@inproceedings{8623, abstract = {We introduce the monitoring of trace properties under assumptions. An assumption limits the space of possible traces that the monitor may encounter. An assumption may result from knowledge about the system that is being monitored, about the environment, or about another, connected monitor. We define monitorability under assumptions and study its theoretical properties. In particular, we show that for every assumption A, the boolean combinations of properties that are safe or co-safe relative to A are monitorable under A. We give several examples and constructions on how an assumption can make a non-monitorable property monitorable, and how an assumption can make a monitorable property monitorable with fewer resources, such as integer registers.}, author = {Henzinger, Thomas A and Sarac, Naci E}, booktitle = {Runtime Verification}, isbn = {9783030605070}, issn = {1611-3349}, location = {Los Angeles, CA, United States}, pages = {3--18}, publisher = {Springer Nature}, title = {{Monitorability under assumptions}}, doi = {10.1007/978-3-030-60508-7_1}, volume = {12399}, year = {2020}, } @article{8679, abstract = {A central goal of artificial intelligence in high-stakes decision-making applications is to design a single algorithm that simultaneously expresses generalizability by learning coherent representations of their world and interpretable explanations of its dynamics. Here, we combine brain-inspired neural computation principles and scalable deep learning architectures to design compact neural controllers for task-specific compartments of a full-stack autonomous vehicle control system. We discover that a single algorithm with 19 control neurons, connecting 32 encapsulated input features to outputs by 253 synapses, learns to map high-dimensional inputs into steering commands. This system shows superior generalizability, interpretability and robustness compared with orders-of-magnitude larger black-box learning systems. The obtained neural agents enable high-fidelity autonomy for task-specific parts of a complex autonomous system.}, author = {Lechner, Mathias and Hasani, Ramin and Amini, Alexander and Henzinger, Thomas A and Rus, Daniela and Grosu, Radu}, issn = {2522-5839}, journal = {Nature Machine Intelligence}, pages = {642--652}, publisher = {Springer Nature}, title = {{Neural circuit policies enabling auditable autonomy}}, doi = {10.1038/s42256-020-00237-3}, volume = {2}, year = {2020}, } @inproceedings{8704, abstract = {Traditional robotic control suits require profound task-specific knowledge for designing, building and testing control software. The rise of Deep Learning has enabled end-to-end solutions to be learned entirely from data, requiring minimal knowledge about the application area. We design a learning scheme to train end-to-end linear dynamical systems (LDS)s by gradient descent in imitation learning robotic domains. We introduce a new regularization loss component together with a learning algorithm that improves the stability of the learned autonomous system, by forcing the eigenvalues of the internal state updates of an LDS to be negative reals. We evaluate our approach on a series of real-life and simulated robotic experiments, in comparison to linear and nonlinear Recurrent Neural Network (RNN) architectures. Our results show that our stabilizing method significantly improves test performance of LDS, enabling such linear models to match the performance of contemporary nonlinear RNN architectures. A video of the obstacle avoidance performance of our method on a mobile robot, in unseen environments, compared to other methods can be viewed at https://youtu.be/mhEsCoNao5E.}, author = {Lechner, Mathias and Hasani, Ramin and Rus, Daniela and Grosu, Radu}, booktitle = {Proceedings - IEEE International Conference on Robotics and Automation}, isbn = {9781728173955}, issn = {10504729}, location = {Paris, France}, pages = {5446--5452}, publisher = {IEEE}, title = {{Gershgorin loss stabilizes the recurrent neural network compartment of an end-to-end robot learning scheme}}, doi = {10.1109/ICRA40945.2020.9196608}, year = {2020}, } @inproceedings{8750, abstract = {Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle systems with uncertain parameters and inputs, where the uncertainties are bound to given intervals. The method is evaluated on the plant model of an experimental electro-mechanical braking system with periodic controller. In this model, the fast-switching controller dynamics requires simulation time scales of the order of nanoseconds. Accurate set-based computations for relatively large time horizons are known to be expensive. However, by appropriately decoupling the time variable with respect to the spatial variables, and enclosing the uncertain parameters using interval matrix maps acting on zonotopes, we show that the computation time can be lowered to 5000 times faster with respect to previous works. This is a step forward in formal verification of hybrid systems because reduced run-times allow engineers to introduce more expressiveness in their models with a relatively inexpensive computational cost.