@article{3332, abstract = {Given an algebraic hypersurface O in ℝd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3.}, author = {Kerber, Michael and Sagraloff, Michael}, journal = {Graphs and Combinatorics}, number = {3}, pages = {419 -- 430}, publisher = {Springer}, title = {{A note on the complexity of real algebraic hypersurfaces}}, doi = {10.1007/s00373-011-1020-7}, volume = {27}, year = {2011}, } @article{3334, author = {Edelsbrunner, Herbert and Pach, János and Ziegler, Günter}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {1 -- 2}, publisher = {Springer}, title = {{Letter from the new editors-in-chief}}, doi = {10.1007/s00454-010-9313-9}, volume = {45}, year = {2011}, } @inbook{3335, abstract = {We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, α. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of α, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. These can be tuned to consist of specific morphological elements of the Cosmic Web, i.e. clusters, filaments, or sheets. To elucidate the relative prominence of the various Betti numbers in different stages of morphological evolution, we introduce the concept of alpha tracks. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web. We also demonstrate that the scale-dependence of the Betti numbers yields a promising measure of cosmological parameters, with a potential to help in determining the nature of dark energy and to probe primordial non-Gaussianities. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field. Finally, we introduce the concept of persistent homology. It measures scale levels of the mass distribution and allows us to separate small from large scale features. Within the context of the hierarchical cosmic structure formation, persistence provides a natural formalism for a multiscale topology study of the Cosmic Web.}, author = {Van De Weygaert, Rien and Vegter, Gert and Edelsbrunner, Herbert and Jones, Bernard and Pranav, Pratyush and Park, Changbom and Hellwing, Wojciech and Eldering, Bob and Kruithof, Nico and Bos, Patrick and Hidding, Johan and Feldbrugge, Job and Ten Have, Eline and Van Engelen, Matti and Caroli, Manuel and Teillaud, Monique}, booktitle = {Transactions on Computational Science XIV}, editor = {Gavrilova, Marina and Tan, Kenneth and Mostafavi, Mir}, pages = {60 -- 101}, publisher = {Springer}, title = {{Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web}}, doi = {10.1007/978-3-642-25249-5_3}, volume = {6970}, year = {2011}, } @inproceedings{3336, abstract = {We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.}, author = {Chen, Chao and Freedman, Daniel and Lampert, Christoph}, booktitle = {CVPR: Computer Vision and Pattern Recognition}, isbn = {978-1-4577-0394-2}, location = {Colorado Springs, CO, United States}, pages = {2089 -- 2096}, publisher = {IEEE}, title = {{Enforcing topological constraints in random field image segmentation}}, doi = {10.1109/CVPR.2011.5995503}, year = {2011}, } @inproceedings{3337, abstract = {Playing table tennis is a difficult task for robots, especially due to their limitations of acceleration. A key bottleneck is the amount of time needed to reach the desired hitting position and velocity of the racket for returning the incoming ball. Here, it often does not suffice to simply extrapolate the ball's trajectory after the opponent returns it but more information is needed. Humans are able to predict the ball's trajectory based on the opponent's moves and, thus, have a considerable advantage. Hence, we propose to incorporate an anticipation system into robot table tennis players, which enables the robot to react earlier while the opponent is performing the striking movement. Based on visual observation of the opponent's racket movement, the robot can predict the aim of the opponent and adjust its movement generation accordingly. The policies for deciding how and when to react are obtained by reinforcement learning. We conduct experiments with an existing robot player to show that the learned reaction policy can significantly improve the performance of the overall system.}, author = {Wang, Zhikun and Lampert, Christoph and Mülling, Katharina and Schölkopf, Bernhard and Peters, Jan}, location = {San Francisco, USA}, pages = {332 -- 337}, publisher = {IEEE}, title = {{Learning anticipation policies for robot table tennis}}, doi = {10.1109/IROS.2011.6094892}, year = {2011}, } @unpublished{3338, abstract = {We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves inde- pendently and simultaneously; the current state and the two moves determine the successor state. We study concurrent games with ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respec- tively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite- precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as power- ful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.