@article{21661, abstract = {Model checking undiscounted reachability and expected-reward properties on Markov decision processes (MDPs) are key for the verification of systems that act under uncertainty. Popular algorithms are policy iteration and variants of value iteration; in tool competitions, most participants rely on the latter. These algorithms generally need worst-case exponential time. However, the problem can equally be formulated as a linear programme, solvable in polynomial time. In this paper, we give a detailed overview of today’s state-of-the-art algorithms for MDP model checking with a focus on performance and correctness. We highlight their fundamental differences, and describe various optimizations and implementation variants. We experimentally compare floating-point and exact-arithmetic implementations of all algorithms on three benchmark sets using two probabilistic model checkers. Our results show that (optimistic) value iteration is a sensible default, but other algorithms are preferable in specific settings. This paper thereby provides a guide for MDP verification practitioners—tool builders and users alike.}, author = {Hartmanns, Arnd and Junges, Sebastian and Quatmann, Tim and Weininger, Maximilian}, issn = {1433-2787}, journal = {International Journal on Software Tools for Technology Transfer}, keywords = {Quantitative model checking, Markov decision process, Linear programming, Value iteration, Policy iteration}, publisher = {Springer Nature}, title = {{The revised practitioner’s guide to MDP model checking algorithms}}, doi = {10.1007/s10009-026-00848-y}, year = {2026}, } @inproceedings{21717, abstract = {Robust Markov Decision Processes (RMDPs) generalize classical MDPs that consider uncertainties in transition probabilities by defining a set of possible transition functions. An objective is a set of runs (or infinite trajectories) of the RMDP, and the value for an objective is the maximal probability that the agent can guarantee against the adversarial environment. We consider (a) reachability objectives, where given a target set of states, the goal is to eventually arrive at one of them; and (b) parity objectives, which are a canonical representation for ω-regular objectives. The qualitative analysis problem asks whether the objective can be ensured with probability 1. In this work, we study the qualitative problem for reachability and parity objectives on RMDPs without making any assumption over the structures of the RMDPs, e.g., unichain or aperiodic. Our contributions are twofold. We first present efficient algorithms with oracle access to uncertainty sets that solve qualitative problems of reachability and parity objectives. We then report experimental results demonstrating the effectiveness of our oracle-based approach on classical RMDP examples from the literature scaling up to thousands of states.}, author = {Asadi, Ali and Chatterjee, Krishnendu and Kafshdar Goharshadi, Ehsan and Karrabi, Mehrdad and Shafiee, Ali}, booktitle = {Proceedings of the 40th AAAI Conference on Artificial Intelligence}, issn = {2374-3468}, location = {Singapore, Singapore}, number = {43}, pages = {36137--36145}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Qualitative analysis of ω-regular objectives on robust MDPs}}, doi = {10.1609/aaai.v40i43.40931}, volume = {40}, year = {2026}, } @inproceedings{21722, abstract = {Partially observable Markov decision processes (POMDPs) are a central model for uncertainty in sequential decision making. The most basic objective is the reachability objective, where a target set must be eventually visited, and the more general parity objectives can model all omega-regular specifications. For such objectives, the computational analysis problems are the following: (a) qualitative analysis that asks whether the objective can be satisfied with probability 1 (almost-sure winning) or probability arbitrarily close to 1 (limit-sure winning); and (b) quantitative analysis that asks for the approximation of the optimal probability of satisfying the objective. For general POMDPs, almost-sure analysis for reachability objectives is EXPTIME-complete, but limit-sure and quantitative analyses for reachability objectives are undecidable; almost-sure, limit-sure, and quantitative analyses for parity objectives are all undecidable. A special class of POMDPs, called revealing POMDPs, has been studied recently in several works, and for this subclass the almost-sure analysis for parity objectives was shown to be EXPTIME-complete. In this work, we show that for revealing POMDPs the limit-sure analysis for parity objectives is EXPTIME-complete, and even the quantitative analysis for parity objectives can be achieved in EXPTIME.