Document

**Published in:** LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Nondeterministic good-for-MDPs (GFM) automata are for MDP model checking and reinforcement learning what good-for-games automata are for reactive synthesis: a more compact alternative to deterministic automata that displays nondeterminism, but only so much that it can be resolved locally, such that a syntactic product can be analysed. GFM has recently been introduced as a property for reinforcement learning, where the simpler Büchi acceptance conditions it allows to use is key. However, while there are classic and novel techniques to obtain automata that are GFM, there has not been a decision procedure for checking whether or not an automaton is GFM. We show that GFM-ness is decidable and provide an EXPTIME decision procedure as well as a PSPACE-hardness proof.

Sven Schewe, Qiyi Tang, and Tansholpan Zhanabekova. Deciding What Is Good-For-MDPs. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 35:1-35:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{schewe_et_al:LIPIcs.CONCUR.2023.35, author = {Schewe, Sven and Tang, Qiyi and Zhanabekova, Tansholpan}, title = {{Deciding What Is Good-For-MDPs}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {35:1--35:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-299-0}, ISSN = {1868-8969}, year = {2023}, volume = {279}, editor = {P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.35}, URN = {urn:nbn:de:0030-drops-190290}, doi = {10.4230/LIPIcs.CONCUR.2023.35}, annote = {Keywords: B\"{u}chi automata, Markov Decision Processes, Omega-regular objectives, Reinforcement learning} }

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**Published in:** LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

We introduce a method for translating an alternating weak Büchi automaton (AWA), which corresponds to a Linear Dynamic Logic (LDL) formula, to an unambiguous Büchi automaton (UBA). Our translations generalise constructions for Linear Temporal Logic (LTL), a less expressive specification language than LDL. In classical constructions, LTL formulas are first translated to alternating very weak automata (AVAs) - automata that have only singleton strongly connected components (SCCs); the AVAs are then handled by efficient disambiguation procedures. However, general AWAs can have larger SCCs, which complicates disambiguation. Currently, the only available disambiguation procedure has to go through an intermediate construction of nondeterministic Büchi automata (NBAs), which would incur an exponential blow-up of its own. We introduce a translation from general AWAs to UBAs with a singly exponential blow-up, which also immediately provides a singly exponential translation from LDL to UBAs. Interestingly, the complexity of our translation is smaller than the best known disambiguation algorithm for NBAs (broadly (0.53n)ⁿ vs. (0.76n)ⁿ), while the input of our construction can be exponentially more succinct.

Yong Li, Sven Schewe, and Moshe Y. Vardi. Singly Exponential Translation of Alternating Weak Büchi Automata to Unambiguous Büchi Automata. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 37:1-37:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{li_et_al:LIPIcs.CONCUR.2023.37, author = {Li, Yong and Schewe, Sven and Vardi, Moshe Y.}, title = {{Singly Exponential Translation of Alternating Weak B\"{u}chi Automata to Unambiguous B\"{u}chi Automata}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {37:1--37:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-299-0}, ISSN = {1868-8969}, year = {2023}, volume = {279}, editor = {P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.37}, URN = {urn:nbn:de:0030-drops-190313}, doi = {10.4230/LIPIcs.CONCUR.2023.37}, annote = {Keywords: B\"{u}chi automata, unambiguous automata, alternation, weak, disambiguation} }

Document

**Published in:** LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

While finite automata have minimal DFAs as a simple and natural normal form, deterministic omega-automata do not currently have anything similar. One reason for this is that a normal form for omega-regular languages has to speak about more than acceptance - for example, to have a normal form for a parity language, it should relate every infinite word to some natural color for this language. This raises the question of whether or not a concept such as a natural color of an infinite word (for a given language) exists, and, if it does, how it relates back to automata.
We define the natural color of a word purely based on an omega-regular language, and show how this natural color can be traced back from any deterministic parity automaton after two cheap and simple automaton transformations. The resulting streamlined automaton does not necessarily accept every word with its natural color, but it has a "co-run", which is like a run, but can once move to a language equivalent state, whose color is the natural color, and no co-run with a higher color exists.
The streamlined automaton defines, for every color c, a good-for-games co-Büchi automaton that recognizes the words whose natural colors with respect to the represented language are at least c. This provides a canonical representation for every ω-regular language, because good-for-games co-Büchi automata have a canonical minimal - and cheap to obtain - representation for every co-Büchi language.

