30 Search Results for "Kiefer, Stefan"

Document
DOI: 10.4230/LIPIcs.CONCUR.2022.9
On the Sequential Probability Ratio Test in Hidden Markov Models

Authors: Oscar Darwin and Stefan Kiefer

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
We consider the Sequential Probability Ratio Test applied to Hidden Markov Models. Given two Hidden Markov Models and a sequence of observations generated by one of them, the Sequential Probability Ratio Test attempts to decide which model produced the sequence. We show relationships between the execution time of such an algorithm and Lyapunov exponents of random matrix systems. Further, we give complexity results about the execution time taken by the Sequential Probability Ratio Test.
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Oscar Darwin and Stefan Kiefer. On the Sequential Probability Ratio Test in Hidden Markov Models. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{darwin_et_al:LIPIcs.CONCUR.2022.9,
  author =	{Darwin, Oscar and Kiefer, Stefan},
  title =	{{On the Sequential Probability Ratio Test in Hidden Markov Models}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.9},
  URN =		{urn:nbn:de:0030-drops-170728},
  doi =		{10.4230/LIPIcs.CONCUR.2022.9},
  annote =	{Keywords: Markov chains, hidden Markov models, probabilistic systems, verification}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.32
Strategies for MDP Bisimilarity Equivalence and Inequivalence

Authors: Stefan Kiefer and Qiyi Tang

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
A labelled Markov decision process (MDP) is a labelled Markov chain with nondeterminism; i.e., together with a strategy a labelled MDP induces a labelled Markov chain. Motivated by applications to the verification of probabilistic noninterference in security, we study problems whether there exist strategies such that the labelled MDPs become bisimilarity equivalent/inequivalent. We show that the equivalence problem is decidable; in fact, it is EXPTIME-complete and becomes NP-complete if one of the MDPs is a Markov chain. Concerning the inequivalence problem, we show that (1) it is decidable in polynomial time; (2) if there are strategies for inequivalence then there are memoryless strategies for inequivalence; (3) such memoryless strategies can be computed in polynomial time.
Cite as

Stefan Kiefer and Qiyi Tang. Strategies for MDP Bisimilarity Equivalence and Inequivalence. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kiefer_et_al:LIPIcs.CONCUR.2022.32,
  author =	{Kiefer, Stefan and Tang, Qiyi},
  title =	{{Strategies for MDP Bisimilarity Equivalence and Inequivalence}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.32},
  URN =		{urn:nbn:de:0030-drops-170955},
  doi =		{10.4230/LIPIcs.CONCUR.2022.32},
  annote =	{Keywords: Markov decision processes, Markov chains}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.126
Lower Bounds for Unambiguous Automata via Communication Complexity

Authors: Mika Göös, Stefan Kiefer, and Weiqiang Yuan

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. 1) Complement: There is a language L recognised by an n-state UFA such that the complement language ̅L requires NFAs with n^Ω̃(log n) states. This improves on a lower bound by Raskin. 2) Union: There are languages L₁, L₂ recognised by n-state UFAs such that the union L₁∪L₂ requires UFAs with n^Ω̃(log n) states. 3) Separation: There is a language L such that both L and ̅L are recognised by n-state NFAs but such that L requires UFAs with n^Ω(log n) states. This refutes a conjecture by Colcombet.
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Mika Göös, Stefan Kiefer, and Weiqiang Yuan. Lower Bounds for Unambiguous Automata via Communication Complexity. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 126:1-126:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goos_et_al:LIPIcs.ICALP.2022.126,
  author =	{G\"{o}\"{o}s, Mika and Kiefer, Stefan and Yuan, Weiqiang},
  title =	{{Lower Bounds for Unambiguous Automata via Communication Complexity}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{126:1--126:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.126},
  URN =		{urn:nbn:de:0030-drops-164679},
  doi =		{10.4230/LIPIcs.ICALP.2022.126},
  annote =	{Keywords: Unambiguous automata, communication complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.48
Approximate Bisimulation Minimisation