}, author = {Forets, Marcelo and Freire, Daniel and Schilling, Christian}, booktitle = {18th ACM-IEEE International Conference on Formal Methods and Models for System Design}, isbn = {9781728191485}, location = {Virtual Conference}, publisher = {IEEE}, title = {{Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions}}, doi = {10.1109/MEMOCODE51338.2020.9314994}, year = {2020}, } @article{8790, abstract = {Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this article, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.}, author = {Bogomolov, Sergiy and Forets, Marcelo and Frehse, Goran and Potomkin, Kostiantyn and Schilling, Christian}, issn = {19374151}, journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, number = {11}, pages = {4018--4029}, publisher = {IEEE}, title = {{Reachability analysis of linear hybrid systems via block decomposition}}, doi = {10.1109/TCAD.2020.3012859}, volume = {39}, year = {2020}, } @article{6761, abstract = {In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability.}, author = {Avni, Guy and Henzinger, Thomas A and Kupferman, Orna}, issn = {03043975}, journal = {Theoretical Computer Science}, pages = {42--55}, publisher = {Elsevier}, title = {{Dynamic resource allocation games}}, doi = {10.1016/j.tcs.2019.06.031}, volume = {807}, year = {2020}, } @inproceedings{7348, abstract = {The monitoring of event frequencies can be used to recognize behavioral anomalies, to identify trends, and to deduce or discard hypotheses about the underlying system. For example, the performance of a web server may be monitored based on the ratio of the total count of requests from the least and most active clients. Exact frequency monitoring, however, can be prohibitively expensive; in the above example it would require as many counters as there are clients. In this paper, we propose the efficient probabilistic monitoring of common frequency properties, including the mode (i.e., the most common event) and the median of an event sequence. We define a logic to express composite frequency properties as a combination of atomic frequency properties. Our main contribution is an algorithm that, under suitable probabilistic assumptions, can be used to monitor these important frequency properties with four counters, independent of the number of different events. Our algorithm samples longer and longer subwords of an infinite event sequence. We prove the almost-sure convergence of our algorithm by generalizing ergodic theory from increasing-length prefixes to increasing-length subwords of an infinite sequence. A similar algorithm could be used to learn a connected Markov chain of a given structure from observing its outputs, to arbitrary precision, for a given confidence. }, author = {Ferrere, Thomas and Henzinger, Thomas A and Kragl, Bernhard}, booktitle = {28th EACSL Annual Conference on Computer Science Logic}, isbn = {9783959771320}, issn = {1868-8969}, location = {Barcelona, Spain}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Monitoring event frequencies}}, doi = {10.4230/LIPIcs.CSL.2020.20}, volume = {152}, year = {2020}, } @article{7426, abstract = {This paper presents a novel abstraction technique for analyzing Lyapunov and asymptotic stability of polyhedral switched systems. A polyhedral switched system is a hybrid system in which the continuous dynamics is specified by polyhedral differential inclusions, the invariants and guards are specified by polyhedral sets and the switching between the modes do not involve reset of variables. A finite state weighted graph abstracting the polyhedral switched system is constructed from a finite partition of the state–space, such that the satisfaction of certain graph conditions, such as the absence of cycles with product of weights on the edges greater than (or equal) to 1, implies the stability of the system. However, the graph is in general conservative and hence, the violation of the graph conditions does not imply instability. If the analysis fails to establish stability due to the conservativeness in the approximation, a counterexample (cycle with product of edge weights greater than or equal to 1) indicating a potential reason for the failure is returned. Further, a more precise approximation of the switched system can be constructed by considering a finer partition of the state–space in the construction of the finite weighted graph. We present experimental results on analyzing stability of switched systems using the above method.