive and succinct. In: 46th International Symposium
on Mathematical Foundations of Computer Science. Vol 202. Schloss Dagstuhl
- Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.MFCS.2021.53'
apa: 'Guha, S., Jecker, I. R., Lehtinen, K., & Zimmermann, M. (2021). A bit
of nondeterminism makes pushdown automata expressive and succinct. In 46th
International Symposium on Mathematical Foundations of Computer Science (Vol.
202). Tallinn, Estonia: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2021.53'
chicago: Guha, Shibashis, Ismael R Jecker, Karoliina Lehtinen, and Martin Zimmermann.
“A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct.” In
46th International Symposium on Mathematical Foundations of Computer Science,
Vol. 202. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.MFCS.2021.53.
ieee: S. Guha, I. R. Jecker, K. Lehtinen, and M. Zimmermann, “A bit of nondeterminism
makes pushdown automata expressive and succinct,” in 46th International Symposium
on Mathematical Foundations of Computer Science, Tallinn, Estonia, 2021, vol.
202.
ista: 'Guha S, Jecker IR, Lehtinen K, Zimmermann M. 2021. A bit of nondeterminism
makes pushdown automata expressive and succinct. 46th International Symposium
on Mathematical Foundations of Computer Science. MFCS: Mathematical Foundations
of Computer Science, LIPIcs, vol. 202, 53.'
mla: Guha, Shibashis, et al. “A Bit of Nondeterminism Makes Pushdown Automata Expressive
and Succinct.” 46th International Symposium on Mathematical Foundations of
Computer Science, vol. 202, 53, Schloss Dagstuhl - Leibniz Zentrum für Informatik,
2021, doi:10.4230/LIPIcs.MFCS.2021.53.
short: S. Guha, I.R. Jecker, K. Lehtinen, M. Zimmermann, in:, 46th International
Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl -
Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-08-27
location: Tallinn, Estonia
name: 'MFCS: Mathematical Foundations of Computer Science'
start_date: 2021-08-23
date_created: 2021-10-03T22:01:23Z
date_published: 2021-08-18T00:00:00Z
date_updated: 2022-05-13T08:21:56Z
day: '18'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2021.53
ec_funded: 1
external_id:
arxiv:
- '2105.02611'
file:
- access_level: open_access
checksum: f4d407d43a97330c3fb11e6a7a6fbfb2
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-06T12:44:05Z
date_updated: 2021-10-06T12:44:05Z
file_id: '10097'
file_name: 2021_LIPIcs_Guha.pdf
file_size: 825567
relation: main_file
success: 1
file_date_updated: 2021-10-06T12:44:05Z
has_accepted_license: '1'
intvolume: ' 202'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 46th International Symposium on Mathematical Foundations of Computer
Science
publication_identifier:
isbn:
- 978-3-9597-7201-3
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: A bit of nondeterminism makes pushdown automata expressive and succinct
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 202
year: '2021'
...
---
_id: '10630'
abstract:
- lang: eng
text: In the Intersection Non-emptiness problem, we are given a list of finite automata
A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine
whether some string w ∈ Σ^* lies in the intersection of the languages accepted
by the automata in the list. We analyze the complexity of the Intersection Non-emptiness
problem under the promise that all input automata accept a language in some level
of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy.
Automata accepting languages from the lowest levels of these hierarchies arise
naturally in the context of model checking. We identify a dichotomy in the dot-depth
hierarchy by showing that the problem is already NP-complete when all input automata
accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all
automata accept a language from the level B_1. Conversely, we identify a tetrachotomy
in the Straubing-Thérien hierarchy. More precisely, we show that the problem is
in AC^0 when restricted to level L_0; complete for L or NL, depending on the input
representation, when restricted to languages in the level L_{1/2}; NP-complete
when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally,
PSPACE-complete when the input automata accept languages in level L_2 or higher.
Moreover, we show that the proof technique used to show containment in NP for
DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context
of NFAs. To prove this, we identify a family of languages that provide an exponential
separation between the state complexity of general NFAs and that of partially
ordered NFAs. To the best of our knowledge, this is the first superpolynomial
separation between these two models of computation.
acknowledgement: "We like to thank Lukas Fleischer and Michael Wehar for our discussions.