}, author = {Asadi, Ali and Chatterjee, Krishnendu and Lurie, David and Saona Urmeneta, Raimundo J}, booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, issn = {2374-3468}, location = {Singapore, Singapore}, number = {43}, pages = {36146--36154}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Revealing POMDPs: Qualitative and quantitative analysis for parity objectives}}, doi = {10.1609/aaai.v40i43.40932}, volume = {40}, year = {2026}, } @inproceedings{21411, abstract = {To achieve fast recovery from link failures, most modern communication networks feature fully decentralized fast re-routing mechanisms. These re-routing mechanisms rely on pre-installed static re-routing rules at the nodes (the routers), which depend only on local failure information, namely on the failed links incident to the node. Ideally, a network is perfectly resilient: the re-routing rules ensure that packets are always successfully routed to their destinations as long as the source and the destination are still physically connected in the underlying network after the failures. Unfortunately, there are examples where achieving perfect resilience is not possible. Surprisingly, only very little is known about the algorithmic aspect of when and how perfect resilience can be achieved. We investigate the computational complexity of analyzing such local fast re-routing mechanisms. Our main result is a negative one: we show that even checking whether a given set of static re-routing rules ensures perfect resilience is coNP-complete. Additionally, we investigate other fundamental variations of the problem. In particular, we show that our coNP-completeness proof also applies to scenarios where the re-routing rules have specific patterns (known as skipping in the literature). On the positive side, for scenarios where nodes do not have information about the link from which a packet arrived (the so-called in-port), we present a linear-time algorithm to realize perfect resilience whenever possible (which we show can also be determined in linear time). }, author = {Bentert, Matthias and Ceylan, Esra and Hübner, Valentin and Schmid, Stefan and Srba, Jiří}, booktitle = {29th International Conference on Principles of Distributed Systems}, isbn = {9783959774093}, issn = {1868-8969}, location = {Iaşi, Romania}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Fast re-routing in networks: On the complexity of perfect resilience}}, doi = {10.4230/LIPIcs.OPODIS.2025.31}, volume = {361}, year = {2026}, } @misc{21668, abstract = {This artifact allows to review and reproduce the experiments from the paper *A Revised Practitioner's Guide to MDP Model Checking Algorithms*. The package contains all original logfiles and derived data used to generate the plots as in the paper. Furthermore, the artifact contains the model checking tools `Storm` and `mcsta` in the version exercised in the paper, the used Docker container, as well as benchmark instances and execution scripts to reproduce the experiments. See also the artifact of the conference paper: https://zenodo.org/records/7509474}, author = {Hartmanns, Arnd and Junges, Sebastian and Quatmann, Tim and Weininger, Maximilian}, publisher = {Zenodo}, title = {{Benchmark data for the revised practitioner's guide to MDP model checking algorithms}}, doi = {10.5281/ZENODO.14500423}, year = {2025}, } @inproceedings{19375, abstract = {Despite the advances in probabilistic model checking, the scalability of the verification methods remains limited. In particular, the state space often becomes extremely large when instantiating parameterized Markov decision processes (MDPs) even with moderate values. Synthesizing policies for such huge MDPs is beyond the reach of available tools. We propose a learning-based approach to obtain a reasonable policy for such huge MDPs. The idea is to generalize optimal policies obtained by model-checking small instances to larger ones using decision-tree learning. Consequently, our method bypasses the need for explicit state-space exploration of large models, providing a practical solution to the state-space explosion problem. We demonstrate the efficacy of our approach by performing extensive experimentation on the relevant models from the quantitative verification benchmark set. The experimental results indicate that our policies perform well, even when the size of the model is orders of magnitude beyond the reach of state-of-the-art analysis tools.