@article{14657, abstract = {Natural selection is usually studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we explore how natural selection acts on mutants that have the same reproductive rate, but different population structures. In our framework, population structure is given by a graph that specifies where offspring can disperse. The invading mutant disperses offspring on a different graph than the resident wild-type. We find that more densely connected dispersal graphs tend to increase the invader’s fixation probability, but the exact relationship between structure and fixation probability is subtle. We present three main results. First, we prove that if both invader and resident are on complete dispersal graphs, then removing a single edge in the invader’s dispersal graph reduces its fixation probability. Second, we show that for certain island models higher invader’s connectivity increases its fixation probability, but the magnitude of the effect depends on the exact layout of the connections. Third, we show that for lattices the effect of different connectivity is comparable to that of different fitness: for large population size, the invader’s fixation probability is either constant or exponentially small, depending on whether it is more or less connected than the resident.}, author = {Tkadlec, Josef and Kaveh, Kamran and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {1742-5662}, journal = {Journal of the Royal Society Interface}, number = {208}, publisher = {Royal Society}, title = {{Evolutionary dynamics of mutants that modify population structure}}, doi = {10.1098/rsif.2023.0355}, volume = {20}, year = {2023}, } @article{12787, abstract = {Populations evolve in spatially heterogeneous environments. While a certain trait might bring a fitness advantage in some patch of the environment, a different trait might be advantageous in another patch. Here, we study the Moran birth–death process with two types of individuals in a population stretched across two patches of size N, each patch favouring one of the two types. We show that the long-term fate of such populations crucially depends on the migration rate μ between the patches. To classify the possible fates, we use the distinction between polynomial (short) and exponential (long) timescales. We show that when μ is high then one of the two types fixates on the whole population after a number of steps that is only polynomial in N. By contrast, when μ is low then each type holds majority in the patch where it is favoured for a number of steps that is at least exponential in N. Moreover, we precisely identify the threshold migration rate μ⋆ that separates those two scenarios, thereby exactly delineating the situations that support long-term coexistence of the two types. We also discuss the case of various cycle graphs and we present computer simulations that perfectly match our analytical results.}, author = {Svoboda, Jakub and Tkadlec, Josef and Kaveh, Kamran and Chatterjee, Krishnendu}, issn = {1471-2946}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, number = {2271}, publisher = {The Royal Society}, title = {{Coexistence times in the Moran process with environmental heterogeneity}}, doi = {10.1098/rspa.2022.0685}, volume = {479}, year = {2023}, } @inproceedings{15023, abstract = {Reinforcement learning has shown promising results in learning neural network policies for complicated control tasks. However, the lack of formal guarantees about the behavior of such policies remains an impediment to their deployment. We propose a novel method for learning a composition of neural network policies in stochastic environments, along with a formal certificate which guarantees that a specification over the policy's behavior is satisfied with the desired probability. Unlike prior work on verifiable RL, our approach leverages the compositional nature of logical specifications provided in SpectRL, to learn over graphs of probabilistic reach-avoid specifications. The formal guarantees are provided by learning neural network policies together with reach-avoid supermartingales (RASM) for the graph’s sub-tasks and then composing them into a global policy. We also derive a tighter lower bound compared to previous work on the probability of reach-avoidance implied by a RASM, which is required to find a compositional policy with an acceptable probabilistic threshold for complex tasks with multiple edge policies. We implement a prototype of our approach and evaluate it on a Stochastic Nine Rooms environment.}, author = {Zikelic, Dorde and Lechner, Mathias and Verma, Abhinav and Chatterjee, Krishnendu and Henzinger, Thomas A}, booktitle = {37th Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {New Orleans, LA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Compositional policy learning in stochastic control systems with formal guarantees}}, year = {2023}, } @misc{23142, abstract = {It contains the benchmarks and the results of comparison between STORM, PET and MultiGain for the QComp category of Long-Run Average rewards.