@inproceedings{11459, abstract = {We present a novel approach to differential cost analysis that, given a program revision, attempts to statically bound the difference in resource usage, or cost, between the two program versions. Differential cost analysis is particularly interesting because of the many compelling applications for it, such as detecting resource-use regressions at code-review time or proving the absence of certain side-channel vulnerabilities. One prior approach to differential cost analysis is to apply relational reasoning that conceptually constructs a product program on which one can over-approximate the difference in costs between the two program versions. However, a significant challenge in any relational approach is effectively aligning the program versions to get precise results. In this paper, our key insight is that we can avoid the need for and the limitations of program alignment if, instead, we bound the difference of two cost-bound summaries rather than directly bounding the concrete cost difference. In particular, our method computes a threshold value for the maximal difference in cost between two program versions simultaneously using two kinds of cost-bound summaries---a potential function that evaluates to an upper bound for the cost incurred in the first program and an anti-potential function that evaluates to a lower bound for the cost incurred in the second. Our method has a number of desirable properties: it can be fully automated, it allows optimizing the threshold value on relative cost, it is suitable for programs that are not syntactically similar, and it supports non-determinism. We have evaluated an implementation of our approach on a number of program pairs collected from the literature, and we find that our method computes tight threshold values on relative cost in most examples.}, author = {Zikelic, Dorde and Chang, Bor-Yuh Evan and Bolignano, Pauline and Raimondi, Franco}, booktitle = {Proceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation}, isbn = {9781450392655}, location = {San Diego, CA, United States}, pages = {442--457}, publisher = {Association for Computing Machinery}, title = {{Differential cost analysis with simultaneous potentials and anti-potentials}}, doi = {10.1145/3519939.3523435}, year = {2022}, } @article{12257, abstract = {Structural balance theory is an established framework for studying social relationships of friendship and enmity. These relationships are modeled by a signed network whose energy potential measures the level of imbalance, while stochastic dynamics drives the network toward a state of minimum energy that captures social balance. It is known that this energy landscape has local minima that can trap socially aware dynamics, preventing it from reaching balance. Here we first study the robustness and attractor properties of these local minima. We show that a stochastic process can reach them from an abundance of initial states and that some local minima cannot be escaped by mild perturbations of the network. Motivated by these anomalies, we introduce best-edge dynamics (BED), a new plausible stochastic process. We prove that BED always reaches balance and that it does so fast in various interesting settings.}, author = {Chatterjee, Krishnendu and Svoboda, Jakub and Zikelic, Dorde and Pavlogiannis, Andreas and Tkadlec, Josef}, issn = {2470-0053}, journal = {Physical Review E}, number = {3}, publisher = {American Physical Society}, title = {{Social balance on networks: Local minima and best-edge dynamics}}, doi = {10.1103/physreve.106.034321}, volume = {106}, year = {2022}, } @article{12280, abstract = {In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate.}, author = {Schmid, Laura and Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin}, issn = {1553-7358}, journal = {PLOS Computational Biology}, keywords = {Computational Theory and Mathematics, Cellular and Molecular Neuroscience, Genetics, Molecular Biology, Ecology, Modeling and Simulation, Ecology, Evolution, Behavior and Systematics}, number = {6}, publisher = {Public Library of Science}, title = {{Direct reciprocity between individuals that use different strategy spaces}}, doi = {10.1371/journal.pcbi.1010149}, volume = {18}, year = {2022}, } @article{9311, abstract = {Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function. }, author = {Chatterjee, Krishnendu and Saona Urmeneta, Raimundo J and Ziliotto, Bruno}, issn = {1526-5471}, journal = {Mathematics of Operations Research}, keywords = {Management Science and Operations Research, General Mathematics, Computer