Found 3 Possible Name Variants:

Document

**Published in:** LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of mean-payoff does not reflect possible fluctuations from the mean-payoff along a run, we propose definitions and algorithms for capturing the stability of the system, and give algorithms for deciding if a given mean payoff and stability objective can be ensured in the system.

Tomas Brazdil, Vojtech Forejt, Antonin Kucera, and Petr Novotny. Stability in Graphs and Games. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{brazdil_et_al:LIPIcs.CONCUR.2016.10, author = {Brazdil, Tomas and Forejt, Vojtech and Kucera, Antonin and Novotny, Petr}, title = {{Stability in Graphs and Games}}, booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)}, pages = {10:1--10:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-017-0}, ISSN = {1868-8969}, year = {2016}, volume = {59}, editor = {Desharnais, Jos\'{e}e and Jagadeesan, Radha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.10}, URN = {urn:nbn:de:0030-drops-61784}, doi = {10.4230/LIPIcs.CONCUR.2016.10}, annote = {Keywords: Games, Stability, Mean-Payoff, Window Objectives} }

Document

**Published in:** LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Solvency games, introduced by Berger et al., provide an abstract framework for modelling decisions of a risk-averse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where, in addition to stochastic environment and fixed increments and decrements to the investor's wealth, we introduce
interest, which is earned or paid on the current level of savings or debt, respectively.
We study problems related to the minimum initial wealth sufficient to avoid bankruptcy (i.e. steady decrease of the wealth) with probability at least p. We present an exponential time algorithm which approximates this minimum initial wealth, and show that a polynomial time approximation is not possible unless P=NP.
For the qualitative case, i.e. p=1, we show that the problem whether a given number is larger than or equal to the minimum initial wealth belongs to NP \cap coNP, and show that a polynomial time algorithm would yield a polynomial time algorithm for mean-payoff games, existence of which is a longstanding open problem. We also identify some classes of solvency MDPs for which this problem is in P. In all above cases the algorithms also give corresponding bankruptcy avoiding strategies.

Tomás Brázdil, Taolue Chen, Vojtech Forejt, Petr Novotný, and Aistis Simaitis. Solvency Markov Decision Processes with Interest. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 487-499, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2013.487, author = {Br\'{a}zdil, Tom\'{a}s and Chen, Taolue and Forejt, Vojtech and Novotn\'{y}, Petr and Simaitis, Aistis}, title = {{Solvency Markov Decision Processes with Interest}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}, pages = {487--499}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-64-4}, ISSN = {1868-8969}, year = {2013}, volume = {24}, editor = {Seth, Anil and Vishnoi, Nisheeth K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.487}, URN = {urn:nbn:de:0030-drops-43959}, doi = {10.4230/LIPIcs.FSTTCS.2013.487}, annote = {Keywords: Markov decision processes, algorithms, complexity, market models.} }

Document

**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation. For this we embed the IMC into a game that is played with the environment. We devise algorithms that enable us to derive bounds on reachability probabilities that are assured to hold in any composition context.

Tomas Brazdil, Holger Hermanns, Jan Krcal, Jan Kretinsky, and Vojtech Rehak. Verification of Open Interactive Markov Chains. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 474-485, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2012.474, author = {Brazdil, Tomas and Hermanns, Holger and Krcal, Jan and Kretinsky, Jan and Rehak, Vojtech}, title = {{Verification of Open Interactive Markov Chains}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {474--485}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.474}, URN = {urn:nbn:de:0030-drops-38826}, doi = {10.4230/LIPIcs.FSTTCS.2012.474}, annote = {Keywords: IMC, compositional verification, synthesis, time bounded reachability, discretization} }

Document

**Published in:** LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for server j. We propose to extend Jackson networks by "branching" and by "control" features. Both extensions are new and substantially expand the modelling power of Jackson networks. On the other hand, the extensions raise computational questions, particularly concerning the stability of the networks, i.e, the ergodicity of the underlying Markov chain. We show for our extended model that it is decidable in polynomial time if there exists a controller that achieves stability. Moreover, if such a controller exists, one can efficiently compute a static randomized controller which stabilizes the network in a very strong sense; in particular, all moments of the queue sizes are finite.