}, author = {Chatterjee, Krishnendu}, booktitle = {arXiv}, pages = {1 -- 51}, publisher = {ArXiv}, title = {{Bounded rationality in concurrent parity games}}, year = {2011}, } @unpublished{3339, abstract = {Turn-based stochastic games and its important subclass Markov decision processes (MDPs) provide models for systems with both probabilistic and nondeterministic behaviors. We consider turn-based stochastic games with two classical quantitative objectives: discounted-sum and long-run average objectives. The game models and the quantitative objectives are widely used in probabilistic verification, planning, optimal inventory control, network protocol and performance analysis. Games and MDPs that model realistic systems often have very large state spaces, and probabilistic abstraction techniques are necessary to handle the state-space explosion. The commonly used full-abstraction techniques do not yield space-savings for systems that have many states with similar value, but does not necessarily have similar transition structure. A semi-abstraction technique, namely Magnifying-lens abstractions (MLA), that clusters states based on value only, disregarding differences in their transition relation was proposed for qualitative objectives (reachability and safety objectives). In this paper we extend the MLA technique to solve stochastic games with discounted-sum and long-run average objectives. We present the MLA technique based abstraction-refinement algorithm for stochastic games and MDPs with discounted-sum objectives. For long-run average objectives, our solution works for all MDPs and a sub-class of stochastic games where every state has the same value. }, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Pritam, Roy}, booktitle = {arXiv}, pages = {17}, publisher = {ArXiv}, title = {{Magnifying lens abstraction for stochastic games with discounted and long-run average objectives}}, year = {2011}, } @inproceedings{3342, abstract = {We consider Markov decision processes (MDPs) with ω-regular specifications given as parity objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. The algorithms for the computation of the almost-sure winning set for parity objectives iteratively use the solutions for the almost-sure winning set for Büchi objectives (a special case of parity objectives). Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes O(nm) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs often have constant out-degree, and then our symbolic algorithm takes O(nn) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires O(nK) symbolic steps, where K is the maximal number of edges of strongly connected components (scc’s) of the MDP. The win-lose algorithm requires symbolic computation of scc’s. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5·n symbolic steps, whereas our new algorithm takes 4 ·n symbolic steps.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Joglekar, Manas and Nisarg, Shah}, editor = {Gopalakrishnan, Ganesh and Qadeer, Shaz}, location = {Snowbird, USA}, pages = {260 -- 276}, publisher = {Springer}, title = {{Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives}}, doi = {10.1007/978-3-642-22110-1_21}, volume = {6806}, year = {2011}, } @inproceedings{3343, abstract = {We present faster and dynamic algorithms for the following problems arising in probabilistic verification: Computation of the maximal end-component (mec) decomposition of Markov decision processes (MDPs), and of the almost sure winning set for reachability and parity objectives in MDPs. We achieve the following running time for static algorithms in MDPs with graphs of n vertices and m edges: (1) O(m · min{ √m, n2/3 }) for the mec decomposition, improving the longstanding O(m·n) bound; (2) O(m·n2/3) for reachability objectives, improving the previous O(m · √m) bound for m > n4/3; and (3) O(m · min{ √m, n2/3 } · log(d)) for parity objectives with d priorities, improving the previous O(m · √m · d) bound. We also give incremental and decremental algorithms in linear time for mec decomposition and reachability objectives and O(m · log d) time for parity ob jectives.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H}, location = {San Francisco, SA, United States}, pages = {1318 -- 1336}, publisher = {SIAM}, title = {{Faster and dynamic algorithms for maximal end-component decomposition and related graph problems in probabilistic verification}}, doi = {10.1137/1.9781611973082.101}, year = {2011}, } @inproceedings{3344, abstract = {Games played on graphs provide the mathematical framework to analyze several important problems in computer science as well as mathematics, such as the synthesis problem of Church, model checking of open reactive systems and many others. On the basis of mode of interaction of the players these games can be classified as follows: (a) turn-based (players make moves in turns); and (b) concurrent (players make moves simultaneously). On the basis of the information available to the players these games can be classified as follows: (a) perfect-information (players have perfect view of the game); and (b) partial-information (players have partial view of the game). In this talk we will consider all these classes of games with reachability objectives, where the goal of one player is to reach a set of target vertices of the graph, and the goal of the opponent player is to prevent the player from reaching the target. We will survey the results for various classes of games, and the results range from linear time decision algorithms to EXPTIME-complete problems to undecidable problems.