}, author = {Azeem, Muqsit and Chakraborty, Debraj and Kanav, Sudeep and Kretinsky, Jan and Mohagheghi, Mohammadsadegh and Mohr, Stefanie and Weininger, Maximilian}, booktitle = {26th International Conference on Verification, Model Checking, and Abstract Interpretation}, isbn = {9783031827020}, issn = {1611-3349}, location = {Denver, CO, United States}, pages = {97--120}, publisher = {Springer Nature}, title = {{1–2–3–Go! Policy synthesis for parameterized Markov decision processes via decision-tree learning and generalization}}, doi = {10.1007/978-3-031-82703-7_5}, volume = {15530}, year = {2025}, } @inproceedings{19445, abstract = {In reconfiguration, we are given two solutions to a graph problem, such as Vertex Cover or Dominating Set, with each solution represented by a placement of tokens on vertices of the graph. Our task is to reconfigure one into the other using small steps while ensuring the intermediate configurations of tokens are also valid solutions. The two commonly studied settings are Token Jumping and Token Sliding, which allows moving a single token to an arbitrary or an adjacent vertex, respectively. We introduce new rules that generalize Token Jumping, parameterized by the number of tokens allowed to move at once and by the maximum distance of each move. Our main contribution is identifying minimal rules that allow reconfiguring any possible given solution into any other for Independent Set, Vertex Cover, and Dominating Set. For each minimal rule, we also provide an efficient algorithm that finds a corresponding reconfiguration sequence. We further focus on the rule that allows each token to move to an adjacent vertex in a single step. This natural variant turns out to be the minimal rule that guarantees reconfigurability for Vertex Cover. We determine the computational complexity of deciding whether a (shortest) reconfiguration sequence exists under this rule for the three studied problems. While reachability for Vertex Cover is shown to be in P, finding a shortest sequence is shown to be NP-complete. For Independent Set and Dominating Set, even reachability is shown to be PSPACE-complete.}, author = {Křišťan, Jan Matyáš and Svoboda, Jakub}, booktitle = {19th International Conference and Workshops on Algorithms and Computation}, isbn = {9789819628445}, issn = {1611-3349}, location = {Chengdu, China}, pages = {244--265}, publisher = {Springer Nature}, title = {{Reconfiguration using generalized token jumping}}, doi = {10.1007/978-981-96-2845-2_16}, volume = {15411}, year = {2025}, } @article{19499, abstract = {Quantum hardware is inherently fragile and noisy. We find that the accuracy of traditional quantum error correction algorithms can be improved depending on the hardware. Given different hardware specifications, we automatically synthesize hardware-optimal algorithms for parity correction, qubit resetting, and GHZ (Greenberger–Horne–Zeilinger) state preparation. Using stochastic techniques from computer science, our method presents a computational tool to compute exact accuracy guarantees and synthesize optimal algorithms that are often different from traditional ones. We also show that improvements can be gained with respect to the Qiskit transpiler as we compute the hardware-optimal qubit mapping for the GHZ state-preparation problem.}, author = {Muroya Lei, Stefanie and Chatterjee, Krishnendu and Henzinger, Thomas A}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {12}, publisher = {National Academy of Sciences}, title = {{Hardware-optimal quantum algorithms}}, doi = {10.1073/pnas.2419273122}, volume = {122}, year = {2025}, } @article{19508, abstract = {We consider random two-player zero-sum dynamic games with perfect information on a class of infinite directed graphs. Starting from a fixed vertex, the players take turns to move a token along the edges of the graph. Every vertex is assigned a payoff known in advance by both players. Every time the token visits a vertex, Player 2 pays Player 1 the corresponding payoff. We consider a distribution over such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that, when the duration of the game tends to infinity, the value converges almost surely to a constant at an exponential rate dominated in terms of the expansion. On the other hand, for the infinite d-ary tree (that does not fall into the previous class of graphs), we show convergence at a double-exponential rate.