Tomáš Brázdil and Stefan Kiefer. Stabilization of Branching Queueing Networks. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 507-518, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{brazdil_et_al:LIPIcs.STACS.2012.507, author = {Br\'{a}zdil, Tom\'{a}\v{s} and Kiefer, Stefan}, title = {{Stabilization of Branching Queueing Networks}}, booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)}, pages = {507--518}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-35-4}, ISSN = {1868-8969}, year = {2012}, volume = {14}, editor = {D\"{u}rr, Christoph and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.507}, URN = {urn:nbn:de:0030-drops-34133}, doi = {10.4230/LIPIcs.STACS.2012.507}, annote = {Keywords: continuous-time Markov decision processes, infinite-state systems, performance analysis} }

Document

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

We study the computational complexity of basic decision problems for one-counter simple stochastic games (OC-SSGs), under various objectives. OC-SSGs are 2-player turn-based stochastic games played on the transition graph of classic one-counter automata. We study primarily the termination objective, where the goal of one player is to maximize the probability of reaching counter value 0, while the other player wishes to avoid this. Partly motivated by the goal of understanding termination objectives, we also study certain ``limit'' and ``long run average'' reward objectives that are closely related to some well-studied objectives for stochastic games with rewards. Examples of problems we address include: does player 1 have a
strategy to ensure that the counter eventually hits 0, i.e., terminates, almost surely, regardless of what player 2 does? Or that the $liminf$ (or $limsup$) counter value equals $infty$ with a desired
probability? Or that the long run average reward is $>0$ with desired probability? We show that the qualitative termination problem
for OC-SSGs is in $NP$ intersect $coNP$, and is in P-time for 1-player OC-SSGs, or equivalently for one-counter Markov Decision Processes (OC-MDPs). Moreover, we show that quantitative limit problems for OC-SSGs are in $NP$ intersect $coNP$, and are in P-time for 1-player OC-MDPs. Both qualitative limit problems and qualitative termination problems for OC-SSGs are already at least as hard as Condon's quantitative decision problem for finite-state SSGs.

Tomás Brázdil, Václav Brozek, and Kousha Etessami. One-Counter Stochastic Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 108-119, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2010.108, author = {Br\'{a}zdil, Tom\'{a}s and Brozek, V\'{a}clav and Etessami, Kousha}, title = {{One-Counter Stochastic Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {108--119}, 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.2010.108}, URN = {urn:nbn:de:0030-drops-28571}, doi = {10.4230/LIPIcs.FSTTCS.2010.108}, annote = {Keywords: one-counter automata, simple stochastic games, Markov decision process, termination, limit, long run average reward} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We investigate the problem of evaluating memory consumption for systems modelled by probabilistic pushdown automata (pPDA). The space needed by a runof a pPDA is the maximal height reached by the stack during the run. Theproblem is motivated by the investigation of depth-first computations that playan important role for space-efficient schedulings of multithreaded programs.
We study the computation of both the distribution of the memory consumption and its expectation. For the distribution, we show that a naive method incurs anexponential blow-up, and that it can be avoided using linear equation systems.We also suggest a possibly even faster approximation method.Given~$\varepsilon>0$, these methods allow to compute bounds on the memoryconsumption that are exceeded with a probability of at most~$\varepsilon$.
For the expected memory consumption, we show that whether it is infinite can be decided in polynomial time for stateless pPDA (pBPA) and in polynomial space for pPDA. We also provide an iterative method for approximating theexpectation. We show how to compute error bounds of our approximation methodand analyze its convergence speed. We prove that our method convergeslinearly, i.e., the number of accurate bits of the approximation is a linear function of the number of iterations.