Rüdiger Ehlers and Sven Schewe. Natural Colors of Infinite Words. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 36:1-36:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ehlers_et_al:LIPIcs.FSTTCS.2022.36, author = {Ehlers, R\"{u}diger and Schewe, Sven}, title = {{Natural Colors of Infinite Words}}, booktitle = {42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)}, pages = {36:1--36:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-261-7}, ISSN = {1868-8969}, year = {2022}, volume = {250}, editor = {Dawar, Anuj and Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.36}, URN = {urn:nbn:de:0030-drops-174280}, doi = {10.4230/LIPIcs.FSTTCS.2022.36}, annote = {Keywords: parity automata, automata over infinite words, \omega-regular languages} }

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**Published in:** LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

This paper discusses the hardness of finding minimal good-for-games (GFG) Büchi, Co-Büchi, and parity automata with state based acceptance. The problem appears to sit between finding small deterministic and finding small nondeterministic automata, where minimality is NP-complete and PSPACE-complete, respectively. However, recent work of Radi and Kupferman has shown that minimising Co-Büchi automata with transition based acceptance is tractable, which suggests that the complexity of minimising GFG automata might be cheaper than minimising deterministic automata.
We show for the standard state based acceptance that the minimality of a GFG automaton is NP-complete for Büchi, Co-Büchi, and parity GFG automata. The proofs are a surprisingly straight forward generalisation of the proofs from deterministic Büchi automata: they use a similar reductions, and the same hard class of languages.

Sven Schewe. Minimising Good-For-Games Automata Is NP-Complete. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 56:1-56:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{schewe:LIPIcs.FSTTCS.2020.56, author = {Schewe, Sven}, title = {{Minimising Good-For-Games Automata Is NP-Complete}}, booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)}, pages = {56:1--56:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-174-0}, ISSN = {1868-8969}, year = {2020}, volume = {182}, editor = {Saxena, Nitin and Simon, Sunil}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.56}, URN = {urn:nbn:de:0030-drops-132973}, doi = {10.4230/LIPIcs.FSTTCS.2020.56}, annote = {Keywords: Good-for-Games Automata, Automata Minimisation} }

Document

**Published in:** LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

This paper investigates the use of model-free reinforcement learning to compute the optimal value in two-player stochastic games with parity objectives. In this setting, two decision makers, player Min and player Max, compete on a finite game arena - a stochastic game graph with unknown but fixed probability distributions - to minimize and maximize, respectively, the probability of satisfying a parity objective. We give a reduction from stochastic parity games to a family of stochastic reachability games with a parameter ε, such that the value of a stochastic parity game equals the limit of the values of the corresponding simple stochastic games as the parameter ε tends to 0. Since this reduction does not require the knowledge of the probabilistic transition structure of the underlying game arena, model-free reinforcement learning algorithms, such as minimax Q-learning, can be used to approximate the value and mutual best-response strategies for both players in the underlying stochastic parity game. We also present a streamlined reduction from 1 1/2-player parity games to reachability games that avoids recourse to nondeterminism. Finally, we report on the experimental evaluations of both reductions.

Ernst Moritz Hahn, Mateo Perez, Sven Schewe, Fabio Somenzi, Ashutosh Trivedi, and Dominik Wojtczak. Model-Free Reinforcement Learning for Stochastic Parity Games. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 21:1-21:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hahn_et_al:LIPIcs.CONCUR.2020.21, author = {Hahn, Ernst Moritz and Perez, Mateo and Schewe, Sven and Somenzi, Fabio and Trivedi, Ashutosh and Wojtczak, Dominik}, title = {{Model-Free Reinforcement Learning for Stochastic Parity Games}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {21:1--21:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-160-3}, ISSN = {1868-8969}, year = {2020}, volume = {171}, editor = {Konnov, Igor and Kov\'{a}cs, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.21}, URN = {urn:nbn:de:0030-drops-128332}, doi = {10.4230/LIPIcs.CONCUR.2020.21}, annote = {Keywords: Reinforcement learning, Stochastic games, Omega-regular objectives} }