}, author = {Garcia Soto, Miriam and Prabhakar, Pavithra}, issn = {1751-570X}, journal = {Nonlinear Analysis: Hybrid Systems}, number = {5}, publisher = {Elsevier}, title = {{Abstraction based verification of stability of polyhedral switched systems}}, doi = {10.1016/j.nahs.2020.100856}, volume = {36}, year = {2020}, } @inproceedings{7505, abstract = {Neural networks have demonstrated unmatched performance in a range of classification tasks. Despite numerous efforts of the research community, novelty detection remains one of the significant limitations of neural networks. The ability to identify previously unseen inputs as novel is crucial for our understanding of the decisions made by neural networks. At runtime, inputs not falling into any of the categories learned during training cannot be classified correctly by the neural network. Existing approaches treat the neural network as a black box and try to detect novel inputs based on the confidence of the output predictions. However, neural networks are not trained to reduce their confidence for novel inputs, which limits the effectiveness of these approaches. We propose a framework to monitor a neural network by observing the hidden layers. We employ a common abstraction from program analysis - boxes - to identify novel behaviors in the monitored layers, i.e., inputs that cause behaviors outside the box. For each neuron, the boxes range over the values seen in training. The framework is efficient and flexible to achieve a desired trade-off between raising false warnings and detecting novel inputs. We illustrate the performance and the robustness to variability in the unknown classes on popular image-classification benchmarks.}, author = {Henzinger, Thomas A and Lukina, Anna and Schilling, Christian}, booktitle = {24th European Conference on Artificial Intelligence}, location = {Santiago de Compostela, Spain}, pages = {2433--2440}, publisher = {IOS Press}, title = {{Outside the box: Abstraction-based monitoring of neural networks}}, doi = {10.3233/FAIA200375}, volume = {325}, year = {2020}, } @inproceedings{9040, abstract = {Machine learning and formal methods have complimentary benefits and drawbacks. In this work, we address the controller-design problem with a combination of techniques from both fields. The use of black-box neural networks in deep reinforcement learning (deep RL) poses a challenge for such a combination. Instead of reasoning formally about the output of deep RL, which we call the wizard, we extract from it a decision-tree based model, which we refer to as the magic book. Using the extracted model as an intermediary, we are able to handle problems that are infeasible for either deep RL or formal methods by themselves. First, we suggest, for the first time, a synthesis procedure that is based on a magic book. We synthesize a stand-alone correct-by-design controller that enjoys the favorable performance of RL. Second, we incorporate a magic book in a bounded model checking (BMC) procedure. BMC allows us to find numerous traces of the plant under the control of the wizard, which a user can use to increase the trustworthiness of the wizard and direct further training.}, author = {Alamdari, Par Alizadeh and Avni, Guy and Henzinger, Thomas A and Lukina, Anna}, booktitle = {Proceedings of the 20th Conference on Formal Methods in Computer-Aided Design}, isbn = {9783854480426}, issn = {2708-7824}, location = {Online Conference}, pages = {138--147}, publisher = {TU Wien Academic Press}, title = {{Formal methods with a touch of magic}}, doi = {10.34727/2020/isbn.978-3-85448-042-6_21}, year = {2020}, } @inproceedings{9103, abstract = {We introduce LRT-NG, a set of techniques and an associated toolset that computes a reachtube (an over-approximation of the set of reachable states over a given time horizon) of a nonlinear dynamical system. LRT-NG significantly advances the state-of-the-art Langrangian Reachability and its associated tool LRT. From a theoretical perspective, LRT-NG is superior to LRT in three ways. First, it uses for the first time an analytically computed metric for the propagated ball which is proven to minimize the ball’s volume. We emphasize that the metric computation is the centerpiece of all bloating-based techniques. Secondly, it computes the next reachset as the intersection of two balls: one based on the Cartesian metric and the other on the new metric. While the two metrics were previously considered opposing approaches, their joint use considerably tightens the reachtubes. Thirdly, it avoids the "wrapping effect" associated with the validated integration of the center of the reachset, by optimally absorbing the interval approximation in the radius of the next ball. From a tool-development perspective, LRT-NG is superior to LRT in two ways. First, it is a standalone tool that no longer relies on CAPD. This required the implementation of the Lohner method and a Runge-Kutta time-propagation method. Secondly, it has an improved interface, allowing the input model and initial conditions to be provided as external input files. Our experiments on a comprehensive set of benchmarks, including two Neural ODEs, demonstrates LRT-NG’s superior performance compared to LRT, CAPD, and Flow*.