Tomas Brazdil, Javier Esparza, and Stefan Kiefer. On the Memory Consumption of Probabilistic Pushdown Automata. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 49-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2306, author = {Brazdil, Tomas and Esparza, Javier and Kiefer, Stefan}, title = {{On the Memory Consumption of Probabilistic Pushdown Automata}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {49--60}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2306}, URN = {urn:nbn:de:0030-drops-23067}, doi = {10.4230/LIPIcs.FSTTCS.2009.2306}, annote = {Keywords: Pushdown automata, probabilistic systems, verification} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We study continuous-time stochastic games with time-bounded
reachability objectives. We show that each vertex in such a game
has a \emph{value} (i.e., an equilibrium probability), and we
classify the conditions under which optimal strategies exist.
Finally, we show how to compute optimal strategies in finite uniform
games, and how to compute $\varepsilon$-optimal strategies in
finitely-branching games with bounded rates (for finite games, we
provide detailed complexity estimations).

Tomas Brazdil, Vojtech Forejt, Jan Krcal, Jan Kretinsky, and Antonin Kucera. Continuous-Time Stochastic Games with Time-Bounded Reachability. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 61-72, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2307, author = {Brazdil, Tomas and Forejt, Vojtech and Krcal, Jan and Kretinsky, Jan and Kucera, Antonin}, title = {{Continuous-Time Stochastic Games with Time-Bounded Reachability}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {61--72}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2307}, URN = {urn:nbn:de:0030-drops-23077}, doi = {10.4230/LIPIcs.FSTTCS.2009.2307}, annote = {Keywords: Continuous time stochastic systems, time bounded reachability, stochastic games} }

Document

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

We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint `${>}0$' or `${=}1$'. The goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied, while the other player aims at the opposite. We show that the winner in such games can be determined in $\textbf{NP} \cap \textbf{co-NP}$. Further, we prove that the winning regions for both players are regular, and we design algorithms which compute the associated finite-state automata. Finally, we show that winning strategies can be synthesized effectively.

Tomas Brazdil, Vaclav Brozek, Antonin Kucera, and Jan Obdrzalek. Qualitative Reachability in Stochastic BPA Games. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 207-218, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.STACS.2009.1837, author = {Brazdil, Tomas and Brozek, Vaclav and Kucera, Antonin and Obdrzalek, Jan}, title = {{Qualitative Reachability in Stochastic BPA Games}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {207--218}, 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.2009.1837}, URN = {urn:nbn:de:0030-drops-18375}, doi = {10.4230/LIPIcs.STACS.2009.1837}, annote = {Keywords: Stochastic games, Reachability, Pushdown automata} }

Document

**Published in:** LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of mean-payoff does not reflect possible fluctuations from the mean-payoff along a run, we propose definitions and algorithms for capturing the stability of the system, and give algorithms for deciding if a given mean payoff and stability objective can be ensured in the system.

Tomas Brazdil, Vojtech Forejt, Antonin Kucera, and Petr Novotny. Stability in Graphs and Games. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{brazdil_et_al:LIPIcs.CONCUR.2016.10, author = {Brazdil, Tomas and Forejt, Vojtech and Kucera, Antonin and Novotny, Petr}, title = {{Stability in Graphs and Games}}, booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)}, pages = {10:1--10:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-017-0}, ISSN = {1868-8969}, year = {2016}, volume = {59}, editor = {Desharnais, Jos\'{e}e and Jagadeesan, Radha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.10}, URN = {urn:nbn:de:0030-drops-61784}, doi = {10.4230/LIPIcs.CONCUR.2016.10}, annote = {Keywords: Games, Stability, Mean-Payoff, Window Objectives} }

