12 Search Results for "Kalu�a, Vojtech"

Document
DOI: 10.4230/LIPIcs.CCC.2023.25
Trade-Offs Between Entanglement and Communication

Authors: Srinivasan Arunachalam and Uma Girish

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on n bits for which reducing the entanglement increases the classical communication complexity exponentially. Our separations are as follows. For every k ≥ ~1: Q‖^* versus R2^*: We show that quantum simultaneous protocols with Θ̃(k⁵log³n) qubits of entanglement can exponentially outperform two-way randomized protocols with O(k) qubits of entanglement. This resolves an open problem from [Dmitry Gavinsky, 2008] and improves the state-of-the-art separations between quantum simultaneous protocols with entanglement and two-way randomized protocols without entanglement [Gavinsky, 2019; Girish et al., 2022]. R‖^* versus Q‖^*: We show that classical simultaneous protocols with Θ̃(k log n) qubits of entanglement can exponentially outperform quantum simultaneous protocols with O(k) qubits of entanglement, resolving an open question from [Gavinsky et al., 2006; Gavinsky, 2019]. The best result prior to our work was a relational separation against protocols without entanglement [Gavinsky et al., 2006]. R‖^* versus R1^*: We show that classical simultaneous protocols with Θ̃(k log n) qubits of entanglement can exponentially outperform randomized one-way protocols with O(k) qubits of entanglement. Prior to our work, only a relational separation was known [Dmitry Gavinsky, 2008].
Cite as

Srinivasan Arunachalam and Uma Girish. Trade-Offs Between Entanglement and Communication. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 25:1-25:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{arunachalam_et_al:LIPIcs.CCC.2023.25,
  author =	{Arunachalam, Srinivasan and Girish, Uma},
  title =	{{Trade-Offs Between Entanglement and Communication}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{25:1--25:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.25},
  URN =		{urn:nbn:de:0030-drops-182957},
  doi =		{10.4230/LIPIcs.CCC.2023.25},
  annote =	{Keywords: quantum, communication complexity, exponential separation, boolean hidden matching, forrelation, xor lemma}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.72
A Variant of the VC-Dimension with Applications to Depth-3 Circuits

Authors: Peter Frankl, Svyatoslav Gryaznov, and Navid Talebanfard

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
We introduce the following variant of the VC-dimension. Given S ⊆ {0,1}ⁿ and a positive integer d, we define 𝕌_d(S) to be the size of the largest subset I ⊆ [n] such that the projection of S on every subset of I of size d is the d-dimensional cube. We show that determining the largest cardinality of a set with a given 𝕌_d dimension is equivalent to a Turán-type problem related to the total number of cliques in a d-uniform hypergraph. This allows us to beat the Sauer-Shelah lemma for this notion of dimension. We use this to obtain several results on Σ₃^k-circuits, i.e., depth-3 circuits with top gate OR and bottom fan-in at most k: - Tight relationship between the number of satisfying assignments of a 2-CNF and the dimension of the largest projection accepted by it, thus improving Paturi, Saks, and Zane (Comput. Complex. '00). - Improved Σ₃³-circuit lower bounds for affine dispersers for sublinear dimension. Moreover, we pose a purely hypergraph-theoretic conjecture under which we get further improvement. - We make progress towards settling the Σ₃² complexity of the inner product function and all degree-2 polynomials over 𝔽₂ in general. The question of determining the Σ₃³ complexity of IP was recently posed by Golovnev, Kulikov, and Williams (ITCS'21).
Cite as

Peter Frankl, Svyatoslav Gryaznov, and Navid Talebanfard. A Variant of the VC-Dimension with Applications to Depth-3 Circuits. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 72:1-72:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{frankl_et_al:LIPIcs.ITCS.2022.72,
  author =	{Frankl, Peter and Gryaznov, Svyatoslav and Talebanfard, Navid},
  title =	{{A Variant of the VC-Dimension with Applications to Depth-3 Circuits}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{72:1--72:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.72},
  URN =		{urn:nbn:de:0030-drops-156680},
  doi =		{10.4230/LIPIcs.ITCS.2022.72},
  annote =	{Keywords: VC-dimension, Hypergraph, Clique, Affine Disperser, Circuit}
}
Document
DOI: 10.4230/LIPIcs.TIME.2021.17
1½-Player Stochastic StopWatch Games