Document

Complete Volume

**Published in:** LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

LIPIcs, Volume 118, CONCUR'18, Complete Volume

Sven Schewe and Lijun Zhang. LIPIcs, Volume 118, CONCUR'18, Complete Volume. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@Proceedings{schewe_et_al:LIPIcs.CONCUR.2018, title = {{LIPIcs, Volume 118, CONCUR'18, Complete Volume}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018}, URN = {urn:nbn:de:0030-drops-97431}, doi = {10.4230/LIPIcs.CONCUR.2018}, annote = {Keywords: Theory of Computation} }

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Front Matter

**Published in:** LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Front Matter, Table of Contents, Preface, Conference Organization

Sven Schewe and Lijun Zhang. Front Matter, Table of Contents, Preface, Conference Organization. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 0:i-0:xxi, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{schewe_et_al:LIPIcs.CONCUR.2018.0, author = {Schewe, Sven and Zhang, Lijun}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {0:i--0:xxi}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.0}, URN = {urn:nbn:de:0030-drops-95386}, doi = {10.4230/LIPIcs.CONCUR.2018.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

**Published in:** LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Quantitative extensions of parity games have recently attracted significant interest. These extensions include parity games with energy and payoff conditions as well as finitary parity games and their generalization to parity games with costs. Finitary parity games enjoy a special status among these extensions, as they offer a native combination of the qualitative and quantitative aspects in infinite games: the quantitative aspect of finitary parity games is a quality measure for the qualitative aspect, as it measures the limit superior of the time it takes to answer an odd color by a larger even one. Finitary parity games have been extended to parity games with costs, where each transition is labelled with a non-negative weight that reflects the costs incurred by taking it. We lift this restriction and consider parity games with costs with arbitrary integer weights. We show that solving such games is in NP cap co-NP, the signature complexity for games of this type. We also show that the protagonist has finite-state winning strategies, and provide tight exponential bounds for the memory he needs to win the game. Naturally, the antagonist may need infinite memory to win. Finally, we present tight bounds on the quality of winning strategies for the protagonist.

Sven Schewe, Alexander Weinert, and Martin Zimmermann. Parity Games with Weights. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 36:1-36:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{schewe_et_al:LIPIcs.CSL.2018.36, author = {Schewe, Sven and Weinert, Alexander and Zimmermann, Martin}, title = {{Parity Games with Weights}}, booktitle = {27th EACSL Annual Conference on Computer Science Logic (CSL 2018)}, pages = {36:1--36:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-088-0}, ISSN = {1868-8969}, year = {2018}, volume = {119}, editor = {Ghica, Dan R. and Jung, Achim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.36}, URN = {urn:nbn:de:0030-drops-97037}, doi = {10.4230/LIPIcs.CSL.2018.36}, annote = {Keywords: Infinite Games, Quantitative Games, Parity Games} }

Document

**Published in:** LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Prefetching constitutes a valuable tool toward the goal of efficient Web surfing. As a result, estimating the amount of resources that need to be preloaded during a surfer's browsing becomes an important task. In this regard, prefetching can be modeled as a two-player combinatorial game [Fomin et al., Theoretical Computer Science 2014], where a surfer and a marker alternately play on a given graph (representing the Web graph). During its turn, the marker chooses a set of k nodes to mark (prefetch), whereas the surfer, represented as a token resting on graph nodes, moves to a neighboring node (Web resource). The surfer's objective is to reach an unmarked node before all nodes become marked and the marker wins. Intuitively, since the surfer is step-by-step traversing a subset of nodes in the Web graph, a satisfactory prefetching procedure would load in cache (without any delay) all resources lying in the neighborhood of this growing subset.
Motivated by the above, we consider the following maximization problem to which we refer to as the Maximum Rooted Connected Expansion (MRCE) problem. Given a graph G and a root node v_0, we wish to find a subset of vertices S such that S is connected, S contains v_0 and the ratio |N[S]|/|S| is maximized, where N[S] denotes the closed neighborhood of S, that is, N[S] contains all nodes in S and all nodes with at least one neighbor in S.
We prove that the problem is NP-hard even when the input graph G is restricted to be a split graph. On the positive side, we demonstrate a polynomial time approximation scheme for split graphs. Furthermore, we present a 1/6(1-1/e)-approximation algorithm for general graphs based on techniques for the Budgeted Connected Domination problem [Khuller et al., SODA 2014]. Finally, we provide a polynomial-time algorithm for the special case of interval graphs. Our algorithm returns an optimal solution for MRCE in O(n^3) time, where n is the number of nodes in G.