Document

**Published in:** LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Solvency games, introduced by Berger et al., provide an abstract framework for modelling decisions of a risk-averse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where, in addition to stochastic environment and fixed increments and decrements to the investor's wealth, we introduce
interest, which is earned or paid on the current level of savings or debt, respectively.
We study problems related to the minimum initial wealth sufficient to avoid bankruptcy (i.e. steady decrease of the wealth) with probability at least p. We present an exponential time algorithm which approximates this minimum initial wealth, and show that a polynomial time approximation is not possible unless P=NP.
For the qualitative case, i.e. p=1, we show that the problem whether a given number is larger than or equal to the minimum initial wealth belongs to NP \cap coNP, and show that a polynomial time algorithm would yield a polynomial time algorithm for mean-payoff games, existence of which is a longstanding open problem. We also identify some classes of solvency MDPs for which this problem is in P. In all above cases the algorithms also give corresponding bankruptcy avoiding strategies.

Tomás Brázdil, Taolue Chen, Vojtech Forejt, Petr Novotný, and Aistis Simaitis. Solvency Markov Decision Processes with Interest. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 487-499, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2013.487, author = {Br\'{a}zdil, Tom\'{a}s and Chen, Taolue and Forejt, Vojtech and Novotn\'{y}, Petr and Simaitis, Aistis}, title = {{Solvency Markov Decision Processes with Interest}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}, pages = {487--499}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-64-4}, ISSN = {1868-8969}, year = {2013}, volume = {24}, editor = {Seth, Anil and Vishnoi, Nisheeth K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.487}, URN = {urn:nbn:de:0030-drops-43959}, doi = {10.4230/LIPIcs.FSTTCS.2013.487}, annote = {Keywords: Markov decision processes, algorithms, complexity, market models.} }

Document

**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation. For this we embed the IMC into a game that is played with the environment. We devise algorithms that enable us to derive bounds on reachability probabilities that are assured to hold in any composition context.

Tomas Brazdil, Holger Hermanns, Jan Krcal, Jan Kretinsky, and Vojtech Rehak. Verification of Open Interactive Markov Chains. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 474-485, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2012.474, author = {Brazdil, Tomas and Hermanns, Holger and Krcal, Jan and Kretinsky, Jan and Rehak, Vojtech}, title = {{Verification of Open Interactive Markov Chains}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {474--485}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.474}, URN = {urn:nbn:de:0030-drops-38826}, doi = {10.4230/LIPIcs.FSTTCS.2012.474}, annote = {Keywords: IMC, compositional verification, synthesis, time bounded reachability, discretization} }

Document

**Published in:** LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for server j. We propose to extend Jackson networks by "branching" and by "control" features. Both extensions are new and substantially expand the modelling power of Jackson networks. On the other hand, the extensions raise computational questions, particularly concerning the stability of the networks, i.e, the ergodicity of the underlying Markov chain. We show for our extended model that it is decidable in polynomial time if there exists a controller that achieves stability. Moreover, if such a controller exists, one can efficiently compute a static randomized controller which stabilizes the network in a very strong sense; in particular, all moments of the queue sizes are finite.

Tomáš Brázdil and Stefan Kiefer. Stabilization of Branching Queueing Networks. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 507-518, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{brazdil_et_al:LIPIcs.STACS.2012.507, author = {Br\'{a}zdil, Tom\'{a}\v{s} and Kiefer, Stefan}, title = {{Stabilization of Branching Queueing Networks}}, booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)}, pages = {507--518}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-35-4}, ISSN = {1868-8969}, year = {2012}, volume = {14}, editor = {D\"{u}rr, Christoph and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.507}, URN = {urn:nbn:de:0030-drops-34133}, doi = {10.4230/LIPIcs.STACS.2012.507}, annote = {Keywords: continuous-time Markov decision processes, infinite-state systems, performance analysis} }