Science Applications}, number = {1}, pages = {100--119}, publisher = {Institute for Operations Research and the Management Sciences}, title = {{Finite-memory strategies in POMDPs with long-run average objectives}}, doi = {10.1287/moor.2020.1116}, volume = {47}, year = {2022}, } @inproceedings{12170, abstract = {We present PET, a specialized and highly optimized framework for partial exploration on probabilistic systems. Over the last decade, several significant advances in the analysis of Markov decision processes employed partial exploration. In a nutshell, this idea allows to focus computation on specific parts of the system, guided by heuristics, while maintaining correctness. In particular, only relevant parts of the system are constructed on demand, which in turn potentially allows to omit constructing large parts of the system. Depending on the model, this leads to dramatic speed-ups, in extreme cases even up to an arbitrary factor. PET unifies several previous implementations and provides a flexible framework to easily implement partial exploration for many further problems. Our experimental evaluation shows significant improvements compared to the previous implementations while vastly reducing the overhead required to add support for additional properties.}, author = {Meggendorfer, Tobias}, booktitle = {20th International Symposium on Automated Technology for Verification and Analysis}, isbn = {9783031199912}, issn = {1611-3349}, location = {Virtual}, pages = {320--326}, publisher = {Springer Nature}, title = {{PET – A partial exploration tool for probabilistic verification}}, doi = {10.1007/978-3-031-19992-9_20}, volume = {13505}, year = {2022}, } @article{11402, abstract = {Fixed-horizon planning considers a weighted graph and asks to construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping-time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary as the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping-time T, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, issn = {1090-2724}, journal = {Journal of Computer and System Sciences}, pages = {1--21}, publisher = {Elsevier}, title = {{Graph planning with expected finite horizon}}, doi = {10.1016/j.jcss.2022.04.003}, volume = {129}, year = {2022}, } @inproceedings{12775, abstract = {We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a sequence of approximations converging to the true value in the limit, our aim is to obtain an algorithm with guarantees on the precision of the approximation. As this problem is undecidable in general, assumptions on the MDP are necessary. Our main contribution is to identify sufficient assumptions that are as weak as possible, thus approaching the "boundary" of which systems can be correctly and reliably analyzed. To this end, we also argue why each of our assumptions is necessary for algorithms based on processing finitely many observations. We present two solution variants. The first one provides converging lower bounds under weaker assumptions than typical ones from previous works concerned with guarantees. The second one then utilizes stronger assumptions to additionally provide converging upper bounds. Altogether, we obtain an anytime algorithm, i.e. yielding a sequence of approximants with known and iteratively improving precision, converging to the true value in the limit. Besides, due to the generality of our assumptions, our algorithms are very general templates, readily allowing for various heuristics from literature in contrast to, e.g., a specific discretization algorithm. Our theoretical contribution thus paves the way for future practical improvements without sacrificing correctness guarantees.}, author = {Grover, Kush and Kretinsky, Jan and Meggendorfer, Tobias and Weininger, Maimilian}, booktitle = {33rd International Conference on Concurrency Theory }, issn = {1868-8969}, location = {Warsaw, Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Anytime guarantees for reachability in uncountable Markov decision processes}}, doi = {10.4230/LIPIcs.CONCUR.2022.11}, volume = {243}, year = {2022}, } @inproceedings{12000, abstract = {We consider the quantitative problem of obtaining lower-bounds on the probability of termination of a given non-deterministic probabilistic program. Specifically, given a non-termination threshold p∈[0,1], we aim for certificates proving that the program terminates with probability at least 1−p. The basic idea of our approach is to find a terminating stochastic invariant, i.e. a subset SI of program states such that (i) the probability of the program ever