@article{19595, abstract = {We investigate the locality of magnetic response in polycyclic aromatic molecules using a novel deep-learning approach. Our method employs graph neural networks (GNNs) with a graph-of-rings representation to predict nucleus independent chemical shifts (NICS) in the space around the molecule. We train a series of models, each time reducing the size of the largest molecules used in training. The accuracy of prediction remains high (MAE < 0.5 ppm), even when training the model only on molecules with up to four rings, thus providing strong evidence for the locality of magnetic response. To overcome the known problem of generalization of GNNs, we implement a k-hop expansion strategy and succeed in achieving accurate predictions for molecules with up to 15 rings (almost 4 times the size of the largest training example). Our findings have implications for understanding the magnetic response in complex molecules and demonstrate a promising approach to overcoming GNN scalability limitations. Furthermore, the trained models enable rapid characterization, without the need for more expensive DFT calculations.}, author = {Davidson, Yair and Philipp, Aviad and Chakraborty, Sabyasachi and Bronstein, Alexander and Gershoni-Poranne, Renana}, issn = {1089-7690}, journal = {Journal of Chemical Physics}, number = {14}, publisher = {AIP Publishing}, title = {{How local is “local”? Deep learning reveals locality of the induced magnetic field of polycyclic aromatic hydrocarbons}}, doi = {10.1063/5.0257558}, volume = {162}, year = {2025}, } @article{17468, abstract = {Oxygen redox chemistry is central to life1 and many human-made technologies, such as in energy storage2,3,4. The large energy gain from oxygen redox reactions is often connected with the occurrence of harmful reactive oxygen species3,5,6. Key species are superoxide and the highly reactive singlet oxygen3,4,5,6,7, which may evolve from superoxide. However, the factors determining the formation of singlet oxygen, rather than the relatively unreactive triplet oxygen, are unknown. Here we report that the release of triplet or singlet oxygen is governed by individual Marcus normal and inverted region behaviour. We found that as the driving force for the reaction increases, the initially dominant evolution of triplet oxygen slows down, and singlet oxygen evolution becomes predominant with higher maximum kinetics. This behaviour also applies to the widely observed superoxide disproportionation, in which one superoxide is oxidized by another, in both non-aqueous and aqueous systems, with Lewis and Brønsted acidity controlling the driving forces. Singlet oxygen yields governed by these conditions are relevant, for example, in batteries or cellular organelles in which superoxide forms. Our findings suggest ways to understand and control spin states and kinetics in oxygen redox chemistry, with implications for fields, including life sciences, pure chemistry and energy storage.}, author = {Mondal, Soumyadip and Nguyen, Huyen T.K. and Hauschild, Robert and Freunberger, Stefan Alexander}, issn = {1476-4687}, journal = {Nature}, number = {8085}, pages = {601–605}, publisher = {Springer Nature}, title = {{Marcus kinetics control singlet and triplet oxygen evolving from superoxide}}, doi = {10.1038/s41586-025-09587-7}, volume = {646}, 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{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{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}, } @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}, } @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}, } @article{19074, abstract = {The public goods game is among the most studied metaphors of cooperation in groups. In this game, individuals can use their endowments to make contributions towards a good that benefits everyone. Each individual, however, is tempted to free-ride on the contributions of others. Herein, we study repeated public goods games among asymmetric players. Previous work has explored to which extent asymmetry allows for full cooperation, such that players contribute their full endowment each round. However, by design that work focusses on equilibria where individuals make the same contribution each round. Instead, here we consider players whose contributions along the equilibrium path can change from one round to the next. We do so for three different models – one without any budget constraints, one with endowment constraints, and one in which individuals can save their current endowment to be used in subsequent rounds. In each case, we explore two key quantities: the welfare and the resource efficiency that can be achieved in equilibrium. Welfare corresponds to the sum of all players’ payoffs. Resource efficiency relates this welfare to the total contributions made by the players. Compared to constant contribution sequences, we find that time-dependent contributions can improve resource efficiency across all three models. Moreover, they can improve the players’ welfare in the model with savings.}, author = {Hübner, Valentin and Hilbe, Christian and Staab, Manuel and Kleshnina, Maria and Chatterjee, Krishnendu}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {1617--1645}, publisher = {Springer Nature}, title = {{Time-dependent strategies in repeated asymmetric public goods games}}, doi = {10.1007/s13235-025-00627-5}, volume = {15}, year = {2025}, } @inproceedings{20299, abstract = {Deterministic Markov Decision Processes (DMDPs) are a mathematical framework for decision-making where the outcomes and future possible actions are deterministically determined by the current action taken. DMDPs can be viewed as a finite directed weighted graph, where in each step, the controller chooses an outgoing edge. An objective is a measurable function on runs (or infinite trajectories) of the DMDP, and the value for an objective is the maximal cumulative reward (or weight) that the controller can guarantee. We consider the classical mean-payoff (aka limit-average) objective, which is a basic and fundamental objective. Howard's policy iteration algorithm is a popular method for solving DMDPs with mean-payoff objectives. Although Howard's algorithm performs well in practice, as experimental studies suggested, the best known upper bound is exponential and the current known lower bound is as follows: For the input size I, the algorithm requires (math formular) iterations, where (math formular) hides the poly-logarithmic factors, i.e., the current lower bound on iterations is sub-linear with respect to the input size. Our main result is an improved lower bound for this fundamental algorithm where we show that for the input size I, the algorithm requires (math formular) iterations.