Document

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

We study the computational complexity of basic decision problems for one-counter simple stochastic games (OC-SSGs), under various objectives. OC-SSGs are 2-player turn-based stochastic games played on the transition graph of classic one-counter automata. We study primarily the termination objective, where the goal of one player is to maximize the probability of reaching counter value 0, while the other player wishes to avoid this. Partly motivated by the goal of understanding termination objectives, we also study certain ``limit'' and ``long run average'' reward objectives that are closely related to some well-studied objectives for stochastic games with rewards. Examples of problems we address include: does player 1 have a
strategy to ensure that the counter eventually hits 0, i.e., terminates, almost surely, regardless of what player 2 does? Or that the $liminf$ (or $limsup$) counter value equals $infty$ with a desired
probability? Or that the long run average reward is $>0$ with desired probability? We show that the qualitative termination problem
for OC-SSGs is in $NP$ intersect $coNP$, and is in P-time for 1-player OC-SSGs, or equivalently for one-counter Markov Decision Processes (OC-MDPs). Moreover, we show that quantitative limit problems for OC-SSGs are in $NP$ intersect $coNP$, and are in P-time for 1-player OC-MDPs. Both qualitative limit problems and qualitative termination problems for OC-SSGs are already at least as hard as Condon's quantitative decision problem for finite-state SSGs.

Tomás Brázdil, Václav Brozek, and Kousha Etessami. One-Counter Stochastic Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 108-119, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2010.108, author = {Br\'{a}zdil, Tom\'{a}s and Brozek, V\'{a}clav and Etessami, Kousha}, title = {{One-Counter Stochastic Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {108--119}, 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.2010.108}, URN = {urn:nbn:de:0030-drops-28571}, doi = {10.4230/LIPIcs.FSTTCS.2010.108}, annote = {Keywords: one-counter automata, simple stochastic games, Markov decision process, termination, limit, long run average reward} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We investigate the problem of evaluating memory consumption for systems modelled by probabilistic pushdown automata (pPDA). The space needed by a runof a pPDA is the maximal height reached by the stack during the run. Theproblem is motivated by the investigation of depth-first computations that playan important role for space-efficient schedulings of multithreaded programs.
We study the computation of both the distribution of the memory consumption and its expectation. For the distribution, we show that a naive method incurs anexponential blow-up, and that it can be avoided using linear equation systems.We also suggest a possibly even faster approximation method.Given~$\varepsilon>0$, these methods allow to compute bounds on the memoryconsumption that are exceeded with a probability of at most~$\varepsilon$.
For the expected memory consumption, we show that whether it is infinite can be decided in polynomial time for stateless pPDA (pBPA) and in polynomial space for pPDA. We also provide an iterative method for approximating theexpectation. We show how to compute error bounds of our approximation methodand analyze its convergence speed. We prove that our method convergeslinearly, i.e., the number of accurate bits of the approximation is a linear function of the number of iterations.

Tomas Brazdil, Javier Esparza, and Stefan Kiefer. On the Memory Consumption of Probabilistic Pushdown Automata. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 49-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2306, author = {Brazdil, Tomas and Esparza, Javier and Kiefer, Stefan}, title = {{On the Memory Consumption of Probabilistic Pushdown Automata}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {49--60}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2306}, URN = {urn:nbn:de:0030-drops-23067}, doi = {10.4230/LIPIcs.FSTTCS.2009.2306}, annote = {Keywords: Pushdown automata, probabilistic systems, verification} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We study continuous-time stochastic games with time-bounded
reachability objectives. We show that each vertex in such a game
has a \emph{value} (i.e., an equilibrium probability), and we
classify the conditions under which optimal strategies exist.
Finally, we show how to compute optimal strategies in finite uniform
games, and how to compute $\varepsilon$-optimal strategies in
finitely-branching games with bounded rates (for finite games, we
provide detailed complexity estimations).