}, author = {Attia, Luc and Lichev, Lyuben and Mitsche, Dieter and Saona Urmeneta, Raimundo J and Ziliotto, Bruno}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {1517--1535}, publisher = {Springer Nature}, title = {{Random zero-sum dynamic games on infinite directed graphs}}, doi = {10.1007/s13235-025-00636-4}, volume = {15}, year = {2025}, } @inproceedings{19600, abstract = {In this work, we explore route discovery in private payment channel networks. We first determine what “ideal" privacy for a routing protocol means in this setting. We observe that protocols achieving this strong privacy definition exist by leveraging Multi-Party Computation but they are inherently inefficient as they must involve the entire network. We then present protocols with weaker privacy guarantees but much better efficiency (involving only a small fraction of the nodes). The core idea is that both sender and receiver gossip a message which propagates through the network, and the moment any node in the network receives both messages, a path is found. In our first protocol the message is always sent to all neighbouring nodes with a delay proportional to the fees of that edge. In our second protocol the message is only sent to one neighbour chosen randomly with a probability proportional to its degree. We additionally propose a more realistic notion of privacy in order to measure the privacy leakage of our protocols in practice. Our realistic notion of privacy challenges an adversary that join the network with a fixed budget to create channels to guess the sender and receiver of a transaction upon receiving messages from our protocols. Simulations of our protocols on the Lightning network topology (for random transactions and uniform fees) show that 1) forming edges with high degree nodes is a more effective attack strategy for the adversary, 2) there is a tradeoff between the number of nodes involved in our protocols (privacy) and the optimality of the discovered path, and 3) our protocols involve a very small fraction of the network on average.}, author = {Avarikioti, Zeta and Bastankhah, Mahsa and Maddah-Ali, Mohammad Ali and Pietrzak, Krzysztof Z and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {Computer Security. ESORICS 2024 International Workshops}, isbn = {9783031823480}, issn = {1611-3349}, location = {Bydgoszcz, Poland}, pages = {207--223}, publisher = {Springer Nature}, title = {{Route discovery in private payment channel networks}}, doi = {10.1007/978-3-031-82349-7_15}, volume = {15263}, year = {2025}, } @inproceedings{19666, abstract = {Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities. In *robust* MDP (RMDP), every action is associated with an *uncertainty set* of probability distributions, modelling that transition probabilities are not known precisely. Based on the known theoretical connection to stochastic games, we provide a framework for solving RMDPs that is generic, reliable, and efficient. It is *generic* both with respect to the model, allowing for a wide range of uncertainty sets, including but not limited to intervals, L1- or L2-balls, and polytopes; and with respect to the objective, including long-run average reward, undiscounted total reward, and stochastic shortest path. It is *reliable*, as our approach not only converges in the limit, but provides precision guarantees at any time during the computation. It is *efficient* because -- in contrast to state-of-the-art approaches -- it avoids explicitly constructing the underlying stochastic game. Consequently, our prototype implementation outperforms existing tools by several orders of magnitude and can solve RMDPs with a million states in under a minute.}, author = {Meggendorfer, Tobias and Weininger, Maximilian and Wienhöft, Patrick}, booktitle = {Proceedings of the 39th AAAI Conference on Artificial Intelligence}, issn = {2374-3468}, location = {Philadelphia, PA, United States}, number = {25}, pages = {26631--26641}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Solving robust Markov decision processes: Generic, reliable, efficient}}, doi = {10.1609/aaai.v39i25.34865}, volume = {39}, year = {2025}, } @inproceedings{19667, abstract = {The problem of checking satisfiability of linear real arithmetic (LRA) and non-linear real arithmetic (NRA) formulas has broad applications, in particular, they are at the heart of logic-related applications such as logic for artificial intelligence, program analysis, etc. While there has been much work on checking satisfiability of unquantified LRA and NRA formulas, the problem of checking satisfiability of quantified LRA and NRA formulas remains a significant challenge. The main bottleneck in the existing methods is a computationally expensive quantifier elimination