leaving SI is no more than p, and (ii) almost-surely, the program either leaves SI or terminates. While stochastic invariants are already well-known, we provide the first proof that the idea above is not only sound, but also complete for quantitative termination analysis. We then introduce a novel sound and complete characterization of stochastic invariants that enables template-based approaches for easy synthesis of quantitative termination certificates, especially in affine or polynomial forms. Finally, by combining this idea with the existing martingale-based methods that are relatively complete for qualitative termination analysis, we obtain the first automated, sound, and relatively complete algorithm for quantitative termination analysis. Notably, our completeness guarantees for quantitative termination analysis are as strong as the best-known methods for the qualitative variant. Our prototype implementation demonstrates the effectiveness of our approach on various probabilistic programs. We also demonstrate that our algorithm certifies lower bounds on termination probability for probabilistic programs that are beyond the reach of previous methods.}, author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Meggendorfer, Tobias and Zikelic, Dorde}, booktitle = {Proceedings of the 34th International Conference on Computer Aided Verification}, isbn = {9783031131844}, issn = {1611-3349}, location = {Haifa, Israel}, pages = {55--78}, publisher = {Springer}, title = {{Sound and complete certificates for auantitative termination analysis of probabilistic programs}}, doi = {10.1007/978-3-031-13185-1_4}, volume = {13371}, year = {2022}, } @article{12511, abstract = {We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the literature, verifying stability in stochastic control systems is an open problem. The few existing works on this topic either consider only specialized forms of stochasticity or make restrictive assumptions on the system, rendering them inapplicable to learning algorithms with neural network policies. In this work, we present an approach for general nonlinear stochastic control problems with two novel aspects: (a) instead of classical stochastic extensions of Lyapunov functions, we use ranking supermartingales (RSMs) to certify a.s. asymptotic stability, and (b) we present a method for learning neural network RSMs. We prove that our approach guarantees a.s. asymptotic stability of the system and provides the first method to obtain bounds on the stabilization time, which stochastic Lyapunov functions do not. Finally, we validate our approach experimentally on a set of nonlinear stochastic reinforcement learning environments with neural network policies.}, author = {Lechner, Mathias and Zikelic, Dorde and Chatterjee, Krishnendu and Henzinger, Thomas A}, isbn = {9781577358350}, issn = {2374-3468}, journal = {Proceedings of the AAAI Conference on Artificial Intelligence}, keywords = {General Medicine}, number = {7}, pages = {7326--7336}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Stability verification in stochastic control systems via neural network supermartingales}}, doi = {10.1609/aaai.v36i7.20695}, volume = {36}, year = {2022}, } @unpublished{14601, abstract = {In this work, we address the problem of learning provably stable neural network policies for stochastic control systems. While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of how to learn such policies is little explored. Here, we study the effectiveness of jointly learning a policy together with a martingale certificate that proves its stability using a single learning algorithm. We observe that the joint optimization problem becomes easily stuck in local minima when starting from a randomly initialized policy. Our results suggest that some form of pre-training of the policy is required for the joint optimization to repair and verify the policy successfully.}, author = {Zikelic, Dorde and Lechner, Mathias and Chatterjee, Krishnendu and Henzinger, Thomas A}, booktitle = {arXiv}, title = {{Learning stabilizing policies in stochastic control systems}}, doi = {10.48550/arXiv.2205.11991}, year = {2022}, } @unpublished{14600, abstract = {We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold $p\in[0,1]$ over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on $3$ stochastic non-linear reinforcement learning tasks.