}, author = {Asadi, Ali and Chatterjee, Krishnendu and De Raaij, Jakob}, booktitle = {The 41st Conference on Uncertainty in Artificial Intelligence}, issn = {2640-3498}, location = {Rio de Janeiro, Brazil}, pages = {223--232}, publisher = {ML Research Press}, title = {{Lower bound on Howard policy iteration for deterministic Markov Decision Processes}}, volume = {286}, year = {2025}, } @inproceedings{20297, abstract = {A standard model that arises in several applications in sequential decision-making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in POMDPs is the reachability objective, where given a target set of states, the goal is to eventually arrive at one of them. The limit-sure problem asks whether reachability can be ensured with probability arbitrarily close to 1. In general, the limit-sure reachability problem for POMDPs is undecidable. However, in many practical cases, the most relevant question is the existence of policies with a small amount of memory. In this work, we study the limit-sure reachability problem for POMDPs with a fixed amount of memory. We establish that the computational complexity of the problem is NP-complete.}, author = {Asadi, Ali and Chatterjee, Krishnendu and Saona Urmeneta, Raimundo J and Shafiee, Ali}, booktitle = {The 41st Conference on Uncertainty in Artificial Intelligence}, issn = {2640-3498}, location = {Rio de Janeiro, Brazil}, pages = {238--247}, publisher = {ML Research Press}, title = {{Limit-sure reachability for small memory policies in POMDPs is NP-complete}}, volume = {286}, year = {2025}, } @inproceedings{20296, abstract = {Learning-based systems are increasingly deployed across various domains, yet the complexity of traditional neural networks poses significant challenges for formal verification. Unlike conventional neural networks, learned Logic Gate Networks (LGNs) replace multiplications with Boolean logic gates, yielding a sparse, netlist-like architecture that is inherently more amenable to symbolic verification, while still delivering promising performance. In this paper, we introduce a SAT encoding for verifying global robustness and fairness in LGNs. We evaluate our method on five benchmark datasets, including a newly constructed 5-class variant, and find that LGNs are both verification-friendly and maintain strong predictive performance.}, author = {Kresse, Fabian and Yu, Zhengqi and Lampert, Christoph and Henzinger, Thomas A}, booktitle = {2nd International Conferenceon Neuro-Symbolic Systems}, issn = {2640-3498}, location = {Philadephia, PA, United States}, publisher = {ML Research Press}, title = {{Logic gate neural networks are good for verification}}, volume = {288}, 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{20302, abstract = {LocalSGD and SCAFFOLD are widely used methods in distributed stochastic optimization, with numerous applications in machine learning, large-scale data processing, and federated learning. However, rigorously establishing their theoretical advantages over simpler methods, such as minibatch SGD (MbSGD), has proven challenging, as existing analyses often rely on strong assumptions, unrealistic premises, or overly restrictive scenarios. In this work, we revisit the convergence properties of LocalSGD and SCAFFOLD under a variety of existing or weaker conditions, including gradient similarity, Hessian similarity, weak convexity, and Lipschitz continuity of the Hessian. Our analysis shows that (i) LocalSGD achieves faster convergence compared to MbSGD for weakly convex functions without requiring stronger gradient similarity assumptions; (ii) LocalSGD benefits significantly from higher-order similarity and smoothness; and (iii) SCAFFOLD demonstrates faster convergence than MbSGD for a broader class of non-quadratic functions. These theoretical insights provide a clearer understanding of the conditions under which LocalSGD and SCAFFOLD outperform MbSGD.}, author = {Luo, Ruichen and Stich, Sebastian U. and Horváth, Samuel and Takáč, Martin}, booktitle = {The 28th International Conference on Artificial Intelligence and Statistics}, issn = {2640-3498}, location = {Mai Khao, Thailand}, pages = {2539--2547}, publisher = {ML Research Press}, title = {{Revisiting LocalSGD and SCAFFOLD: Improved rates and missing analysis}}, volume = {258}, year = {2025}, } @article{20646, abstract = {Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by projecting quantum evolution onto a classical dynamical system within a variational manifold. In classical systems, periodic orbits play a crucial role in understanding the structure of the phase space and the long-term behavior of the system. However, finding periodic orbits is generally difficult, and their existence and properties in generic TDVP dynamics over matrix product states have remained largely unexplored. In this work, we develop an algorithm to systematically identify and characterize periodic orbits in TDVP dynamics. Applying our method to the periodically kicked Ising model, we uncover both stable and unstable periodic orbits. We characterize the Kolmogorov-Arnold-Moser tori in the vicinity of stable periodic orbits and track the change of the periodic orbits as we modify the Hamiltonian parameters. We observe that periodic orbits exist at any value of the coupling constant of the kicked Ising model between prethermal and fully thermalizing regimes, but their relevance to quantum dynamics and imprint on quantum eigenstates diminishes as the system leaves the prethermal regime. Our results demonstrate that periodic orbits provide valuable insights into the TDVP approximation of quantum many-body evolution and establish a closer connection between quantum and classical chaos.