This work started at the Schloss Dagstuhl Event 20483 Moderne Aspekte der Komplexitätstheorie
in der Automatentheorie https://www.dagstuhl.de/20483.\r\n"
alternative_title:
- LIPIcs
article_number: '34'
article_processing_charge: No
arxiv: 1
author:
- first_name: Emmanuel
full_name: Arrighi, Emmanuel
last_name: Arrighi
- first_name: Henning
full_name: Fernau, Henning
last_name: Fernau
- first_name: Stefan
full_name: Hoffmann, Stefan
last_name: Hoffmann
- first_name: Markus
full_name: Holzer, Markus
last_name: Holzer
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Mateus
full_name: De Oliveira Oliveira, Mateus
last_name: De Oliveira Oliveira
- first_name: Petra
full_name: Wolf, Petra
last_name: Wolf
citation:
ama: 'Arrighi E, Fernau H, Hoffmann S, et al. On the complexity of intersection
non-emptiness for star-free language classes. In: 41st IARCS Annual Conference
on Foundations of Software Technology and Theoretical Computer Science. Vol
213. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.FSTTCS.2021.34'
apa: 'Arrighi, E., Fernau, H., Hoffmann, S., Holzer, M., Jecker, I. R., De Oliveira
Oliveira, M., & Wolf, P. (2021). On the complexity of intersection non-emptiness
for star-free language classes. In 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science (Vol. 213). Virtual:
Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34'
chicago: Arrighi, Emmanuel, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismael
R Jecker, Mateus De Oliveira Oliveira, and Petra Wolf. “On the Complexity of Intersection
Non-Emptiness for Star-Free Language Classes.” In 41st IARCS Annual Conference
on Foundations of Software Technology and Theoretical Computer Science, Vol.
213. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34.
ieee: E. Arrighi et al., “On the complexity of intersection non-emptiness
for star-free language classes,” in 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science, Virtual, 2021, vol.
213.
ista: 'Arrighi E, Fernau H, Hoffmann S, Holzer M, Jecker IR, De Oliveira Oliveira
M, Wolf P. 2021. On the complexity of intersection non-emptiness for star-free
language classes. 41st IARCS Annual Conference on Foundations of Software Technology
and Theoretical Computer Science. FSTTCS: Foundations of Software Technology and
Theoretical Computer Science, LIPIcs, vol. 213, 34.'
mla: Arrighi, Emmanuel, et al. “On the Complexity of Intersection Non-Emptiness
for Star-Free Language Classes.” 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science, vol. 213, 34, Schloss
Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.FSTTCS.2021.34.
short: E. Arrighi, H. Fernau, S. Hoffmann, M. Holzer, I.R. Jecker, M. De Oliveira
Oliveira, P. Wolf, in:, 41st IARCS Annual Conference on Foundations of Software
Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz Zentrum
für Informatik, 2021.
conference:
end_date: 2021-12-17
location: Virtual
name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science'
start_date: 2021-12-15
date_created: 2022-01-16T23:01:29Z
date_published: 2021-11-29T00:00:00Z
date_updated: 2022-01-17T10:56:19Z
day: '29'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.FSTTCS.2021.34
ec_funded: 1
external_id:
arxiv:
- '2110.01279'
file:
- access_level: open_access
checksum: d5a82ba893c3bc5da5914edbb3efb92b
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-17T10:49:03Z
date_updated: 2022-01-17T10:49:03Z
file_id: '10634'
file_name: 2021_LIPIcs_Arrighi.pdf
file_size: 844224
relation: main_file
success: 1
file_date_updated: 2022-01-17T10:49:03Z
has_accepted_license: '1'
intvolume: ' 213'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 41st IARCS Annual Conference on Foundations of Software Technology and
Theoretical Computer Science
publication_identifier:
isbn:
- 978-3-9597-7215-0
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the complexity of intersection non-emptiness for star-free language classes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 213
year: '2021'
...