Tomas Brazdil, Vojtech Forejt, Jan Krcal, Jan Kretinsky, and Antonin Kucera. Continuous-Time Stochastic Games with Time-Bounded Reachability. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 61-72, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2307, author = {Brazdil, Tomas and Forejt, Vojtech and Krcal, Jan and Kretinsky, Jan and Kucera, Antonin}, title = {{Continuous-Time Stochastic Games with Time-Bounded Reachability}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {61--72}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2307}, URN = {urn:nbn:de:0030-drops-23077}, doi = {10.4230/LIPIcs.FSTTCS.2009.2307}, annote = {Keywords: Continuous time stochastic systems, time bounded reachability, stochastic games} }

Document

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

We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint `${>}0$' or `${=}1$'. The goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied, while the other player aims at the opposite. We show that the winner in such games can be determined in $\textbf{NP} \cap \textbf{co-NP}$. Further, we prove that the winning regions for both players are regular, and we design algorithms which compute the associated finite-state automata. Finally, we show that winning strategies can be synthesized effectively.

Tomas Brazdil, Vaclav Brozek, Antonin Kucera, and Jan Obdrzalek. Qualitative Reachability in Stochastic BPA Games. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 207-218, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.STACS.2009.1837, author = {Brazdil, Tomas and Brozek, Vaclav and Kucera, Antonin and Obdrzalek, Jan}, title = {{Qualitative Reachability in Stochastic BPA Games}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {207--218}, 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.2009.1837}, URN = {urn:nbn:de:0030-drops-18375}, doi = {10.4230/LIPIcs.STACS.2009.1837}, annote = {Keywords: Stochastic games, Reachability, Pushdown automata} }

Document

**Published in:** LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of mean-payoff does not reflect possible fluctuations from the mean-payoff along a run, we propose definitions and algorithms for capturing the stability of the system, and give algorithms for deciding if a given mean payoff and stability objective can be ensured in the system.

Tomas Brazdil, Vojtech Forejt, Antonin Kucera, and Petr Novotny. Stability in Graphs and Games. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{brazdil_et_al:LIPIcs.CONCUR.2016.10, author = {Brazdil, Tomas and Forejt, Vojtech and Kucera, Antonin and Novotny, Petr}, title = {{Stability in Graphs and Games}}, booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)}, pages = {10:1--10:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-017-0}, ISSN = {1868-8969}, year = {2016}, volume = {59}, editor = {Desharnais, Jos\'{e}e and Jagadeesan, Radha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.10}, URN = {urn:nbn:de:0030-drops-61784}, doi = {10.4230/LIPIcs.CONCUR.2016.10}, annote = {Keywords: Games, Stability, Mean-Payoff, Window Objectives} }

Document

**Published in:** LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Solvency games, introduced by Berger et al., provide an abstract framework for modelling decisions of a risk-averse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where, in addition to stochastic environment and fixed increments and decrements to the investor's wealth, we introduce
interest, which is earned or paid on the current level of savings or debt, respectively.
We study problems related to the minimum initial wealth sufficient to avoid bankruptcy (i.e. steady decrease of the wealth) with probability at least p. We present an exponential time algorithm which approximates this minimum initial wealth, and show that a polynomial time approximation is not possible unless P=NP.
For the qualitative case, i.e. p=1, we show that the problem whether a given number is larger than or equal to the minimum initial wealth belongs to NP \cap coNP, and show that a polynomial time algorithm would yield a polynomial time algorithm for mean-payoff games, existence of which is a longstanding open problem. We also identify some classes of solvency MDPs for which this problem is in P. In all above cases the algorithms also give corresponding bankruptcy avoiding strategies.

Tomás Brázdil, Taolue Chen, Vojtech Forejt, Petr Novotný, and Aistis Simaitis. Solvency Markov Decision Processes with Interest. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 487-499, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2013.487, author = {Br\'{a}zdil, Tom\'{a}s and Chen, Taolue and Forejt, Vojtech and Novotn\'{y}, Petr and Simaitis, Aistis}, title = {{Solvency Markov Decision Processes with Interest}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}, pages = {487--499}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-64-4}, ISSN = {1868-8969}, year = {2013}, volume = {24}, editor = {Seth, Anil and Vishnoi, Nisheeth K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.487}, URN = {urn:nbn:de:0030-drops-43959}, doi = {10.4230/LIPIcs.FSTTCS.2013.487}, annote = {Keywords: Markov decision processes, algorithms, complexity, market models.} }

Document

**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation. For this we embed the IMC into a game that is played with the environment. We devise algorithms that enable us to derive bounds on reachability probabilities that are assured to hold in any composition context.