}, author = {Zikelic, Dorde and Lechner, Mathias and Henzinger, Thomas A and Chatterjee, Krishnendu}, booktitle = {arXiv}, title = {{Learning control policies for stochastic systems with reach-avoid guarantees}}, doi = {10.48550/ARXIV.2210.05308}, year = {2022}, } @inproceedings{10052, abstract = {A deterministic finite automaton (DFA) 𝒜 is composite if its language L(𝒜) can be decomposed into an intersection ⋂_{i = 1}^k L(𝒜_i) of languages of smaller DFAs. Otherwise, 𝒜 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.}, author = {Jecker, Ismael R and Mazzocchi, Nicolas and Wolf, Petra}, booktitle = {32nd International Conference on Concurrency Theory}, isbn = {978-3-9597-7203-7}, issn = {1868-8969}, location = {Paris, France}, publisher = {Schloss Dagstuhl - Leibniz Zentrum für Informatik}, title = {{Decomposing permutation automata}}, doi = {10.4230/LIPIcs.CONCUR.2021.18}, volume = {203}, year = {2021}, } @inproceedings{10054, abstract = {Graphs and games on graphs are fundamental models for the analysis of reactive systems, in particular, for model-checking and the synthesis of reactive systems. The class of ω-regular languages provides a robust specification formalism for the desired properties of reactive systems. In the classical infinitary formulation of the liveness part of an ω-regular specification, a "good" event must happen eventually without any bound between the good events. A stronger notion of liveness is bounded liveness, which requires that good events happen within d transitions. Given a graph or a game graph with n vertices, m edges, and a bounded liveness objective, the previous best-known algorithmic bounds are as follows: (i) O(dm) for graphs, which in the worst-case is O(n³); and (ii) O(n² d²) for games on graphs. Our main contributions improve these long-standing algorithmic bounds. For graphs we present: (i) a randomized algorithm with one-sided error with running time O(n^{2.5} log n) for the bounded liveness objectives; and (ii) a deterministic linear-time algorithm for the complement of bounded liveness objectives. For games on graphs, we present an O(n² d) time algorithm for the bounded liveness objectives.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Kale, Sagar Sudhir and Svozil, Alexander}, booktitle = {48th International Colloquium on Automata, Languages, and Programming}, isbn = {978-3-95977-195-5}, issn = {1868-8969}, location = {Glasgow, Scotland}, publisher = {Schloss Dagstuhl - Leibniz Zentrum für Informatik}, title = {{Faster algorithms for bounded liveness in graphs and game graphs}}, doi = {10.4230/LIPIcs.ICALP.2021.124}, volume = {198}, year = {2021}, } @inproceedings{10075, abstract = {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.}, author = {Guha, Shibashis and Jecker, Ismael R and Lehtinen, Karoliina and Zimmermann, Martin}, booktitle = {46th International Symposium on Mathematical Foundations of Computer Science}, isbn = {978-3-9597-7201-3}, issn = {1868-8969}, location = {Tallinn, Estonia}, publisher = {Schloss Dagstuhl - Leibniz Zentrum für Informatik}, title = {{A bit of nondeterminism makes pushdown automata expressive and succinct}}, doi = {10.4230/LIPIcs.MFCS.2021.53}, volume = {202}, year = {2021}, } @inproceedings{10630, abstract = {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.}, author = {Arrighi, Emmanuel and Fernau, Henning and Hoffmann, Stefan and Holzer, Markus and Jecker, Ismael R and De Oliveira Oliveira, Mateus and Wolf, Petra}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, isbn = {978-3-9597-7215-0}, issn = {1868-8969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz Zentrum für Informatik}, title = {{On the complexity of intersection non-emptiness for star-free language classes}}, doi = {10.4230/LIPIcs.FSTTCS.2021.34}, volume = {213}, year = {2021}, } @inproceedings{10629, abstract = {Product graphs arise naturally in formal verification and program analysis. For example, the analysis of two concurrent threads requires the product of two component control-flow graphs, and for language inclusion of deterministic automata the product of two automata is constructed. In many cases, the component graphs have constant treewidth, e.g., when the input contains control-flow graphs of programs. We consider the algorithmic analysis of products of two constant-treewidth graphs with respect to three classic specification languages, namely, (a) algebraic properties, (b) mean-payoff properties, and (c) initial credit for energy properties. Our main contributions are as follows. Consider a graph G that is the product of two constant-treewidth graphs of size n each. First, given an idempotent semiring, we present an algorithm that computes the semiring transitive closure of G in time Õ(n⁴). Since the output has size Θ(n⁴), our algorithm