Ioannis Lamprou, Russell Martin, Sven Schewe, Ioannis Sigalas, and Vassilis Zissimopoulos. Maximum Rooted Connected Expansion. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 25:1-25:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{lamprou_et_al:LIPIcs.MFCS.2018.25, author = {Lamprou, Ioannis and Martin, Russell and Schewe, Sven and Sigalas, Ioannis and Zissimopoulos, Vassilis}, title = {{Maximum Rooted Connected Expansion}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {25:1--25:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.25}, URN = {urn:nbn:de:0030-drops-96076}, doi = {10.4230/LIPIcs.MFCS.2018.25}, annote = {Keywords: prefetching, domination, expansion, ratio} }

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Complete Volume

**Published in:** LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

LIPIcs, Volume 90, TIME'17, Complete Volume

Sven Schewe, Thomas Schneider, and Jef Wijsen. LIPIcs, Volume 90, TIME'17, Complete Volume. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@Proceedings{schewe_et_al:LIPIcs.TIME.2017, title = {{LIPIcs, Volume 90, TIME'17, Complete Volume}}, booktitle = {24th International Symposium on Temporal Representation and Reasoning (TIME 2017)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-052-1}, ISSN = {1868-8969}, year = {2017}, volume = {90}, editor = {Schewe, Sven and Schneider, Thomas and Wijsen, Jef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017}, URN = {urn:nbn:de:0030-drops-80233}, doi = {10.4230/LIPIcs.TIME.2017}, annote = {Keywords: Distributed Systems, Design Tools and Techniques, Software/Program Verification, Security and Protection, Models of Computation, Specifying and Verifying and Reasoning about Programs, Mathematical Logic, \lbrackNumerical Linear Algebra\rbrack Linear Systems, Graph Theory} }

Document

Front Matter

**Published in:** LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

Front Matter, Table of Contents, Preface, Organization, List of Authors

Sven Schewe, Thomas Schneider, and Jef Wijsen. Front Matter, Table of Contents, Preface, Organization, List of Authors. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 0:i-0:xiv, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{schewe_et_al:LIPIcs.TIME.2017.0, author = {Schewe, Sven and Schneider, Thomas and Wijsen, Jef}, title = {{Front Matter, Table of Contents, Preface, Organization, List of Authors}}, booktitle = {24th International Symposium on Temporal Representation and Reasoning (TIME 2017)}, pages = {0:i--0:xiv}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-052-1}, ISSN = {1868-8969}, year = {2017}, volume = {90}, editor = {Schewe, Sven and Schneider, Thomas and Wijsen, Jef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017.0}, URN = {urn:nbn:de:0030-drops-79117}, doi = {10.4230/LIPIcs.TIME.2017.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Organization, List of Authors} }

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**Published in:** LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

The bottleneck in the quantitative analysis of Markov chains and Markov decision processes against specifications given in LTL or as some form of nondeterministic Büchi automata is the inclusion of a determinisation step of the automaton under consideration.
In this paper, we show that full determinisation can be avoided: subset and breakpoint constructions suffice. We have implemented our approach - both explicit and symbolic versions - in a prototype tool. Our experiments show that our prototype can compete with mature tools like PRISM.

Ernst Moritz Hahn, Guangyuan Li, Sven Schewe, Andrea Turrini, and Lijun Zhang. Lazy Probabilistic Model Checking without Determinisation. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 354-367, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hahn_et_al:LIPIcs.CONCUR.2015.354, author = {Hahn, Ernst Moritz and Li, Guangyuan and Schewe, Sven and Turrini, Andrea and Zhang, Lijun}, title = {{Lazy Probabilistic Model Checking without Determinisation}}, booktitle = {26th International Conference on Concurrency Theory (CONCUR 2015)}, pages = {354--367}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-91-0}, ISSN = {1868-8969}, year = {2015}, volume = {42}, editor = {Aceto, Luca and de Frutos Escrig, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.354}, URN = {urn:nbn:de:0030-drops-53918}, doi = {10.4230/LIPIcs.CONCUR.2015.354}, annote = {Keywords: Markov decision processes, model checking, PLTL, determinisation} }

Document

**Published in:** LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

While model checking PCTL for Markov chains is decidable in polynomial-time, the decidability of PCTL satisfiability is a long standing open problem. While general satisfiability is an intriguing challenge from a purely theoretical point of view, we argue that general solutions would not be of interest to practitioners: such solutions could be too big to be implementable or even infinite. Inspired by bounded synthesis techniques, we turn to the more applied
problem of seeking models of a bounded size: we restrict our search to
implementable - and therefore reasonably simple - models. We propose a
procedure to decide whether or not a given PCTL formula has an implementable model by reducing it to an SMT problem. We have implemented our techniques and found that they can be applied to the practical problem of sanity checking - a procedure that allows a system designer to check whether their formula has an unexpectedly small model.