Tomas Brazdil, Holger Hermanns, Jan Krcal, Jan Kretinsky, and Vojtech Rehak. Verification of Open Interactive Markov Chains. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 474-485, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2012.474, author = {Brazdil, Tomas and Hermanns, Holger and Krcal, Jan and Kretinsky, Jan and Rehak, Vojtech}, title = {{Verification of Open Interactive Markov Chains}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {474--485}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.474}, URN = {urn:nbn:de:0030-drops-38826}, doi = {10.4230/LIPIcs.FSTTCS.2012.474}, annote = {Keywords: IMC, compositional verification, synthesis, time bounded reachability, discretization} }

Document

**Published in:** LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for server j. We propose to extend Jackson networks by "branching" and by "control" features. Both extensions are new and substantially expand the modelling power of Jackson networks. On the other hand, the extensions raise computational questions, particularly concerning the stability of the networks, i.e, the ergodicity of the underlying Markov chain. We show for our extended model that it is decidable in polynomial time if there exists a controller that achieves stability. Moreover, if such a controller exists, one can efficiently compute a static randomized controller which stabilizes the network in a very strong sense; in particular, all moments of the queue sizes are finite.

Tomáš Brázdil and Stefan Kiefer. Stabilization of Branching Queueing Networks. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 507-518, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{brazdil_et_al:LIPIcs.STACS.2012.507, author = {Br\'{a}zdil, Tom\'{a}\v{s} and Kiefer, Stefan}, title = {{Stabilization of Branching Queueing Networks}}, booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)}, pages = {507--518}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-35-4}, ISSN = {1868-8969}, year = {2012}, volume = {14}, editor = {D\"{u}rr, Christoph and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.507}, URN = {urn:nbn:de:0030-drops-34133}, doi = {10.4230/LIPIcs.STACS.2012.507}, annote = {Keywords: continuous-time Markov decision processes, infinite-state systems, performance analysis} }

Document

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

We study the computational complexity of basic decision problems for one-counter simple stochastic games (OC-SSGs), under various objectives. OC-SSGs are 2-player turn-based stochastic games played on the transition graph of classic one-counter automata. We study primarily the termination objective, where the goal of one player is to maximize the probability of reaching counter value 0, while the other player wishes to avoid this. Partly motivated by the goal of understanding termination objectives, we also study certain ``limit'' and ``long run average'' reward objectives that are closely related to some well-studied objectives for stochastic games with rewards. Examples of problems we address include: does player 1 have a
strategy to ensure that the counter eventually hits 0, i.e., terminates, almost surely, regardless of what player 2 does? Or that the $liminf$ (or $limsup$) counter value equals $infty$ with a desired
probability? Or that the long run average reward is $>0$ with desired probability? We show that the qualitative termination problem
for OC-SSGs is in $NP$ intersect $coNP$, and is in P-time for 1-player OC-SSGs, or equivalently for one-counter Markov Decision Processes (OC-MDPs). Moreover, we show that quantitative limit problems for OC-SSGs are in $NP$ intersect $coNP$, and are in P-time for 1-player OC-MDPs. Both qualitative limit problems and qualitative termination problems for OC-SSGs are already at least as hard as Condon's quantitative decision problem for finite-state SSGs.