step. In this work, we propose a novel method for efficient quantifier elimination in quantified LRA and NRA formulas. We propose a template-based Skolemization approach, where we automatically synthesize linear/polynomial Skolem functions in order to eliminate quantifiers in the formula. The key technical ingredient in our approach are Positivstellensätze theorems from algebraic geometry, which allow for an efficient manipulation of polynomial inequalities. Our method offers a range of appealing theoretical properties combined with a strong practical performance. On the theory side, our method is sound, semi-complete, and runs in subexponential time and polynomial space, as opposed to existing sound and complete quantifier elimination methods that run in doubly-exponential time and at least exponential space. On the practical side, our experiments show superior performance compared to state of the art SMT solvers in terms of the number of solved instances and runtime, both on LRA and on NRA benchmarks.}, author = {Chatterjee, Krishnendu and Kafshdar Goharshadi, Ehsan and Karrabi, Mehrdad and Motwani, Harshit J. and Seeliger, Maximilian and Zikelic, Dorde}, booktitle = {Proceedings of the 39th AAAI Conference on Artificial Intelligence}, issn = {2374-3468}, location = {Philadelphia, PA, United States}, number = {11}, pages = {11158--11166}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Quantified linear and polynomial arithmetic satisfiability via template-based skolemization}}, doi = {10.1609/aaai.v39i11.33213}, volume = {39}, year = {2025}, } @inproceedings{19669, abstract = {We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability condition; (C2) the non-negative coefficients condition; (C3) the sum upto 1 condition; and (C4) the only min or only max operator condition. Several seminal results in the literature focus on special cases. For example, turn-based stochastic games correspond to conditions C2 and C3; and Markov decision process to conditions C2, C3, and C4. However, the systematic computational complexity study of all the cases has not been explored, which we address in this work. Some highlights of our results are: with conditions C2 and C4, and with conditions C3 and C4, the problem is NP-complete, whereas with condition C1 only, the problem is in UP intersects coUP. Finally, we establish the computational complexity of the decision problem of checking the respective conditions.}, author = {Chatterjee, Krishnendu and Luo, Ruichen and Saona Urmeneta, Raimundo J and Svoboda, Jakub}, booktitle = {Proceedings of the 39th AAAI Conference on Artificial Intelligence}, issn = {2374-3468}, location = {Philadelphia, PA, United States}, number = {11}, pages = {11150--11157}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Linear equations with min and max operators: Computational complexity}}, doi = {10.1609/aaai.v39i11.33212}, volume = {39}, year = {2025}, } @inproceedings{19740, abstract = {Two standard models for probabilistic systems are Markov chains (MCs) and Markov decision processes (MDPs). Classic objectives for such probabilistic models for control and planning problems are reachability and stochastic shortest path. The widely studied algorithmic approach for these problems is the Value Iteration (VI) algorithm which iteratively applies local updates called Bellman updates. There are many practical approaches for VI in the literature but they all require exponentially many Bellman updates for MCs in the worst case. A preprocessing step is an algorithm that is discrete, graph-theoretical, and requires linear space. An important open question is whether, after a polynomial-time preprocessing, VI can be achieved with sub-exponentially many Bellman updates. In this work, we present a new approach for VI based on guessing values. Our theoretical contributions are twofold. First, for MCs, we present an almost-linear-time preprocessing algorithm after which, along with guessing values, VI requires only subexponentially many Bellman updates. Second, we present an improved analysis of the speed of convergence of VI for MDPs. Finally, we present a practical algorithm for MDPs based on our new approach. Experimental results show that our approach provides a considerable improvement over existing VI-based approaches on several benchmark examples from the literature.