}, author = {Grover, Kush and Weiniger, Maximilian and Kretinsky, Jan}, publisher = {Zenodo}, title = {{QComp LRA results}}, doi = {10.5281/zenodo.8219190}, year = {2023}, } @inproceedings{14417, abstract = {Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. In the most general case, the problem is decidable subject to Shanuel’s conjecture. If all inputs are rational, the resulting threshold problem can be solved using algebraic numbers, leading to decidability via a polynomial-time reduction to the existential theory of the reals. Further restrictions on the encoding of the input allow the solution of the threshold problem in NP∩coNP. Finally, an approximation algorithm for the optimal value of ERisk is provided.}, author = {Baier, Christel and Chatterjee, Krishnendu and Meggendorfer, Tobias and Piribauer, Jakob}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959772921}, issn = {1868-8969}, location = {Bordeaux, France}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Entropic risk for turn-based stochastic games}}, doi = {10.4230/LIPIcs.MFCS.2023.15}, volume = {272}, year = {2023}, } @inproceedings{19985, abstract = {We consider a natural problem dealing with weighted packet selection across a rechargeable link, which e.g., finds applications in cryptocurrency networks. The capacity of a link (u, v) is determined by how much nodes u and v allocate for this link. Specifically, the input is a finite ordered sequence of packets that arrive in both directions along a link. Given (u, v) and a packet of weight x going from u to v, node u can either accept or reject the packet. If u accepts the packet, the capacity on link (u, v) decreases by x. Correspondingly, v’s capacity on (u, v) increases by x. If a node rejects the packet, this will entail a cost affinely linear in the weight of the packet. A link is “rechargeable” in the sense that the total capacity of the link has to remain constant, but the allocation of capacity at the ends of the link can depend arbitrarily on the nodes’ decisions. The goal is to minimise the sum of the capacity injected into the link and the cost of rejecting packets. We show that the problem is NP-hard, but can be approximated efficiently with a ratio of (1 + E) . (1 + square3) for some arbitrary E>0.}, author = {Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {30th International Colloquium on Structural Information and Communication Complexity}, isbn = {9783031327322}, issn = {1611-3349}, location = {Alcalá de Henares, Spain}, pages = {576--594}, publisher = {Springer Nature}, title = {{Weighted acket selection for rechargeable links in cryptocurrency networks: Complexity and approximation}}, doi = {10.1007/978-3-031-32733-9_26}, volume = {13892}, year = {2023}, } @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{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{11938, abstract = {A 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 sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ 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(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets 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}, issn = {1526-1719}, journal = {Journal of Graph Algorithms and Applications}, number = {2}, pages = {225--240}, publisher = {Brown University}, title = {{On compatible matchings}}, doi = {10.7155/jgaa.00591}, volume = {26}, 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}, } @inproceedings{12102, abstract = {Given a Markov chain M = (V, v_0, δ), with state space V and a starting state v_0, and a probability threshold ε, an ε-core is a subset C of states that is left with probability at most ε. More formally, C ⊆ V is an ε-core, iff ℙ[reach (V\C)] ≤ ε. Cores have been applied in a wide variety of verification problems over Markov chains, Markov decision processes, and probabilistic programs, as a means of discarding uninteresting and low-probability parts of a probabilistic system and instead being able to focus on the states that are likely to be encountered in a real-world run. In this work, we focus on the problem of computing a minimal ε-core in a Markov chain. Our contributions include both negative and positive results: (i) We show that the decision problem on the existence of an ε-core of a given size is NP-complete. This solves an open problem posed in [Jan Kretínský and Tobias Meggendorfer, 2020]. We additionally show that the problem remains NP-complete even when limited to acyclic Markov chains with bounded maximal vertex degree; (ii) We provide a polynomial time algorithm for computing a minimal ε-core on Markov chains over control-flow graphs of structured programs. A straightforward combination of our algorithm with standard branch prediction techniques allows one to apply the idea of cores to find a subset of program lines that are left with low probability and then focus any desired static analysis on this core subset.