}, author = {Chatterjee, Krishnendu}, editor = {Delzanno, Giorgo and Potapov, Igor}, location = {Genoa, Italy}, pages = {1 -- 1}, publisher = {Springer}, title = {{Graph games with reachability objectives}}, doi = {10.1007/978-3-642-24288-5_1}, volume = {6945}, year = {2011}, } @inproceedings{3345, abstract = {We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, location = {Warsaw, Poland}, pages = {206 -- 218}, publisher = {Springer}, title = {{Energy and mean-payoff parity Markov Decision Processes}}, doi = {10.1007/978-3-642-22993-0_21}, volume = {6907}, year = {2011}, } @inproceedings{3346, abstract = {We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with k reward functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the single-objective case, both randomization and memory are necessary for strategies, and that finite-memory randomized strategies are sufficient. Under the satisfaction objective, in contrast to the single-objective case, infinite memory is necessary for strategies, and that randomized memoryless strategies are sufficient for epsilon-approximation, for all epsilon>;0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of reward functions, for all epsilon>;0. Our results also reveal flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, correct the flaws and obtain improved results.}, author = {Brázdil, Tomáš and Brožek, Václav and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín}, location = {Toronto, Canada}, publisher = {IEEE}, title = {{Two views on multiple mean payoff objectives in Markov Decision Processes}}, doi = {10.1109/LICS.2011.10}, year = {2011}, } @inproceedings{3347, abstract = {The class of omega-regular languages provides a robust specification language in verification. Every omega-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens "eventually". Finitary liveness was proposed by Alur and Henzinger as a stronger formulation of liveness. It requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider automata with finitary acceptance conditions defined by finitary Buchi, parity and Streett languages. We study languages expressible by such automata: we give their topological complexity and present a regular-expression characterization. We compare the expressive power of finitary automata and give optimal algorithms for classical decisions questions. We show that the finitary languages are Sigma 2-complete; we present a complete picture of the expressive power of various classes of automata with finitary and infinitary acceptance conditions; we show that the languages defined by finitary parity automata exactly characterize the star-free fragment of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete and universality as well as language inclusion are PSPACE-complete for finitary parity and Streett automata.}, author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël}, location = {Tarragona, Spain}, pages = {216 -- 226}, publisher = {Springer}, title = {{Finitary languages}}, doi = {10.1007/978-3-642-21254-3_16}, volume = {6638}, year = {2011}, } @inproceedings{3348, abstract = {We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two-player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a linear (in the number of clocks) number of memory bits. Precisely, we show that for safety objectives, a memory of size (3 · |C|+lg(|C|+1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential bound. We also settle the open question of whether winning region controller strategies require memory for safety objectives by showing with an example the necessity of memory for region strategies to win for safety objectives.}, author = {Chatterjee, Krishnendu and Prabhu, Vinayak}, location = {Chicago, USA}, pages = {221 -- 230}, publisher = {Springer}, title = {{Synthesis of memory efficient real time controllers for safety objectives}}, doi = {10.1145/1967701.1967734}, year = {2011}, } @inproceedings{3349, abstract = {Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turn-based or concurrent moves, and deterministic or stochastic transitions. In this paper, we are interested in turn-based games, and specifically in deterministic parity games and stochastic reachability games (also known as simple stochastic games). We present a simple, direct and efficient reduction from deterministic parity games to simple stochastic games: it yields an arena whose size is linear up to a logarithmic factor in size of the original arena.