Nathalie Bertrand, John Fearnley, and Sven Schewe. Bounded Satisfiability for PCTL. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 92-106, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)

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@InProceedings{bertrand_et_al:LIPIcs.CSL.2012.92, author = {Bertrand, Nathalie and Fearnley, John and Schewe, Sven}, title = {{Bounded Satisfiability for PCTL}}, booktitle = {Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL}, pages = {92--106}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-42-2}, ISSN = {1868-8969}, year = {2012}, volume = {16}, editor = {C\'{e}gielski, Patrick and Durand, Arnaud}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.92}, URN = {urn:nbn:de:0030-drops-36667}, doi = {10.4230/LIPIcs.CSL.2012.92}, annote = {Keywords: Satisfiability, Temporal Logic, Probabilistic Logic} }

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**Published in:** LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

We study the time-bounded reachability problem for continuous time Markov decision processes (CTMDPs) and games (CTMGs). Existing techniques for this problem use discretization techniques to break time into discrete intervals, and optimal control is approximated for each interval separately. Current techniques provide an accuracy of O(\epsilon^2) on each interval, which leads to an infeasibly large number of intervals. We propose a sequence of approximations that achieve accuracies of O(\epsilon^3), O(\epsilon^4), and O(\epsilon^5), that allow us to drastically reduce the number of intervals that are considered. For CTMDPs, the resulting algorithms are comparable to the heuristic approach given by Buckholz and Schulz, while also being theoretically justified. All of our results generalise to CTMGs, where our results yield the first practically implementable algorithms for this problem. We also provide positional strategies for both players that achieve similar error bounds.

John Fearnley, Markus Rabe, Sven Schewe, and Lijun Zhang. Efficient Approximation of Optimal Control for Continuous-Time Markov Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 399-410, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)

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@InProceedings{fearnley_et_al:LIPIcs.FSTTCS.2011.399, author = {Fearnley, John and Rabe, Markus and Schewe, Sven and Zhang, Lijun}, title = {{Efficient Approximation of Optimal Control for Continuous-Time Markov Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {399--410}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-34-7}, ISSN = {1868-8969}, year = {2011}, volume = {13}, editor = {Chakraborty, Supratik and Kumar, Amit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.399}, URN = {urn:nbn:de:0030-drops-33547}, doi = {10.4230/LIPIcs.FSTTCS.2011.399}, annote = {Keywords: Continuous time Markov decision processes and games, discretisation} }

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**Published in:** LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

In this paper we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic \buchi, \cobuchi, and parity automata play a similar role in the recognition of $\omega$-regular languages. While it is well known that the minimisation of deterministic finite and weak automata is cheap, the complexity of minimising deterministic \buchi\ and parity automata has remained an open challenge. We establish the NP-completeness of these problems. A second contribution of this paper is the introduction of almost equivalence, an equivalence class for strictly between language equivalence for deterministic \buchi\ or \cobuchi\ automata and language equivalence for deterministic finite automata. Two finite automata are almost equivalent if they, when used as a monitor, provide a different answer only a bounded number of times in any run, and we call the minimal such automaton relatively minimal. Minimisation of DFAs, hyper-minimisation, relative minimisation, and the minimisation of deterministic \buchi\ (or \cobuchi) automata are operations of increasing reduction power, as the respective equivalence relations on automata become coarser from left to right. Besides being a natural equivalence relation for finite automata, almost equivalence is language preserving for weak automata, and can therefore also be viewed as a generalisation of language equivalence for weak automata to a more general class of automata. From the perspective of \buchi\ and \cobuchi\ automata, we gain a cheap algorithm for state-space reduction that also turns out to be beneficial for further heuristic or exhaustive state-space reductions put on top of it.