}, author = {Ahmadi, Ali and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Meggendorfer, Tobias and Safavi Hemami, Roodabeh and Zikelic, Dorde}, booktitle = {42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, isbn = {9783959772617}, issn = {1868-8969}, location = {Madras, India}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Algorithms and hardness results for computing cores of Markov chains}}, doi = {10.4230/LIPIcs.FSTTCS.2022.29}, volume = {250}, 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{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{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}, } @inproceedings{12568, abstract = {We treat the problem of risk-aware control for stochastic shortest path (SSP) on Markov decision processes (MDP). Typically, expectation is considered for SSP, which however is oblivious to the incurred risk. We present an alternative view, instead optimizing conditional value-at-risk (CVaR), an established risk measure. We treat both Markov chains as well as MDP and introduce, through novel insights, two algorithms, based on linear programming and value iteration, respectively. Both algorithms offer precise and provably correct solutions. Evaluation of our prototype implementation shows that risk-aware control is feasible on several moderately sized models.}, author = {Meggendorfer, Tobias}, booktitle = {Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022}, isbn = {1577358767}, issn = {2374-3468}, location = {Virtual}, number = {9}, pages = {9858--9867}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Risk-aware stochastic shortest path}}, doi = {10.1609/aaai.v36i9.21222}, volume = {36}, year = {2022}, } @unpublished{12677, abstract = {In modern sample-driven Prophet Inequality, an adversary chooses a sequence of n items with values v1,v2,…,vn to be presented to a decision maker (DM). The process follows in two phases. In the first phase (sampling phase), some items, possibly selected at random, are revealed to the DM, but she can never accept them. In the second phase, the DM is presented with the other items in a random order and online fashion. For each item, she must make an irrevocable decision to either accept the item and stop the process or reject the item forever and proceed to the next item. The goal of the DM is to maximize the expected value as compared to a Prophet (or offline algorithm) that has access to all information. In this setting, the sampling phase has no cost and is not part of the optimization process. However, in many scenarios, the samples are obtained as part of the decision-making process. We model this aspect as a two-phase Prophet Inequality where an adversary chooses a sequence of 2n items with values v1,v2,…,v2n and the items are randomly ordered. Finally, there are two phases of the Prophet Inequality problem with the first n-items and the rest of the items, respectively. We show that some basic algorithms achieve a ratio of at most 0.450. We present an algorithm that achieves a ratio of at least 0.495. Finally, we show that for every algorithm the ratio it can achieve is at most 0.502. Hence our algorithm is near-optimal.}, author = {Chatterjee, Krishnendu and Mohammadi, Mona and Saona Urmeneta, Raimundo J}, booktitle = {arXiv}, title = {{Repeated prophet inequality with near-optimal bounds}}, doi = {10.48550/ARXIV.2209.14368}, 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}, } @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}, } @article{17061, abstract = {Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one’s own success. However, when two such “selfish” learners interact with each other, the outcome can be detrimental to both, especially when there are conflicts of interest. Here, we explore how a learner can align incentives with a selfish opponent. Moreover, we consider the dynamics that arise when learning rules themselves are subject to evolutionary pressure. By combining extensive simulations and analytical techniques, we demonstrate that selfish learning is unstable in most classical two-player repeated games. If evolution operates on the level of long-run payoffs, selection instead favors learning rules that incorporate social (other-regarding) preferences. To further corroborate these results, we analyze data from a repeated prisoner’s dilemma experiment. We find that selfish learning is insufficient to explain human behavior when there is a trade-off between payoff maximization and fairness.}, author = {McAvoy, Alex and Kates-Harbeck, Julian and Chatterjee, Krishnendu and Hilbe, Christian}, issn = {2752-6542}, journal = {PNAS Nexus}, number = {4}, publisher = {Oxford University Press}, title = {{Evolutionary instability of selfish learning in repeated games}}, doi = {10.1093/pnasnexus/pgac141}, volume = {1}, year = {2022}, } @article{10602, abstract = {Transforming ω-automata into parity automata is traditionally done using appearance records. We present an efficient variant of this idea, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and show that our method produces significantly smaller automata than previous approaches.}, author = {Kretinsky, Jan and Meggendorfer, Tobias and Waldmann, Clara and Weininger, Maximilian}, issn = {1432-0525}, journal = {Acta Informatica}, keywords = {computer networks and communications, information systems, software}, pages = {585--618}, publisher = {Springer Nature}, title = {{Index appearance record with preorders}}, doi = {10.1007/s00236-021-00412-y}, volume = {59}, year = {2022}, }