---
_id: '8533'
abstract:
- lang: eng
text: Game of Life is a simple and elegant model to study dynamical system over
networks. The model consists of a graph where every vertex has one of two types,
namely, dead or alive. A configuration is a mapping of the vertices to the types.
An update rule describes how the type of a vertex is updated given the types of
its neighbors. In every round, all vertices are updated synchronously, which leads
to a configuration update. While in general, Game of Life allows a broad range
of update rules, we focus on two simple families of update rules, namely, underpopulation
and overpopulation, that model several interesting dynamics studied in the literature.
In both settings, a dead vertex requires at least a desired number of live neighbors
to become alive. For underpopulation (resp., overpopulation), a live vertex requires
at least (resp. at most) a desired number of live neighbors to remain alive. We
study the basic computation problems, e.g., configuration reachability, for these
two families of rules. For underpopulation rules, we show that these problems
can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete.
acknowledgement: "Krishnendu Chatterjee: The research was partially supported by the
Vienna Science and\r\nTechnology Fund (WWTF) Project ICT15-003.\r\nIsmaël Jecker:
This project has received funding from the European Union’s Horizon 2020 research\r\nand
innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411."
alternative_title:
- LIPIcs
article_number: 22:1-22:13
article_processing_charge: No
arxiv: 1
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Jakub
full_name: Svoboda, Jakub
id: 130759D2-D7DD-11E9-87D2-DE0DE6697425
last_name: Svoboda
orcid: 0000-0002-1419-3267
citation:
ama: 'Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. Simplified game of life:
Algorithms and complexity. In: 45th International Symposium on Mathematical
Foundations of Computer Science. Vol 170. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2020. doi:10.4230/LIPIcs.MFCS.2020.22'
apa: 'Chatterjee, K., Ibsen-Jensen, R., Jecker, I. R., & Svoboda, J. (2020).
Simplified game of life: Algorithms and complexity. In 45th International Symposium
on Mathematical Foundations of Computer Science (Vol. 170). Prague, Czech
Republic: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2020.22'
chicago: 'Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Ismael R Jecker, and Jakub
Svoboda. “Simplified Game of Life: Algorithms and Complexity.” In 45th International
Symposium on Mathematical Foundations of Computer Science, Vol. 170. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.MFCS.2020.22.'
ieee: 'K. Chatterjee, R. Ibsen-Jensen, I. R. Jecker, and J. Svoboda, “Simplified
game of life: Algorithms and complexity,” in 45th International Symposium on
Mathematical Foundations of Computer Science, Prague, Czech Republic, 2020,
vol. 170.'
ista: 'Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. 2020. Simplified game
of life: Algorithms and complexity. 45th International Symposium on Mathematical
Foundations of Computer Science. MFCS: Symposium on Mathematical Foundations of
Computer Science, LIPIcs, vol. 170, 22:1-22:13.'
mla: 'Chatterjee, Krishnendu, et al. “Simplified Game of Life: Algorithms and Complexity.”
45th International Symposium on Mathematical Foundations of Computer Science,
vol. 170, 22:1-22:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020,
doi:10.4230/LIPIcs.MFCS.2020.22.'
short: K. Chatterjee, R. Ibsen-Jensen, I.R. Jecker, J. Svoboda, in:, 45th International
Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl -
Leibniz-Zentrum für Informatik, 2020.
conference:
end_date: 2020-08-28
location: Prague, Czech Republic
name: 'MFCS: Symposium on Mathematical Foundations of Computer Science'
start_date: 2020-08-24
date_created: 2020-09-20T22:01:36Z
date_published: 2020-08-18T00:00:00Z
date_updated: 2025-06-02T08:53:42Z
day: '18'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2020.22
ec_funded: 1
external_id:
arxiv:
- '2007.02894'
file:
- access_level: open_access
checksum: bbd7c4f55d45f2ff2a0a4ef0e10a77b1
content_type: application/pdf
creator: dernst
date_created: 2020-09-21T13:57:34Z
date_updated: 2020-09-21T13:57:34Z
file_id: '8550'
file_name: 2020_LIPIcs_Chatterjee.pdf
file_size: 491374
relation: main_file
success: 1
file_date_updated: 2020-09-21T13:57:34Z
has_accepted_license: '1'
intvolume: ' 170'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 25892FC0-B435-11E9-9278-68D0E5697425
grant_number: ICT15-003
name: Efficient Algorithms for Computer Aided Verification
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 45th International Symposium on Mathematical Foundations of Computer
Science
publication_identifier:
isbn:
- '9783959771597'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Simplified game of life: Algorithms and complexity'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 170
year: '2020'
...