}, author = {Gruenbacher, Sophie and Cyranka, Jacek and Lechner, Mathias and Islam, Md Ariful and Smolka, Scott A. and Grosu, Radu}, booktitle = {Proceedings of the 59th IEEE Conference on Decision and Control}, isbn = {9781728174471}, issn = {07431546}, location = {Jeju Islang, Korea (South)}, pages = {1556--1563}, publisher = {IEEE}, title = {{Lagrangian reachtubes: The next generation}}, doi = {10.1109/CDC42340.2020.9304042}, volume = {2020}, year = {2020}, } @article{9197, abstract = {In this paper we introduce and study all-pay bidding games, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn, each player submits a sealed legal bid (non-negative and below their remaining budget), which is deducted from their budget and the highest bidder moves the token onto an adjacent vertex. The game ends once a sink is reached, and Player 1 pays Player 2 the outcome that is associated with the sink. The players attempt to maximize their expected outcome. Our games model settings where effort (of no inherent value) needs to be invested in an ongoing and stateful manner. On the negative side, we show that even in simple games on DAGs, optimal strategies may require a distribution over bids with infinite support. A central quantity in bidding games is the ratio of the players budgets. On the positive side, we show a simple FPTAS for DAGs, that, for each budget ratio, outputs an approximation for the optimal strategy for that ratio. We also implement it, show that it performs well, and suggests interesting properties of these games. Then, given an outcome c, we show an algorithm for finding the necessary and sufficient initial ratio for guaranteeing outcome c with probability 1 and a strategy ensuring such. Finally, while the general case has not previously been studied, solving the specific game in which Player 1 wins iff he wins the first two auctions, has been long stated as an open question, which we solve.}, author = {Avni, Guy and Ibsen-Jensen, Rasmus and Tkadlec, Josef}, isbn = {9781577358350}, issn = {2374-3468}, journal = {Proceedings of the AAAI Conference on Artificial Intelligence}, location = {New York, NY, United States}, number = {02}, pages = {1798--1805}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{All-pay bidding games on graphs}}, doi = {10.1609/aaai.v34i02.5546}, volume = {34}, year = {2020}, } @inproceedings{9202, abstract = {We propose a novel hybridization method for stability analysis that over-approximates nonlinear dynamical systems by switched systems with linear inclusion dynamics. We observe that existing hybridization techniques for safety analysis that over-approximate nonlinear dynamical systems by switched affine inclusion dynamics and provide fixed approximation error, do not suffice for stability analysis. Hence, we propose a hybridization method that provides a state-dependent error which converges to zero as the state tends to the equilibrium point. The crux of our hybridization computation is an elegant recursive algorithm that uses partial derivatives of a given function to obtain upper and lower bound matrices for the over-approximating linear inclusion. We illustrate our method on some examples to demonstrate the application of the theory for stability analysis. In particular, our method is able to establish stability of a nonlinear system which does not admit a polynomial Lyapunov function.}, author = {Garcia Soto, Miriam and Prabhakar, Pavithra}, booktitle = {2020 IEEE Real-Time Systems Symposium}, issn = {2576-3172}, location = {Houston, TX, USA }, pages = {244--256}, publisher = {IEEE}, title = {{Hybridization for stability verification of nonlinear switched systems}}, doi = {10.1109/RTSS49844.2020.00031}, year = {2020}, } @inproceedings{9632, abstract = {Second-order information, in the form of Hessian- or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems. Recently, there has been significant interest in utilizing this information in the context of deep neural networks; however, relatively little is known about the quality of existing approximations in this context. Our work examines this question, identifies issues with existing approaches, and proposes a method called WoodFisher to compute a faithful and efficient estimate of the inverse Hessian. Our main application is to neural network compression, where we build on the classic Optimal Brain Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms popular state-of-the-art methods for oneshot pruning. Further, even when iterative, gradual pruning is allowed, our method results in a gain in test accuracy over the state-of-the-art approaches, for standard image classification datasets such as ImageNet ILSVRC. We examine how our method can be extended to take into account first-order information, as well as illustrate its ability to automatically set layer-wise pruning thresholds and perform compression in the limited-data regime. The code is available at the following link, https://github.com/IST-DASLab/WoodFisher.