Authors: Sparsa Roychowdhury

Published in: LIPIcs, Volume 206, 28th International Symposium on Temporal Representation and Reasoning (TIME 2021)

Abstract
Stochastic timed games (STGs), introduced by Bouyer and Forejt, generalize continuous-time Markov chains and timed automata. Depending on the number of players - 2, 1, or 0 - subclasses of stochastic timed games are classified as 2½-player, 1½-player, and ½-player games where the ½ symbolizes the presence of the stochastic player. The qualitative and quantitative reachability problem for STGs was studied in [Patricia Bouyer and Vojtech Forejt, 2009] and [S. Akshay et al., 2016]. In this paper, we introduce stochastic stopwatch games (SSG), an extension of (STG) from clocks to stopwatches. We focus on 1½-player SSGs and prove that with two variables which can be either a clock or a stopwatch, qualitative reachability is decidable, whereas, if we increase the number of variables to three, with at least one stopwatch, the problem becomes undecidable.
Cite as

Sparsa Roychowdhury. 1½-Player Stochastic StopWatch Games. In 28th International Symposium on Temporal Representation and Reasoning (TIME 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 206, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{roychowdhury:LIPIcs.TIME.2021.17,
  author =	{Roychowdhury, Sparsa},
  title =	{{1½-Player Stochastic StopWatch Games}},
  booktitle =	{28th International Symposium on Temporal Representation and Reasoning (TIME 2021)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-206-8},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{206},
  editor =	{Combi, Carlo and Eder, Johann and Reynolds, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2021.17},
  URN =		{urn:nbn:de:0030-drops-147934},
  doi =		{10.4230/LIPIcs.TIME.2021.17},
  annote =	{Keywords: Timed Automata, Stopwatches, Stochastic Timed Games}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.46
Lower Bounds on Avoiding Thresholds

Authors: Robert Ferens, Marek Szykuła, and Vojtěch Vorel

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
For a DFA, a word avoids a subset of states, if after reading that word the automaton cannot be in any state from the subset regardless of its initial state. A subset that admits an avoiding word is avoidable. The k-avoiding threshold of a DFA is the smallest number such that every avoidable subset of size k can be avoided with a word no longer than that number. We study the problem of determining the maximum possible k-avoiding thresholds. For every fixed k ≥ 1, we show a general construction of strongly connected DFAs with n states and the k-avoiding threshold in Θ(n^k). This meets the known upper bound for k ≥ 3. For k = 1 and k = 2, the known upper bounds are respectively in 𝒪(n²) and in 𝒪(n³). For k = 1, we show that 2n-3 is attainable for every number of states n in the class of strongly connected synchronizing binary DFAs, which is supposed to be the best possible in the class of all DFAs for n ≥ 8. For k = 2, we show that the conjectured solution for k = 1 (an upper bound in 𝒪(n)) also implies a tight upper bound in 𝒪(n²) on 2-avoiding threshold. Finally, we discuss the possibility of using k-avoiding thresholds of synchronizing automata to improve upper bounds on the length of the shortest reset words.
Cite as

Robert Ferens, Marek Szykuła, and Vojtěch Vorel. Lower Bounds on Avoiding Thresholds. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ferens_et_al:LIPIcs.MFCS.2021.46,
  author =	{Ferens, Robert and Szyku{\l}a, Marek and Vorel, Vojt\v{e}ch},
  title =	{{Lower Bounds on Avoiding Thresholds}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.46},
  URN =		{urn:nbn:de:0030-drops-144869},
  doi =		{10.4230/LIPIcs.MFCS.2021.46},
  annote =	{Keywords: avoiding word, \v{C}ern\'{y} conjecture, rank conjecture, reset threshold, reset word, synchronizing automaton, synchronizing word}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.2
Reducing (To) the Ranks: Efficient Rank-Based Büchi Automata Complementation