}, author = {Petrova, Elena and Ljubotina, Marko and Yalniz, Gökhan and Serbyn, Maksym}, issn = {2691-3399}, journal = {PRX Quantum}, number = {4}, publisher = {American Physical Society}, title = {{Finding periodic orbits in projected quantum many-body dynamics}}, doi = {10.1103/tldp-kvkd}, volume = {6}, year = {2025}, } @article{20709, abstract = {Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a noncommutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understanding localization in non-Hermitian settings.}, author = {Brighi, Pietro and Ljubotina, Marko and Roccati, Federico and Balducci, Federico}, issn = {2643-1564}, journal = {Physical Review Research}, number = {4}, publisher = {American Physical Society}, title = {{Finite steady-state current defies non-Hermitian many-body localization}}, doi = {10.1103/crwj-x7j8}, volume = {7}, year = {2025}, } @inproceedings{20648, abstract = {Polynomial quantified entailments with existentially and universally quantified variables arise in many problems of verification and program analysis. We present PolyQEnt which is a tool for solving polynomial quantified entailments in which variables on both sides of the implication are real valued or unbounded integers. Our tool provides a unified framework for polynomial quantified entailment problems that arise in several papers in the literature. Our experimental evaluation over a wide range of benchmarks shows the applicability of the tool as well as its benefits as opposed to simply using existing SMT solvers to solve such constraints.}, author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Kafshdar Goharshadi, Ehsan and Karrabi, Mehrdad and Saadat, Milad and Seeliger, Maximilian and Zikelic, Dorde}, booktitle = {23rd International Symposium on Automated Technology for Verification and Analysis}, isbn = {9783032087065}, issn = {1611-3349}, location = {Bengaluru, India}, pages = {411--424}, publisher = {Springer Nature}, title = {{PolyQEnt: A polynomial quantified entailment solver}}, doi = {10.1007/978-3-032-08707-2_19}, volume = {16145}, year = {2025}, } @inproceedings{20690, abstract = {Cumulative prospect theory (CPT) is the first theory for decision-making under uncertainty that combines full theoretical soundness and empirically realistic features [1], [Page 2]. While CPT was originally considered in one-shot settings for risk-aware decision-making, we consider CPT in sequential decision-making. The most fundamental and well-studied models for sequential decision-making are Markov chains (MCs), and their generalization Markov decision processes (MDPs). The complexity theoretic study of MCs and MDPs with CPT is a fundamental problem that has not been addressed in the literature.Our contributions are as follows: First, we present an alternative viewpoint for the CPT-value of MCs and MDPs. This allows us to establish a connection with multi-objective reachability analysis and conclude the strategy complexity result that memoryless randomized strategies are necessary and sufficient for optimality. Second, based on this connection, we provide an algorithm for computing the CPT-value in MDPs with infinite-horizon objectives. We show that the problem is in EXPTIME and fixed-parameter tractable. Moreover, we provide a polynomial-time algorithm for the special case of MCs.}, author = {Brihaye, Thomas and Chatterjee, Krishnendu and Mohr, Stefanie and Weininger, Maximilian}, booktitle = {2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science}, location = {Singapore, Singapore}, pages = {458--471}, publisher = {IEEE}, title = {{Risk-aware Markov decision processes using cumulative prospect theory}}, doi = {10.1109/lics65433.2025.00041}, year = {2025}, } @inproceedings{20689, abstract = {This paper studies the expected value of multiplicative rewards, where rewards obtained in each step are multiplied (instead of the usual addition), in Markov chains (MCs) and Markov decision processes (MDPs). One of the key differences to additive rewards is that the expected value may diverge to ∞ not only due to recurrent, but also due to transient states.For MCs, computing the value is shown to be possible in polynomial time given an oracle for the comparison of succinctly represented integers (CSRI), which is only known to be solvable in polynomial time subject to number-theoretic conjectures. Interestingly, distinguishing whether the value is ∞ or 0 is at least as hard as CSRI, while determining if it is one of these two can be done in polynomial time. In MDPs, the optimal value can be computed in polynomial space. Further refined complexity results and results on the complexity of optimal schedulers are presented. The techniques developed for MDPs additionally allow to solve the multiplicative variant of the stochastic shortest path problem. Finally, for MCs and MDPs where an absorbing state is reached almost surely, all considered problems are solvable in polynomial time.}, author = {Baier, Christel and Chatterjee, Krishnendu and Meggendorfer, Tobias and Piribauer, Jakob}, booktitle = {2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science}, location = {Singapore, Singapore}, pages = {499--512}, publisher = {IEEE}, title = {{Multiplicative rewards in Markovian models}}, doi = {10.1109/lics65433.2025.00044}, year = {2025}, }