}, author = {Singh, Sidak Pal and Alistarh, Dan-Adrian}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713829546}, issn = {10495258}, location = {Vancouver, Canada}, pages = {18098--18109}, publisher = {Curran Associates}, title = {{WoodFisher: Efficient second-order approximation for neural network compression}}, volume = {33}, year = {2020}, } @inproceedings{10877, abstract = {This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with piecewise constant dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In this third edition, six tools have been applied to solve five different benchmark problems in the category for piecewise constant dynamics: BACH, Lyse, Hy- COMP, PHAVer/SX, PHAVerLite, and VeriSiMPL. Compared to last year, a new tool has participated (HyCOMP) and PHAVerLite has replaced PHAVer-lite. The result is a snap- shot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results probably provide the most complete assessment of tools for the safety verification of continuous and hybrid systems with piecewise constant dynamics up to this date.}, author = {Frehse, Goran and Abate, Alessandro and Adzkiya, Dieky and Becchi, Anna and Bu, Lei and Cimatti, Alessandro and Giacobbe, Mirco and Griggio, Alberto and Mover, Sergio and Mufid, Muhammad Syifa'ul and Riouak, Idriss and Tonetta, Stefano and Zaffanella, Enea}, booktitle = {ARCH19. 6th International Workshop on Applied Verification of Continuous and Hybrid Systems}, editor = {Frehse, Goran and Althoff, Matthias}, issn = {2398-7340}, location = {Montreal, Canada}, pages = {1--13}, publisher = {EasyChair}, title = {{ARCH-COMP19 Category Report: Hybrid systems with piecewise constant dynamics}}, doi = {10.29007/rjwn}, volume = {61}, year = {2019}, } @inproceedings{8570, abstract = {This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In its third edition, seven tools have been applied to solve six different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, CORA/SX, HyDRA, Hylaa, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results provide one of the most complete assessments of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.}, author = {Althoff, Matthias and Bak, Stanley and Forets, Marcelo and Frehse, Goran and Kochdumper, Niklas and Ray, Rajarshi and Schilling, Christian and Schupp, Stefan}, booktitle = {EPiC Series in Computing}, issn = {23987340}, location = {Montreal, Canada}, pages = {14--40}, publisher = {EasyChair}, title = {{ARCH-COMP19 Category Report: Continuous and hybrid systems with linear continuous dynamics}}, doi = {10.29007/bj1w}, volume = {61}, year = {2019}, } @article{6752, abstract = {Two-player games on graphs are widely studied in formal methods, as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. The following bidding rule was previously defined and called Richman bidding. Both players have separate budgets, which sum up to 1. In each turn, a bidding takes place: Both players submit bids simultaneously, where a bid is legal if it does not exceed the available budget, and the higher bidder pays his bid to the other player and moves the token. The central question studied in bidding games is a necessary and sufficient initial budget for winning the game: a threshold budget in a vertex is a value t ∈ [0, 1] such that if Player 1’s budget exceeds t, he can win the game; and if Player 2’s budget exceeds 1 − t, he can win the game. Threshold budgets were previously shown to exist in every vertex of a reachability game, which have an interesting connection with random-turn games—a sub-class of simple stochastic games in which the player who moves is chosen randomly. We show the existence of threshold budgets for a qualitative class of infinite-duration games, namely parity games, and a quantitative class, namely mean-payoff games. The key component of the proof is a quantitative solution to strongly connected mean-payoff bidding games in which we extend the connection with random-turn games to these games, and construct explicit optimal strategies for both players.