Authors: Vojtěch Havlena and Ondřej Lengál

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

Abstract
This paper provides several optimizations of the rank-based approach for complementing Büchi automata. We start with Schewe’s theoretically optimal construction and develop a set of techniques for pruning its state space that are key to obtaining small complement automata in practice. In particular, the reductions (except one) have the property that they preserve (at least some) so-called super-tight runs, which are runs whose ranking is as tight as possible. Our evaluation on a large benchmark shows that the optimizations indeed significantly help the rank-based approach and that, in a large number of cases, the obtained complement is the smallest from those produced by state-of-the-art tools for Büchi complementation.
Cite as

Vojtěch Havlena and Ondřej Lengál. Reducing (To) the Ranks: Efficient Rank-Based Büchi Automata Complementation. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{havlena_et_al:LIPIcs.CONCUR.2021.2,
  author =	{Havlena, Vojt\v{e}ch and Leng\'{a}l, Ond\v{r}ej},
  title =	{{Reducing (To) the Ranks: Efficient Rank-Based B\"{u}chi Automata Complementation}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{2:1--2:19},
  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.2021.2},
  URN =		{urn:nbn:de:0030-drops-143799},
  doi =		{10.4230/LIPIcs.CONCUR.2021.2},
  annote =	{Keywords: B\"{u}chi automata, rank-based complementation, super-tight runs}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2016.10
Stability in Graphs and Games

Authors: Tomas Brazdil, Vojtech Forejt, Antonin Kucera, and Petr Novotny

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

Abstract
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.
Cite as

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-dev.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
DOI: 10.4230/LIPIcs.SoCG.2016.43
Shortest Path Embeddings of Graphs on Surfaces

Authors: Alfredo Hubard, Vojtech Kaluža, Arnaud de Mesmay, and Martin Tancer

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
The classical theorem of Fáry states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generalizations of Fáry's theorem to surfaces equipped with Riemannian metrics. In this setting, we require that every edge is drawn as a shortest path between its two endpoints and we call an embedding with this property a shortest path embedding. The main question addressed in this paper is whether given a closed surface S, there exists a Riemannian metric for which every topologically embeddable graph admits a shortest path embedding. This question is also motivated by various problems regarding crossing numbers on surfaces. We observe that the round metrics on the sphere and the projective plane have this property. We provide flat metrics on the torus and the Klein bottle which also have this property. Then we show that for the unit square flat metric on the Klein bottle there exists a graph without shortest path embeddings. We show, moreover, that for large g, there exist graphs G embeddable into the orientable surface of genus g, such that with large probability a random hyperbolic metric does not admit a shortest path embedding of G, where the probability measure is proportional to the Weil-Petersson volume on moduli space. Finally, we construct a hyperbolic metric on every orientable surface S of genus g, such that every graph embeddable into S can be embedded so that every edge is a concatenation of at most O(g) shortest paths.
Cite as

Alfredo Hubard, Vojtech Kaluža, Arnaud de Mesmay, and Martin Tancer. Shortest Path Embeddings of Graphs on Surfaces. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{hubard_et_al:LIPIcs.SoCG.2016.43,
  author =	{Hubard, Alfredo and Kalu\v{z}a, Vojtech and de Mesmay, Arnaud and Tancer, Martin},
  title =	{{Shortest Path Embeddings of Graphs on Surfaces}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.43},
  URN =		{urn:nbn:de:0030-drops-59356},
  doi =		{10.4230/LIPIcs.SoCG.2016.43},
  annote =	{Keywords: Graph embedding, surface, shortest path, crossing number, hyperbolic geometry}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2015.184
On Frequency LTL in Probabilistic Systems

