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Documents authored by Ajdarów, Michal

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.138
Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs

Authors: Michal Ajdarów, James C. A. Main, Petr Novotný, and Mickael Randour

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Markov decision processes (MDPs) are a canonical model to reason about decision making within a stochastic environment. We study a fundamental class of infinite MDPs: one-counter MDPs (OC-MDPs). They extend finite MDPs via an associated counter taking natural values, thus inducing an infinite MDP over the set of configurations (current state and counter value). We consider two characteristic objectives: reaching a target state (state-reachability), and reaching a target state with counter value zero (selective termination). The synthesis problem for the latter is not known to be decidable and connected to major open problems in number theory. Furthermore, even seemingly simple strategies (e.g., memoryless ones) in OC-MDPs might be impossible to build in practice (due to the underlying infinite configuration space): we need finite, and preferably small, representations. To overcome these obstacles, we introduce two natural classes of concisely represented strategies based on a (possibly infinite) partition of counter values in intervals. For both classes, and both objectives, we study the verification problem (does a given strategy ensure a high enough probability for the objective?), and two synthesis problems (does there exist such a strategy?): one where the interval partition is fixed as input, and one where it is only parameterized. We develop a generic approach based on a compression of the induced infinite MDP that yields decidability in all cases, with all complexities within PSPACE.
Cite as

Michal Ajdarów, James C. A. Main, Petr Novotný, and Mickael Randour. Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 138:1-138:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ajdarow_et_al:LIPIcs.ICALP.2025.138,
  author =	{Ajdar\'{o}w, Michal and Main, James C. A. and Novotn\'{y}, Petr and Randour, Mickael},
  title =	{{Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{138:1--138:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.138},
  URN =		{urn:nbn:de:0030-drops-235157},
  doi =		{10.4230/LIPIcs.ICALP.2025.138},
  annote =	{Keywords: one-counter Markov decision processes, randomised strategies, termination, reachability}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.12
Asymptotic Complexity Estimates for Probabilistic Programs and Their VASS Abstractions

Authors: Michal Ajdarów and Antonín Kučera

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

Abstract
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that this approach is not sufficiently robust, especially in situations when the expectations are infinite. We propose new estimates for the asymptotic analysis of probabilistic programs with non-deterministic choice that overcome this deficiency. Furthermore, we show how to efficiently compute/analyze these estimates for selected classes of programs represented as Markov decision processes over vector addition systems with states.
Cite as

Michal Ajdarów and Antonín Kučera. Asymptotic Complexity Estimates for Probabilistic Programs and Their VASS Abstractions. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ajdarow_et_al:LIPIcs.CONCUR.2023.12,
  author =	{Ajdar\'{o}w, Michal and Ku\v{c}era, Anton{\'\i}n},
  title =	{{Asymptotic Complexity Estimates for Probabilistic Programs and Their VASS Abstractions}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{12:1--12:16},
  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.2023.12},
  URN =		{urn:nbn:de:0030-drops-190065},
  doi =		{10.4230/LIPIcs.CONCUR.2023.12},
  annote =	{Keywords: Probabilistic programs, asymptotic complexity, vector addition systems}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.30
Deciding Polynomial Termination Complexity for VASS Programs

Authors: Michal Ajdarów and Antonín Kučera

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

Abstract
We show that for every fixed degree k ≥ 3, the problem whether the termination/counter complexity of a given demonic VASS is O(n^k), Ω(n^k), and Θ(n^k) is coNP-complete, NP-complete, and DP-complete, respectively. We also classify the complexity of these problems for k ≤ 2. This shows that the polynomial-time algorithm designed for strongly connected demonic VASS in previous works cannot be extended to the general case. Then, we prove that the same problems for VASS games are PSPACE-complete. Again, we classify the complexity also for k ≤ 2. Tractable subclasses of demonic VASS and VASS games are obtained by bounding certain structural parameters, which opens the way to applications in program analysis despite the presented lower complexity bounds.
Cite as

Michal Ajdarów and Antonín Kučera. Deciding Polynomial Termination Complexity for VASS Programs. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ajdarow_et_al:LIPIcs.CONCUR.2021.30,
  author =	{Ajdar\'{o}w, Michal and Ku\v{c}era, Anton{\'\i}n},
  title =	{{Deciding Polynomial Termination Complexity for VASS Programs}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{30:1--30:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.30},
  URN =		{urn:nbn:de:0030-drops-144076},
  doi =		{10.4230/LIPIcs.CONCUR.2021.30},
  annote =	{Keywords: Termination complexity, vector addition systems}
}
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