Authors: Stefan Kiefer and Qiyi Tang

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an approximate bisimulation quotient, obtained by lumping together states that are exactly bisimilar in a slightly perturbed system. We present experiments that show that our algorithms are able to recover the structure of the bisimulation quotient of the unperturbed system.
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Stefan Kiefer and Qiyi Tang. Approximate Bisimulation Minimisation. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kiefer_et_al:LIPIcs.FSTTCS.2021.48,
  author =	{Kiefer, Stefan and Tang, Qiyi},
  title =	{{Approximate Bisimulation Minimisation}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.48},
  URN =		{urn:nbn:de:0030-drops-155599},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.48},
  annote =	{Keywords: Markov chains, Behavioural metrics, Bisimulation}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.5
Enforcing ω-Regular Properties in Markov Chains by Restarting

Authors: Javier Esparza, Stefan Kiefer, Jan Křetínský, and Maximilian Weininger

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
Restarts are used in many computer systems to improve performance. Examples include reloading a webpage, reissuing a request, or restarting a randomized search. The design of restart strategies has been extensively studied by the performance evaluation community. In this paper, we address the problem of designing universal restart strategies, valid for arbitrary finite-state Markov chains, that enforce a given ω-regular property while not knowing the chain. A strategy enforces a property φ if, with probability 1, the number of restarts is finite, and the run of the Markov chain after the last restart satisfies φ. We design a simple "cautious" strategy that solves the problem, and a more sophisticated "bold" strategy with an almost optimal number of restarts.
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Javier Esparza, Stefan Kiefer, Jan Křetínský, and Maximilian Weininger. Enforcing ω-Regular Properties in Markov Chains by Restarting. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{esparza_et_al:LIPIcs.CONCUR.2021.5,
  author =	{Esparza, Javier and Kiefer, Stefan and K\v{r}et{\'\i}nsk\'{y}, Jan and Weininger, Maximilian},
  title =	{{Enforcing \omega-Regular Properties in Markov Chains by Restarting}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.5},
  URN =		{urn:nbn:de:0030-drops-143824},
  doi =		{10.4230/LIPIcs.CONCUR.2021.5},
  annote =	{Keywords: Markov chains, omega-regular properties, runtime enforcement}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.6
Linear-Time Model Checking Branching Processes

Authors: Stefan Kiefer, Pavel Semukhin, and Cas Widdershoven

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
(Multi-type) branching processes are a natural and well-studied model for generating random infinite trees. Branching processes feature both nondeterministic and probabilistic branching, generalizing both transition systems and Markov chains (but not generally Markov decision processes). We study the complexity of model checking branching processes against linear-time omega-regular specifications: is it the case almost surely that every branch of a tree randomly generated by the branching process satisfies the omega-regular specification? The main result is that for LTL specifications this problem is in PSPACE, subsuming classical results for transition systems and Markov chains, respectively. The underlying general model-checking algorithm is based on the automata-theoretic approach, using unambiguous Büchi automata.
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Stefan Kiefer, Pavel Semukhin, and Cas Widdershoven. Linear-Time Model Checking Branching Processes. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kiefer_et_al:LIPIcs.CONCUR.2021.6,
  author =	{Kiefer, Stefan and Semukhin, Pavel and Widdershoven, Cas},
  title =	{{Linear-Time Model Checking Branching Processes}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.6},
  URN =		{urn:nbn:de:0030-drops-143834},
  doi =		{10.4230/LIPIcs.CONCUR.2021.6},
  annote =	{Keywords: model checking, Markov chains, branching processes, automata, computational complexity}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.11
Transience in Countable MDPs

Authors: Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, and Patrick Totzke

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
The Transience objective is not to visit any state infinitely often. While this is not possible in any finite Markov Decision Process (MDP), it can be satisfied in countably infinite ones, e.g., if the transition graph is acyclic. We prove the following fundamental properties of Transience in countably infinite MDPs. 1) There exist uniformly ε-optimal MD strategies (memoryless deterministic) for Transience, even in infinitely branching MDPs. 2) Optimal strategies for Transience need not exist, even if the MDP is finitely branching. However, if an optimal strategy exists then there is also an optimal MD strategy. 3) If an MDP is universally transient (i.e., almost surely transient under all strategies) then many other objectives have a lower strategy complexity than in general MDPs. E.g., ε-optimal strategies for Safety and co-Büchi and optimal strategies for {0,1,2}-Parity (where they exist) can be chosen MD, even if the MDP is infinitely branching.
Cite as

Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, and Patrick Totzke. Transience in Countable MDPs. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kiefer_et_al:LIPIcs.CONCUR.2021.11,
  author =	{Kiefer, Stefan and Mayr, Richard and Shirmohammadi, Mahsa and Totzke, Patrick},
  title =	{{Transience in Countable MDPs}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.11},
  URN =		{urn:nbn:de:0030-drops-143881},
  doi =		{10.4230/LIPIcs.CONCUR.2021.11},
  annote =	{Keywords: Markov decision processes, Parity, Transience}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.43
Equivalence of Hidden Markov Models with Continuous Observations

Authors: Oscar Darwin and Stefan Kiefer

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

Abstract
We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support of the uniform distribution depends on the state of the Hidden Markov Model. Such models generalise the more common version where each observation is drawn from a finite alphabet. We prove that one can determine in polynomial time whether two Hidden Markov Models with continuous observations are equivalent.
Cite as

Oscar Darwin and Stefan Kiefer. Equivalence of Hidden Markov Models with Continuous Observations. 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. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{darwin_et_al:LIPIcs.FSTTCS.2020.43,
  author =	{Darwin, Oscar and Kiefer, Stefan},
  title =	{{Equivalence of Hidden Markov Models with Continuous Observations}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{43:1--43:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.43},
  URN =		{urn:nbn:de:0030-drops-132845},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.43},
  annote =	{Keywords: Markov chains, equivalence, probabilistic systems, verification}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.49
Comparing Labelled Markov Decision Processes

Authors: Stefan Kiefer and Qiyi Tang

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

Abstract
A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of equivalence checking for the verification of anonymity, we study the algorithmic comparison of two labelled MDPs, in particular, whether there exist strategies such that the MDPs become equivalent/inequivalent, both in terms of trace equivalence and in terms of probabilistic bisimilarity. We provide the first polynomial-time algorithms for computing memoryless strategies to make the two labelled MDPs inequivalent if such strategies exist. We also study the computational complexity of qualitative problems about making the total variation distance and the probabilistic bisimilarity distance less than one or equal to one.
Cite as

Stefan Kiefer and Qiyi Tang. Comparing Labelled Markov Decision Processes. 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. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kiefer_et_al:LIPIcs.FSTTCS.2020.49,
  author =	{Kiefer, Stefan and Tang, Qiyi},
  title =	{{Comparing Labelled Markov Decision Processes}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{49:1--49:16},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.49},
  URN =		{urn:nbn:de:0030-drops-132903},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.49},
  annote =	{Keywords: Markov decision processes, Markov chains, Behavioural metrics}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.39
Strategy Complexity of Parity Objectives in Countable MDPs

Authors: Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, and Patrick Totzke

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

Abstract
We study countably infinite MDPs with parity objectives. Unlike in finite MDPs, optimal strategies need not exist, and may require infinite memory if they do. We provide a complete picture of the exact strategy complexity of ε-optimal strategies (and optimal strategies, where they exist) for all subclasses of parity objectives in the Mostowski hierarchy. Either MD-strategies, Markov strategies, or 1-bit Markov strategies are necessary and sufficient, depending on the number of colors, the branching degree of the MDP, and whether one considers ε-optimal or optimal strategies. In particular, 1-bit Markov strategies are necessary and sufficient for ε-optimal (resp. optimal) strategies for general parity objectives.
Cite as

Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, and Patrick Totzke. Strategy Complexity of Parity Objectives in Countable MDPs. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kiefer_et_al:LIPIcs.CONCUR.2020.39,
  author =	{Kiefer, Stefan and Mayr, Richard and Shirmohammadi, Mahsa and Totzke, Patrick},
  title =	{{Strategy Complexity of Parity Objectives in Countable MDPs}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{39:1--39:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.39},
  URN =		{urn:nbn:de:0030-drops-128513},
  doi =		{10.4230/LIPIcs.CONCUR.2020.39},
  annote =	{Keywords: Markov decision processes, Parity objectives, Levy’s zero-one law}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.41
The Big-O Problem for Labelled Markov Chains and Weighted Automata

Authors: Dmitry Chistikov, Stefan Kiefer, Andrzej S. Murawski, and David Purser

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

Abstract
Given two weighted automata, we consider the problem of whether one is big-O of the other, i.e., if the weight of every finite word in the first is not greater than some constant multiple of the weight in the second. We show that the problem is undecidable, even for the instantiation of weighted automata as labelled Markov chains. Moreover, even when it is known that one weighted automaton is big-O of another, the problem of finding or approximating the associated constant is also undecidable. Our positive results show that the big-O problem is polynomial-time solvable for unambiguous automata, coNP-complete for unlabelled weighted automata (i.e., when the alphabet is a single character) and decidable, subject to Schanuel’s conjecture, when the language is bounded (i.e., a subset of w_1^* … w_m^* for some finite words w_1,… ,w_m). On labelled Markov chains, the problem can be restated as a ratio total variation distance, which, instead of finding the maximum difference between the probabilities of any two events, finds the maximum ratio between the probabilities of any two events. The problem is related to ε-differential privacy, for which the optimal constant of the big-O notation is exactly exp(ε).
Cite as

Dmitry Chistikov, Stefan Kiefer, Andrzej S. Murawski, and David Purser. The Big-O Problem for Labelled Markov Chains and Weighted Automata. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chistikov_et_al:LIPIcs.CONCUR.2020.41,
  author =	{Chistikov, Dmitry and Kiefer, Stefan and Murawski, Andrzej S. and Purser, David},
  title =	{{The Big-O Problem for Labelled Markov Chains and Weighted Automata}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{41:1--41:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.41},
  URN =		{urn:nbn:de:0030-drops-128534},
  doi =		{10.4230/LIPIcs.CONCUR.2020.41},
  annote =	{Keywords: weighted automata, labelled Markov chains, probabilistic systems}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.48
On Affine Reachability Problems

Authors: Stefan Jaax and Stefan Kiefer

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et al. that required polynomial updates. Building on recent results on two-dimensional integer matrices, we prove NP-completeness of the mortality problem for 2-dimensional integer matrices with determinants +1 and 0. Motivated by tight connections with 1-dimensional affine reachability problems without control states, we also study the complexity of a number of reachability problems in finitely generated semigroups of 2-dimensional upper-triangular integer matrices.
Cite as

Stefan Jaax and Stefan Kiefer. On Affine Reachability Problems. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 48:1-48:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jaax_et_al:LIPIcs.MFCS.2020.48,
  author =	{Jaax, Stefan and Kiefer, Stefan},
  title =	{{On Affine Reachability Problems}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{48:1--48:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.48},
  URN =		{urn:nbn:de:0030-drops-127148},
  doi =		{10.4230/LIPIcs.MFCS.2020.48},
  annote =	{Keywords: Counter Machines, Matrix Semigroups, Reachability}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2020.3
How to Play in Infinite MDPs (Invited Talk)

Authors: Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke, and Dominik Wojtczak

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Markov decision processes (MDPs) are a standard model for dynamic systems that exhibit both stochastic and nondeterministic behavior. For MDPs with finite state space it is known that for a wide range of objectives there exist optimal strategies that are memoryless and deterministic. In contrast, if the state space is infinite, optimal strategies may not exist, and optimal or ε-optimal strategies may require (possibly infinite) memory. In this paper we consider qualitative objectives: reachability, safety, (co-)Büchi, and other parity objectives. We aim at giving an introduction to a collection of techniques that allow for the construction of strategies with little or no memory in countably infinite MDPs.
Cite as

Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke, and Dominik Wojtczak. How to Play in Infinite MDPs (Invited Talk). In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kiefer_et_al:LIPIcs.ICALP.2020.3,
  author =	{Kiefer, Stefan and Mayr, Richard and Shirmohammadi, Mahsa and Totzke, Patrick and Wojtczak, Dominik},
  title =	{{How to Play in Infinite MDPs}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.3},
  URN =		{urn:nbn:de:0030-drops-124103},
  doi =		{10.4230/LIPIcs.ICALP.2020.3},
  annote =	{Keywords: Markov decision processes}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.115
On the Size of Finite Rational Matrix Semigroups

Authors: Georgina Bumpus, Christoph Haase, Stefan Kiefer, Paul-Ioan Stoienescu, and Jonathan Tanner

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Let n be a positive integer and M a set of rational n × n-matrices such that M generates a finite multiplicative semigroup. We show that any matrix in the semigroup is a product of matrices in M whose length is at most 2^{n (2 n + 3)} g(n)^{n+1} ∈ 2^{O(n² log n)}, where g(n) is the maximum order of finite groups over rational n × n-matrices. This result implies algorithms with an elementary running time for deciding finiteness of weighted automata over the rationals and for deciding reachability in affine integer vector addition systems with states with the finite monoid property.
Cite as

Georgina Bumpus, Christoph Haase, Stefan Kiefer, Paul-Ioan Stoienescu, and Jonathan Tanner. On the Size of Finite Rational Matrix Semigroups. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 115:1-115:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bumpus_et_al:LIPIcs.ICALP.2020.115,
  author =	{Bumpus, Georgina and Haase, Christoph and Kiefer, Stefan and Stoienescu, Paul-Ioan and Tanner, Jonathan},
  title =	{{On the Size of Finite Rational Matrix Semigroups}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{115:1--115:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.115},
  URN =		{urn:nbn:de:0030-drops-125226},
  doi =		{10.4230/LIPIcs.ICALP.2020.115},
  annote =	{Keywords: Matrix semigroups, Burnside problem, weighted automata, vector addition systems}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.123
The Strahler Number of a Parity Game

Authors: Laure Daviaud, Marcin Jurdziński, and K. S. Thejaswini

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. It is proved that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices n and linear in (d/(2k))^k, where d is the number of priorities and k is the Strahler number. This complexity is quasi-polynomial because the Strahler number is at most logarithmic in the number of vertices. The proof is based on a new construction of small Strahler-universal trees. It is shown that the Strahler number of a parity game is a robust, and hence arguably natural, parameter: it coincides with its alternative version based on trees of progress measures and - remarkably - with the register number defined by Lehtinen (2018). It follows that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices and linear in (d/(2k))^k, where k is the register number. This significantly improves the running times and space achieved for parity games of bounded register number by Lehtinen (2018) and by Parys (2020). The running time of the algorithm based on small Strahler-universal trees yields a novel trade-off k ⋅ lg(d/k) = O(log n) between the two natural parameters that measure the structural complexity of a parity game, which allows solving parity games in polynomial time. This includes as special cases the asymptotic settings of those parameters covered by the results of Calude, Jain Khoussainov, Li, and Stephan (2017), of Jurdziński and Lazić (2017), and of Lehtinen (2018), and it significantly extends the range of such settings, for example to d = 2^O(√{lg n}) and k = O(√{lg n}).
Cite as

Laure Daviaud, Marcin Jurdziński, and K. S. Thejaswini. The Strahler Number of a Parity Game. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 123:1-123:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{daviaud_et_al:LIPIcs.ICALP.2020.123,
  author =	{Daviaud, Laure and Jurdzi\'{n}ski, Marcin and Thejaswini, K. S.},
  title =	{{The Strahler Number of a Parity Game}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{123:1--123:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.123},
  URN =		{urn:nbn:de:0030-drops-125304},
  doi =		{10.4230/LIPIcs.ICALP.2020.123},
  annote =	{Keywords: parity game, attractor decomposition, progress measure, universal tree, Strahler number}
}
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