}, author = {Chatterjee, Krishnendu and Jafariraviz, Mahdi and Saona Urmeneta, Raimundo J and Svoboda, Jakub}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906527}, issn = {1611-3349}, location = {Hamilton, ON, Canada}, pages = {217--236}, publisher = {Springer Nature}, title = {{Value iteration with guessing for Markov chains and Markov decision processes}}, doi = {10.1007/978-3-031-90653-4_11}, volume = {15697}, year = {2025}, } @inproceedings{19742, abstract = {Statistical model checking estimates probabilities and expectations of interest in probabilistic system models by using random simulations. Its results come with statistical guarantees. However, many tools use unsound statistical methods that produce incorrect results more often than they claim. In this paper, we provide a comprehensive overview of tools and their correctness, as well as of sound methods available for estimating probabilities from the literature. For expected rewards, we investigate how to bound the path reward distribution to apply sound statistical methods for bounded distributions, of which we recommend the Dvoretzky-Kiefer-Wolfowitz inequality that has not been used in SMC so far. We prove that even reachability rewards can be bounded in theory, and formalise the concept of limit-PAC procedures for a practical solution. The modes SMC tool implements our methods and recommendations, which we use to experimentally confirm our results.}, author = {Budde, Carlos E. and Hartmanns, Arnd and Meggendorfer, Tobias and Weininger, Maximilian and Wienhöft, Patrick}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906428}, issn = {1611-3349}, location = {Hamilton, ON, Canada}, pages = {167--190}, publisher = {Springer Nature}, title = {{Sound statistical model checking for probabilities and expected rewards}}, doi = {10.1007/978-3-031-90643-5_9}, volume = {15696}, year = {2025}, } @inproceedings{19743, abstract = {The possibility of errors in human-engineered formal verification software, such as model checkers, poses a serious threat to the purpose of these tools. An established approach to mitigate this problem are certificates—lightweight, easy-to-check proofs of the verification results. In this paper, we develop novel certificates for model checking of Markov decision processes (MDPs) with quantitative reachability and expected reward properties. Our approach is conceptually simple and relies almost exclusively on elementary fixed point theory. Our certificates work for arbitrary finite MDPs and can be readily computed with little overhead using standard algorithms. We formalize the soundness of our certificates in Isabelle/HOL and provide a formally verified certificate checker. Moreover, we augment existing algorithms in the probabilistic model checker Storm with the ability to produce certificates and demonstrate practical applicability by conducting the first formal certification of the reference results in the Quantitative Verification Benchmark Set.}, author = {Chatterjee, Krishnendu and Quatmann, Tim and Schäffeler, Maximilian and Weininger, Maximilian and Winkler, Tobias and Zilken, Daniel}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906527}, issn = {1611-3349}, location = {Hamilton, ON, Canada}, pages = {130--151}, publisher = {Springer Nature}, title = {{Fixed point certificates for reachability and expected rewards in MDPs}}, doi = {10.1007/978-3-031-90653-4_7}, volume = {15697}, year = {2025}, } @inproceedings{19744, abstract = {We consider the problem of refuting equivalence of probabilistic programs, i.e., the problem of proving that two probabilistic programs induce different output distributions. We study this problem in the context of programs with conditioning (i.e., with observe and score statements), where the output distribution is conditioned by the event that all the observe statements along a run evaluate to true, and where the probability densities of different runs may be updated via the score statements. Building on a recent work on programs without conditioning, we present a new equivalence refutation method for programs with conditioning. Our method is based on weighted restarting, a novel transformation of probabilistic programs with conditioning to the output equivalent probabilistic programs without conditioning that we introduce in this work. Our method is the first to be both a) fully automated, and b) providing provably correct answers. We demonstrate the applicability of our method on a set of programs from the probabilistic inference literature.