Sven Schewe. Beyond Hyper-Minimisation---Minimising DBAs and DPAs is NP-Complete. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 400-411, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)

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@InProceedings{schewe:LIPIcs.FSTTCS.2010.400, author = {Schewe, Sven}, title = {{Beyond Hyper-Minimisation---Minimising DBAs and DPAs is NP-Complete}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {400--411}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-23-1}, ISSN = {1868-8969}, year = {2010}, volume = {8}, editor = {Lodaya, Kamal and Mahajan, Meena}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.400}, URN = {urn:nbn:de:0030-drops-28816}, doi = {10.4230/LIPIcs.FSTTCS.2010.400}, annote = {Keywords: Automata Theory, Complexity, B\"{u}chi Automata, Parity Automata} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 9501, Software Synthesis (2010)

While the components of distributed hardware systems can reasonably be assumed to be synchronised, this is not the case for the components of distributed software systems. This has a strong impact on the class of synthesis problems for which decision procedures exist: While there is a rich family of distributed systems, including pipelines, chains, and rings, for which the realisability and synthesis problem is decidable if the system components are composed synchronously, it is well known that the asynchronous synthesis problem is only decidable for monolithic systems. From a theoretical point of view, this renders distributed software synthesis undecidable, and one is tempted to conclude that synthesis of asynchronous systems, and hence of software, is much harder than the synthesis of synchronous systems. Taking a more practical approach, however, reveals that bounded synthesis, one of the most promising synthesis techniques, can easily be extended to asynchronous systems. This merits the hope that the promising results from bounded synthesis will carry over to asynchronous systems as well.

Sven Schewe. Software Synthesis is Hard – and Simple. In Software Synthesis. Dagstuhl Seminar Proceedings, Volume 9501, pp. 1-4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)

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@InProceedings{schewe:DagSemProc.09501.2, author = {Schewe, Sven}, title = {{Software Synthesis is Hard – and Simple}}, booktitle = {Software Synthesis}, pages = {1--4}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2010}, volume = {9501}, editor = {Ratislav Bodik and Orna Kupferman and Douglas R. Smith and Eran Yahav}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09501.2}, URN = {urn:nbn:de:0030-drops-26702}, doi = {10.4230/DagSemProc.09501.2}, annote = {Keywords: Synthesis, Temporal Logics} }

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**Published in:** LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

The precise complexity of complementing B\"uchi\ automata is an intriguing and long standing problem. While optimal complementation techniques for finite automata are simple -- it suffices to determinize them using a simple subset construction and to dualize the acceptance condition of the resulting automaton -- B\"uchi\ complementation is more involved. Indeed, the construction of an EXPTIME complementation procedure took a quarter of a century from the introduction of B\"uchi\ automata in the early $60$s, and stepwise narrowing the gap between the upper and lower bound to a simple exponent (of $(6e)^n$ for B\"uchi\ automata with $n$ states) took four decades. While the distance between the known upper ($O\big((0.96\,n)^n\big)$) and lower ($\Omega\big((0.76\,n)^n\big)$) bound on the required number of states has meanwhile been significantly reduced, an exponential factor remains between them. Also, the upper bound on the size of the complement automaton is not linear in the bound of its state space. These gaps are unsatisfactory from a theoretical point of view, but also because B\"uchi\ complementation is a useful tool in formal verification, in particular for the language containment problem. This paper proposes a B\"uchi\ complementation algorithm whose complexity meets, modulo a quadratic ($O(n^2)$) factor, the known lower bound for B\"uchi\ complementation. It thus improves over previous constructions by an exponential factor and concludes the quest for optimal B\"uchi\ complementation algorithms.

Sven Schewe. Büchi Complementation Made Tight. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 661-672, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)

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@InProceedings{schewe:LIPIcs.STACS.2009.1854, author = {Schewe, Sven}, title = {{B\"{u}chi Complementation Made Tight}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {661--672}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-09-5}, ISSN = {1868-8969}, year = {2009}, volume = {3}, editor = {Albers, Susanne and Marion, Jean-Yves}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1854}, URN = {urn:nbn:de:0030-drops-18543}, doi = {10.4230/LIPIcs.STACS.2009.1854}, annote = {Keywords: Automata and formal languages, Buchi complementation, Automata theory, Nondeterministic Buchi automata} }

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