is optimal (up to polylog factors). Second, given a mean-payoff objective, we present an O(n³)-time algorithm for deciding whether the value of a starting state is non-negative, improving the previously known O(n⁴) bound. Third, given an initial credit for energy objective, we present an O(n⁵)-time algorithm for computing the minimum initial credit for all nodes of G, improving the previously known O(n⁸) bound. At the heart of our approach lies an algorithm for the efficient construction of strongly-balanced tree decompositions of constant-treewidth graphs. Given a constant-treewidth graph G' of n nodes and a positive integer λ, our algorithm constructs a binary tree decomposition of G' of width O(λ) with the property that the size of each subtree decreases geometrically with rate (1/2 + 2^{-λ}).}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, isbn = {978-3-9597-7215-0}, issn = {1868-8969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Quantitative verification on product graphs of small treewidth}}, doi = {10.4230/LIPIcs.FSTTCS.2021.42}, volume = {213}, year = {2021}, } @inproceedings{10694, abstract = {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.}, author = {Avni, Guy and Jecker, Ismael R and Zikelic, Dorde}, booktitle = {Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms}, editor = {Marx, Dániel}, isbn = {978-1-61197-646-5}, location = {Virtual}, pages = {617--636}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Infinite-duration all-pay bidding games}}, doi = {10.1137/1.9781611976465.38}, year = {2021}, } @inproceedings{10847, abstract = {We study the two-player zero-sum extension of the partially observable stochastic shortest-path problem where one agent has only partial information about the environment. We formulate this problem as a partially observable stochastic game (POSG): given a set of target states and negative rewards for each transition, the player with imperfect information maximizes the expected undiscounted total reward until a target state is reached. The second player with the perfect information aims for the opposite. We base our formalism on POSGs with one-sided observability (OS-POSGs) and give the following contributions: (1) we introduce a novel heuristic search value iteration algorithm that iteratively solves depth-limited variants of the game, (2) we derive the bound on the depth guaranteeing an arbitrary precision, (3) we propose a novel upper-bound estimation that allows early terminations, and (4) we experimentally evaluate the algorithm on a pursuit-evasion game.}, author = {Tomášek, Petr and Horák, Karel and Aradhye, Aditya and Bošanský, Branislav and Chatterjee, Krishnendu}, booktitle = {30th International Joint Conference on Artificial Intelligence}, isbn = {9780999241196}, issn = {1045-0823}, location = {Virtual, Online}, pages = {4182--4189}, publisher = {International Joint Conferences on Artificial Intelligence}, title = {{Solving partially observable stochastic shortest-path games}}, doi = {10.24963/ijcai.2021/575}, year = {2021}, } @inproceedings{9296, abstract = { matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.}, author = {Aichholzer, Oswin and Arroyo Guevara, Alan M and Masárová, Zuzana and Parada, Irene and Perz, Daniel and Pilz, Alexander and Tkadlec, Josef and Vogtenhuber, Birgit}, booktitle = {15th International Conference on Algorithms and Computation}, isbn = {9783030682101}, issn = {16113349}, location = {Yangon, Myanmar}, pages = {221--233}, publisher = {Springer Nature}, title = {{On compatible matchings}}, doi = {10.1007/978-3-030-68211-8_18}, volume = {12635}, year = {2021}, } @inbook{9403, abstract = {Optimal decision making requires individuals to know their available options and to anticipate correctly what consequences these options have. In many social interactions, however, we refrain from gathering all relevant information, even if this information would help us make better decisions and is costless to obtain. This chapter examines several examples of “deliberate ignorance.” Two simple models are proposed to illustrate how ignorance can evolve among self-interested and payoff - maximizing individuals, and open problems are highlighted that lie ahead for future research to explore.}, author = {Schmid, Laura and Hilbe, Christian}, booktitle = {Deliberate Ignorance: Choosing Not To Know}, editor = {Hertwig, Ralph and Engel, Christoph}, isbn = {978-0-262-04559-9}, pages = {139--152}, publisher = {MIT Press}, title = {{The evolution of strategic ignorance in strategic interaction}}, volume = {29}, year = {2021}, }