}, author = {Avni, Guy and Henzinger, Thomas A and Chonev, Ventsislav K}, issn = {1557735X}, journal = {Journal of the ACM}, number = {4}, publisher = {ACM}, title = {{Infinite-duration bidding games}}, doi = {10.1145/3340295}, volume = {66}, year = {2019}, } @inproceedings{6822, abstract = {In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the qualitative winner or quantitative payoff of the game. In bidding games, in each turn, we hold an auction between the two players to determine which player moves the token. Bidding games have largely been studied with concrete bidding mechanisms that are variants of a first-price auction: in each turn both players simultaneously submit bids, the higher bidder moves the token, and pays his bid to the lower bidder in Richman bidding, to the bank in poorman bidding, and in taxman bidding, the bid is split between the other player and the bank according to a predefined constant factor. Bidding games are deterministic games. They have an intriguing connection with a fragment of stochastic games called randomturn games. We study, for the first time, a combination of bidding games with probabilistic behavior; namely, we study bidding games that are played on Markov decision processes, where the players bid for the right to choose the next action, which determines the probability distribution according to which the next vertex is chosen. We study parity and meanpayoff bidding games on MDPs and extend results from the deterministic bidding setting to the probabilistic one.}, author = {Avni, Guy and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Novotny, Petr}, booktitle = { Proceedings of the 13th International Conference of Reachability Problems}, isbn = {978-303030805-6}, issn = {0302-9743}, location = {Brussels, Belgium}, pages = {1--12}, publisher = {Springer}, title = {{Bidding games on Markov decision processes}}, doi = {10.1007/978-3-030-30806-3_1}, volume = {11674}, year = {2019}, } @inproceedings{6884, abstract = {In two-player games on graphs, the players move a token through a graph to produce a finite or infinite path, which determines the qualitative winner or quantitative payoff of the game. We study bidding games in which the players bid for the right to move the token. Several bidding rules were studied previously. In Richman bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Poorman bidding is similar except that the winner of the bidding pays the "bank" rather than the other player. Taxman bidding spans the spectrum between Richman and poorman bidding. They are parameterized by a constant tau in [0,1]: portion tau of the winning bid is paid to the other player, and portion 1-tau to the bank. While finite-duration (reachability) taxman games have been studied before, we present, for the first time, results on infinite-duration taxman games. It was previously shown that both Richman and poorman infinite-duration games with qualitative objectives reduce to reachability games, and we show a similar result here. Our most interesting results concern quantitative taxman games, namely mean-payoff games, where poorman and Richman bidding differ significantly. A central quantity in these games is the ratio between the two players' initial budgets. While in poorman mean-payoff games, the optimal payoff of a player depends on the initial ratio, in Richman bidding, the payoff depends only on the structure of the game. In both games the optimal payoffs can be found using (different) probabilistic connections with random-turn games in which in each turn, instead of bidding, a coin is tossed to determine which player moves. While the value with Richman bidding equals the value of a random-turn game with an un-biased coin, with poorman bidding, the bias in the coin is the initial ratio of the budgets. We give a complete classification of mean-payoff taxman games that is based on a probabilistic connection: the value of a taxman bidding game with parameter tau and initial ratio r, equals the value of a random-turn game that uses a coin with bias F(tau, r) = (r+tau * (1-r))/(1+tau). Thus, we show that Richman bidding is the exception; namely, for every tau <1, the value of the game depends on the initial ratio. Our proof technique simplifies and unifies the previous proof techniques for both Richman and poorman bidding. }, author = {Avni, Guy and Henzinger, Thomas A and Zikelic, Dorde}, location = {Aachen, Germany}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Bidding mechanisms in graph games}}, doi = {10.4230/LIPICS.MFCS.2019.11}, volume = {138}, year = {2019}, } @inproceedings{6885, abstract = {A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a) decidable in polynomial time for integer-valued VASS, and (b) decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c) NP-complete for integer-valued VASS, and (d) undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open. }, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, location = {Amsterdam, Netherlands}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Long-run average behavior of vector addition systems with states}}, doi = {10.4230/LIPICS.CONCUR.2019.27}, volume = {140}, year = {2019}, }