Tomás Brázdil, Václav Brozek, and Kousha Etessami. One-Counter Stochastic Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 108-119, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2010.108, author = {Br\'{a}zdil, Tom\'{a}s and Brozek, V\'{a}clav and Etessami, Kousha}, title = {{One-Counter Stochastic Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {108--119}, 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.2010.108}, URN = {urn:nbn:de:0030-drops-28571}, doi = {10.4230/LIPIcs.FSTTCS.2010.108}, annote = {Keywords: one-counter automata, simple stochastic games, Markov decision process, termination, limit, long run average reward} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We investigate the problem of evaluating memory consumption for systems modelled by probabilistic pushdown automata (pPDA). The space needed by a runof a pPDA is the maximal height reached by the stack during the run. Theproblem is motivated by the investigation of depth-first computations that playan important role for space-efficient schedulings of multithreaded programs.
We study the computation of both the distribution of the memory consumption and its expectation. For the distribution, we show that a naive method incurs anexponential blow-up, and that it can be avoided using linear equation systems.We also suggest a possibly even faster approximation method.Given~$\varepsilon>0$, these methods allow to compute bounds on the memoryconsumption that are exceeded with a probability of at most~$\varepsilon$.
For the expected memory consumption, we show that whether it is infinite can be decided in polynomial time for stateless pPDA (pBPA) and in polynomial space for pPDA. We also provide an iterative method for approximating theexpectation. We show how to compute error bounds of our approximation methodand analyze its convergence speed. We prove that our method convergeslinearly, i.e., the number of accurate bits of the approximation is a linear function of the number of iterations.

Tomas Brazdil, Javier Esparza, and Stefan Kiefer. On the Memory Consumption of Probabilistic Pushdown Automata. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 49-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2306, author = {Brazdil, Tomas and Esparza, Javier and Kiefer, Stefan}, title = {{On the Memory Consumption of Probabilistic Pushdown Automata}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {49--60}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2306}, URN = {urn:nbn:de:0030-drops-23067}, doi = {10.4230/LIPIcs.FSTTCS.2009.2306}, annote = {Keywords: Pushdown automata, probabilistic systems, verification} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We study continuous-time stochastic games with time-bounded
reachability objectives. We show that each vertex in such a game
has a \emph{value} (i.e., an equilibrium probability), and we
classify the conditions under which optimal strategies exist.
Finally, we show how to compute optimal strategies in finite uniform
games, and how to compute $\varepsilon$-optimal strategies in
finitely-branching games with bounded rates (for finite games, we
provide detailed complexity estimations).

Tomas Brazdil, Vojtech Forejt, Jan Krcal, Jan Kretinsky, and Antonin Kucera. Continuous-Time Stochastic Games with Time-Bounded Reachability. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 61-72, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2307, author = {Brazdil, Tomas and Forejt, Vojtech and Krcal, Jan and Kretinsky, Jan and Kucera, Antonin}, title = {{Continuous-Time Stochastic Games with Time-Bounded Reachability}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {61--72}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2307}, URN = {urn:nbn:de:0030-drops-23077}, doi = {10.4230/LIPIcs.FSTTCS.2009.2307}, annote = {Keywords: Continuous time stochastic systems, time bounded reachability, stochastic games} }

Document

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

We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint `${>}0$' or `${=}1$'. The goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied, while the other player aims at the opposite. We show that the winner in such games can be determined in $\textbf{NP} \cap \textbf{co-NP}$. Further, we prove that the winning regions for both players are regular, and we design algorithms which compute the associated finite-state automata. Finally, we show that winning strategies can be synthesized effectively.

Tomas Brazdil, Vaclav Brozek, Antonin Kucera, and Jan Obdrzalek. Qualitative Reachability in Stochastic BPA Games. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 207-218, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{brazdil_et_al:LIPIcs.STACS.2009.1837, author = {Brazdil, Tomas and Brozek, Vaclav and Kucera, Antonin and Obdrzalek, Jan}, title = {{Qualitative Reachability in Stochastic BPA Games}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {207--218}, 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.2009.1837}, URN = {urn:nbn:de:0030-drops-18375}, doi = {10.4230/LIPIcs.STACS.2009.1837}, annote = {Keywords: Stochastic games, Reachability, Pushdown automata} }

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