---
_id: '8534'
abstract:
- lang: eng
text: A regular language L of finite words is composite if there are regular languages
L₁,L₂,…,L_t such that L = ⋂_{i = 1}^t L_i and the index (number of states in a
minimal DFA) of every language L_i is strictly smaller than the index of L. Otherwise,
L is prime. Primality of regular languages was introduced and studied in [O. Kupferman
and J. Mosheiff, 2015], where the complexity of deciding the primality of the
language of a given DFA was left open, with a doubly-exponential gap between the
upper and lower bounds. We study primality for unary regular languages, namely
regular languages with a singleton alphabet. A unary language corresponds to a
subset of ℕ, making the study of unary prime languages closer to that of primality
in number theory. We show that the setting of languages is richer. In particular,
while every composite number is the product of two smaller numbers, the number
t of languages necessary to decompose a composite unary language induces a strict
hierarchy. In addition, a primality witness for a unary language L, namely a word
that is not in L but is in all products of languages that contain L and have an
index smaller than L’s, may be of exponential length. Still, we are able to characterize
compositionality by structural properties of a DFA for L, leading to a LogSpace
algorithm for primality checking of unary DFAs.
acknowledgement: "Ismaël Jecker: This project has received funding from the European
Union’s Horizon\r\n2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No.\r\n754411. Nicolas Mazzocchi: PhD fellowship FRIA from the F.R.S.-FNRS."
alternative_title:
- LIPIcs
article_number: 51:1-51:12
article_processing_charge: No
author:
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
- first_name: Nicolas
full_name: Mazzocchi, Nicolas
last_name: Mazzocchi
citation:
ama: 'Jecker IR, Kupferman O, Mazzocchi N. Unary prime languages. In: 45th International
Symposium on Mathematical Foundations of Computer Science. Vol 170. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.MFCS.2020.51'
apa: 'Jecker, I. R., Kupferman, O., & Mazzocchi, N. (2020). Unary prime languages.
In 45th International Symposium on Mathematical Foundations of Computer Science
(Vol. 170). Prague, Czech Republic: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.MFCS.2020.51'
chicago: Jecker, Ismael R, Orna Kupferman, and Nicolas Mazzocchi. “Unary Prime Languages.”
In 45th International Symposium on Mathematical Foundations of Computer Science,
Vol. 170. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.MFCS.2020.51.
ieee: I. R. Jecker, O. Kupferman, and N. Mazzocchi, “Unary prime languages,” in
45th International Symposium on Mathematical Foundations of Computer Science,
Prague, Czech Republic, 2020, vol. 170.
ista: 'Jecker IR, Kupferman O, Mazzocchi N. 2020. Unary prime languages. 45th International
Symposium on Mathematical Foundations of Computer Science. MFCS: Symposium on
Mathematical Foundations of Computer Science, LIPIcs, vol. 170, 51:1-51:12.'
mla: Jecker, Ismael R., et al. “Unary Prime Languages.” 45th International Symposium
on Mathematical Foundations of Computer Science, vol. 170, 51:1-51:12, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.MFCS.2020.51.
short: I.R. Jecker, O. Kupferman, N. Mazzocchi, in:, 45th International Symposium
on Mathematical Foundations of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2020.
conference:
end_date: 2020-08-28
location: Prague, Czech Republic
name: 'MFCS: Symposium on Mathematical Foundations of Computer Science'
start_date: 2020-08-24
date_created: 2020-09-20T22:01:36Z
date_published: 2020-08-18T00:00:00Z
date_updated: 2021-01-12T08:19:56Z
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doi: 10.4230/LIPIcs.MFCS.2020.51
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publication: 45th International Symposium on Mathematical Foundations of Computer
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title: Unary prime languages
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