}, author = {Chatterjee, Krishnendu and Kafshdar Goharshadi, Ehsan and Novotný, Petr and Zikelic, Dorde}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906527}, issn = {1611-3349}, location = {Hamilton, ON, Canada}, pages = {279--300}, publisher = {Springer Nature}, title = {{Refuting equivalence in probabilistic programs with conditioning}}, doi = {10.1007/978-3-031-90653-4_14}, volume = {15697}, year = {2025}, } @misc{19769, abstract = {Artifact to reproduce the experimental results presented in the article "Sound Statistical Model Checking for Probabilities and Expected Rewards" by Carlos E. Budde, Arnd Hartmanns, Tobias Meggendorfer, Maximilian Weininger, and Patrick Wienhöft (TACAS 2025). The contents include all data and software (formal models, software tools, Python & bash scripts) used in the experimental evaluation presented in sections 3, 4, and 6 of the article. Detailed instructions on how to reproduce the results are bundled in the artifact.}, author = {Budde, Carlos and Hartmanns, Arnd and Meggendorfer, Tobias and Weininger, Maximilian and Wienhöft, Patrick}, publisher = {Zenodo}, title = {{Sound statistical model checking for probabilities and expected rewards (experimental reproduction package)}}, doi = {10.5281/ZENODO.14602066}, year = {2025}, } @misc{19771, abstract = {This artifact allows to review and reproduce the Isabelle proofs and practical experiments from the paper *Fixed Point Certificates for Reachability and Expected Rewards in MDPs*. The contents are two-fold: First, the artifact contains a formally verified certificate checker for the certificates presented in the paper. The formal Isabelle/HOL proofs of the background theory can be inspected, checked by Isabelle and the code extraction can be retraced. Second, the artifact contains a modified version of the model checking tool `Storm` with support for certificate generation. Together with the provided scripts and benchmark files, this allows to reproduce the experiments from the paper. An appropriate subset of the experiments is given to allow a review in a timely manner. In addition, original logfiles from our experiments are provided, allowing a detailed inspection. The package includes convenient installation scripts for [the TACAS 2023 VM](https://doi.org/10.5281/zenodo.7113223) (based on Ubuntu 22.04). A native installation on Linux or macOS systems (including the newer ARM-based machines) is also possible.}, author = {Chatterjee, Krishnendu and Quatmann, Tim and Schäffeler, Maximilian and Weininger, Maximilian and Winkler, Tobias and Zilken, Daniel}, publisher = {Zenodo}, title = {{Artifact: Fixed point certificates for reachability and expected rewards in MDPs}}, doi = {10.5281/ZENODO.14626585}, year = {2025}, } @article{19843, abstract = {Social dilemmas are collective-action problems where individual interests are at odds with group interests. Such dilemmas occur frequently at all scales of human interactions. When dealing with collective-action problems, people often act reciprocally. They adjust their behavior to match the previous behavior of the recipient. The literature distinguishes two kinds of reciprocity. According to direct reciprocity, individuals react to their immediate experiences with the recipient. They are more likely to cooperate if the recipient previously cooperated with them. According to indirect reciprocity, individuals react to the recipient’s general behavior, irrespectively of whether or not they benefited directly. In practice, the two kinds of reciprocity are often intertwined; people typically base their decisions on both direct experiences and indirect observations. Yet only recently have researchers begun to explore how the two kinds of reciprocity interact. So far, this research only addresses a single type of social dilemma, the donation game, where the effects of individual behaviors are independent. Instead, here we allow for all pairwise social dilemmas. By applying novel techniques to generalize the theory of zero-determinant strategies, we establish an important proof of principle: In all social dilemmas, socially optimal outcomes can be sustained as an equilibrium, using either direct or indirect reciprocity, or arbitrary mixtures thereof. These results neither require games to be repeated infinitely often, nor that individual opinions are synchronized. In this way, we considerably generalize the scope of models of reciprocity, and we build further bridges between the literatures on direct and indirect reciprocity.}, author = {Hübner, Valentin and Schmid, Laura and Hilbe, Christian and Chatterjee, Krishnendu}, issn = {2752-6542}, journal = {PNAS Nexus}, number = {5}, publisher = {Oxford University Press}, title = {{Stable strategies of direct and indirect reciprocity across all social dilemmas}}, doi = {10.1093/pnasnexus/pgaf154}, volume = {4}, year = {2025}, }