}, author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël}, location = {Minori, Italy}, pages = {74 -- 86}, publisher = {EPTCS}, title = {{A reduction from parity games to simple stochastic games}}, doi = {10.4204/EPTCS.54.6}, volume = {54}, year = {2011}, } @inproceedings{3350, abstract = {A controller for a discrete game with ω-regular objectives requires attention if, intuitively, it requires measuring the state and switching from the current control action. Minimum attention controllers are preferable in modern shared implementations of cyber-physical systems because they produce the least burden on system resources such as processor time or communication bandwidth. We give algorithms to compute minimum attention controllers for ω-regular objectives in imperfect information discrete two-player games. We show a polynomial-time reduction from minimum attention controller synthesis to synthesis of controllers for mean-payoff parity objectives in games of incomplete information. This gives an optimal EXPTIME-complete synthesis algorithm. We show that the minimum attention controller problem is decidable for infinite state systems with finite bisimulation quotients. In particular, the problem is decidable for timed and rectangular automata.}, author = {Chatterjee, Krishnendu and Majumdar, Ritankar}, editor = {Fahrenberg, Uli and Tripakis, Stavros}, location = {Aalborg, Denmark}, pages = {145 -- 159}, publisher = {Springer}, title = {{Minimum attention controller synthesis for omega regular objectives}}, doi = {10.1007/978-3-642-24310-3_11}, volume = {6919}, year = {2011}, } @inproceedings{3351, abstract = {In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Singh, Rohit}, editor = {Owe, Olaf and Steffen, Martin and Telle, Jan Arne}, location = {Oslo, Norway}, pages = {148 -- 159}, publisher = {Springer}, title = {{On memoryless quantitative objectives}}, doi = {10.1007/978-3-642-22953-4_13}, volume = {6914}, year = {2011}, } @article{3352, abstract = {Exploring the connection of biology with reactive systems to better understand living systems.}, author = {Fisher, Jasmin and Harel, David and Henzinger, Thomas A}, journal = {Communications of the ACM}, number = {10}, pages = {72 -- 82}, publisher = {ACM}, title = {{Biology as reactivity}}, doi = {10.1145/2001269.2001289}, volume = {54}, year = {2011}, } @article{3353, abstract = {Compositional theories are crucial when designing large and complex systems from smaller components. In this work we propose such a theory for synchronous concurrent systems. Our approach follows so-called interface theories, which use game-theoretic interpretations of composition and refinement. These are appropriate for systems with distinct inputs and outputs, and explicit conditions on inputs that must be enforced during composition. Our interfaces model systems that execute in an infinite sequence of synchronous rounds. At each round, a contract must be satisfied. The contract is simply a relation specifying the set of valid input/output pairs. Interfaces can be composed by parallel, serial or feedback composition. A refinement relation between interfaces is defined, and shown to have two main properties: (1) it is preserved by composition, and (2) it is equivalent to substitutability, namely, the ability to replace an interface by another one in any context. Shared refinement and abstraction operators, corresponding to greatest lower and least upper bounds with respect to refinement, are also defined. Input-complete interfaces, that impose no restrictions on inputs, and deterministic interfaces, that produce a unique output for any legal input, are discussed as special cases, and an interesting duality between the two classes is exposed. A number of illustrative examples are provided, as well as algorithms to compute compositions, check refinement, and so on, for finite-state interfaces.}, author = {Tripakis, Stavros and Lickly, Ben and Henzinger, Thomas A and Lee, Edward}, journal = {ACM Transactions on Programming Languages and Systems (TOPLAS)}, number = {4}, publisher = {ACM}, title = {{A theory of synchronous relational interfaces}}, doi = {10.1145/1985342.1985345}, volume = {33}, year = {2011}, } @article{3354, abstract = {We consider two-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. We consider ω-regular winning conditions specified as parity objectives. Both players are allowed to use randomization when choosing their moves. We study the computation of the limit-winning set of states, consisting of the states where the sup-inf value of the game for player 1 is 1: in other words, a state is limit-winning if player 1 can ensure a probability of winning arbitrarily close to 1. We show that the limit-winning set can be computed in O(n2d+2) time, where n is the size of the game structure and 2d is the number of priorities (or colors). The membership problem of whether a state belongs to the limit-winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games. This is because concurrent games do not satisfy two of the most fundamental properties of turn-based parity games. First, in concurrent games limit-winning strategies require randomization; and second, they require infinite memory.}, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Henzinger, Thomas A}, journal = {ACM Transactions on Computational Logic (TOCL)}, number = {4}, publisher = {ACM}, title = {{Qualitative concurrent parity games}}, doi = {10.1145/1970398.1970404}, volume = {12}, year = {2011}, }