Authors: Vojtech Forejt and Jan Krcal

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

Abstract
We study frequency linear-time temporal logic (fLTL) which extends the linear-time temporal logic (LTL) with a path operator G^p expressing that on a path, certain formula holds with at least a given frequency p, thus relaxing the semantics of the usual G operator of LTL. Such logic is particularly useful in probabilistic systems, where some undesirable events such as random failures may occur and are acceptable if they are rare enough. Frequency-related extensions of LTL have been previously studied by several authors, where mostly the logic is equipped with an extended "until" and "globally" operator, leading to undecidability of most interesting problems. For the variant we study, we are able to establish fundamental decidability results. We show that for Markov chains, the problem of computing the probability with which a given fLTL formula holds has the same complexity as the analogous problem for LTL. We also show that for Markov decision processes the problem becomes more delicate, but when restricting the frequency bound p to be 1 and negations not to be outside any G^p operator, we can compute the maximum probability of satisfying the fLTL formula. This can be again performed with the same time complexity as for the ordinary LTL formulas.
Cite as

Vojtech Forejt and Jan Krcal. On Frequency LTL in Probabilistic Systems. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 184-197, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{forejt_et_al:LIPIcs.CONCUR.2015.184,
  author =	{Forejt, Vojtech and Krcal, Jan},
  title =	{{On Frequency LTL in Probabilistic Systems}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{184--197},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.184},
  URN =		{urn:nbn:de:0030-drops-53789},
  doi =		{10.4230/LIPIcs.CONCUR.2015.184},
  annote =	{Keywords: Markov chains, Markov decision processes, LTL, controller synthesis}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2013.487
Solvency Markov Decision Processes with Interest

Authors: Tomás Brázdil, Taolue Chen, Vojtech Forejt, Petr Novotný, and Aistis Simaitis

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

Abstract
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.
Cite as

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-dev.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
DOI: 10.4230/LIPIcs.FSTTCS.2012.448
Bisimilarity of Probabilistic Pushdown Automata

Authors: Vojtech Forejt, Petr Jancar, Stefan Kiefer, and James Worrell

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

Abstract
We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata (without epsilon-transitions). Our first contribution is a general construction that reduces checking bisimilarity of probabilistic transition systems to checking bisimilarity of non-deterministic transition systems. This construction directly yields decidability of bisimilarity for pPDA, as well as an elementary upper bound for the bisimilarity problem on the subclass of probabilistic basic process algebras, i.e., single-state pPDA. We further show that, with careful analysis, the general reduction can be used to prove an EXPTIME upper bound for bisimilarity of probabilistic visibly pushdown automata. Here we also provide a matching lower bound, establishing EXPTIME-completeness. Finally we prove that deciding bisimilarity of probabilistic one-counter automata, another subclass of pPDA, is PSPACE-complete. Here we use a more specialised argument to obtain optimal complexity bounds.
Cite as

Vojtech Forejt, Petr Jancar, Stefan Kiefer, and James Worrell. Bisimilarity of Probabilistic Pushdown Automata. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 448-460, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{forejt_et_al:LIPIcs.FSTTCS.2012.448,
  author =	{Forejt, Vojtech and Jancar, Petr and Kiefer, Stefan and Worrell, James},
  title =	{{Bisimilarity of Probabilistic Pushdown Automata}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{448--460},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.448},
  URN =		{urn:nbn:de:0030-drops-38800},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.448},
  annote =	{Keywords: bisimilarity, probabilistic systems, pushdown automata}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.474
Verification of Open Interactive Markov Chains

Authors: Tomas Brazdil, Holger Hermanns, Jan Krcal, Jan Kretinsky, and Vojtech Rehak

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

Abstract
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.
Cite as

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)

Copy BibTex To Clipboard

@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-dev.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
DOI: 10.4230/LIPIcs.FSTTCS.2009.2307
Continuous-Time Stochastic Games with Time-Bounded Reachability

Authors: Tomas Brazdil, Vojtech Forejt, Jan Krcal, Jan Kretinsky, and Antonin Kucera

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

Abstract
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).
Cite as

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)

Copy BibTex To Clipboard

@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-dev.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}
}
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