4 Search Results for "Piterman, Nir"


Document
Invited Talk
A Brief History of History-Determinism (Invited Talk)

Authors: Karoliina Lehtinen

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
Most nondeterministic automata models are more expressive, or at least more succinct, than their deterministic counterparts; however, this comes at a cost, as deterministic automata tend to have better algorithmic properties. History-deterministic automata are an intermediate model that allows a restricted form of nondeterminism: all nondeterministic choices must be resolvable on-the-fly, with only the knowledge of the word prefix read so far - as opposed to general nondeterminism, which allows for guessing the future of the word. History-deterministic automata combine some of the algorithmic benefits of determinism with some of the increased power of nondeterminism, thus enjoying (some of) the best of both worlds. History-determinism, as it is understood today, has its roots in several independently invented notions: Kupferman, Safra and Vardi’s automata recognising tree languages derived from word languages [Kupferman et al., 2006] (a notion that has been later referred to as automata that are good-for-trees [Udi Boker et al., 2013]), Henzinger and Piterman’s good-for-games automata [Thomas Henzinger and Nir Piterman, 2006], and Colcombet’s history-deterministic automata, introduced in his work on regular cost-automata [Colcombet, 2009]. In the ω-regular setting, where they were initially most studied, the notions of good-for-trees, good-for-games and history-determinism are equivalent, despite differences in their definitions. The key algorithmic appeal of these automata is that like deterministic automata, they have good compositional properties. This makes them particularly useful for applications such as reactive synthesis, where composition of games and automata is at the heart of effective solutions. Since then, history-determinism has received its fair share of attention, not least because of its relevance to synthesis. Indeed it turns out to be a natural and useful form of nondeterminism more broadly, and can be generalised to all sorts of different automata models: alternating automata [Udi Boker and Karoliina Lehtinen, 2019], pushdown automata [Enzo Erlich et al., 2022; Enzo Erlich et al., 2022], timed automata [Thomas A. Henzinger et al., 2022; Sougata Bose et al., 2022], Parikh automata [Enzo Erlich et al., 2022], and quantiative automata [Udi Boker and Karoliina Lehtinen, 2021], to name a few. In each of these models, history-determinism offers some trade-offs between the power of nondeterminism and the algorithmic properties of determinism. In particular, depending on the model, they can be either more expressive or more succinct than their deterministic counterparts, while retaining better algorithmic properties - in particular with respect to deciding universality, language inclusion and games - than fully nondeterministic automata. The drive to extend history-determinism to more powerful automata models has also lead to a better understanding of the properties of these automata, of how they compare to related notions (such as good-for-games automata and determinisability by pruning), and of the various games and tools used to study them. This talk aims to give a broad introduction to the notion of history determinism as well as an overview of some of the recent developements on the topic. It will also highlight some of the many problems that remain open. It is loosely based on a recent survey, written jointly with Udi Boker, which gives an informal presentation of what are, in our view, the key aspects of history-determinism [Udi Boker and Karoliina Lehtinen, 2023].

Cite as

Karoliina Lehtinen. A Brief History of History-Determinism (Invited Talk). In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{lehtinen:LIPIcs.STACS.2023.1,
  author =	{Lehtinen, Karoliina},
  title =	{{A Brief History of History-Determinism}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.1},
  URN =		{urn:nbn:de:0030-drops-176535},
  doi =		{10.4230/LIPIcs.STACS.2023.1},
  annote =	{Keywords: History-determinism, nondeterminism, automata, good-for-games}
}
Document
On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory Requirements of Muller Conditions

Authors: Antonio Casares

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)


Abstract
In this paper, we relate the problem of determining the chromatic memory requirements of Muller conditions with the minimisation of transition-based Rabin automata. Our first contribution is a proof of the NP-completeness of the minimisation of transition-based Rabin automata. Our second contribution concerns the memory requirements of games over graphs using Muller conditions. A memory structure is a finite state machine that implements a strategy and is updated after reading the edges of the game; the special case of chromatic memories being those structures whose update function only consider the colours of the edges. We prove that the minimal amount of chromatic memory required in games using a given Muller condition is exactly the size of a minimal Rabin automaton recognising this condition. Combining these two results, we deduce that finding the chromatic memory requirements of a Muller condition is NP-complete. This characterisation also allows us to prove that chromatic memories cannot be optimal in general, disproving a conjecture by Kopczyński.

Cite as

Antonio Casares. On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory Requirements of Muller Conditions. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{casares:LIPIcs.CSL.2022.12,
  author =	{Casares, Antonio},
  title =	{{On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory Requirements of Muller Conditions}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.12},
  URN =		{urn:nbn:de:0030-drops-157322},
  doi =		{10.4230/LIPIcs.CSL.2022.12},
  annote =	{Keywords: Automata on Infinite Words, Games on Graphs, Arena-Independent Memory, Complexity}
}
Document
Combinations of Qualitative Winning for Stochastic Parity Games

Authors: Krishnendu Chatterjee and Nir Piterman

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)


Abstract
We study Markov decision processes and turn-based stochastic games with parity conditions. There are three qualitative winning criteria, namely, sure winning, which requires all paths to satisfy the condition, almost-sure winning, which requires the condition to be satisfied with probability 1, and limit-sure winning, which requires the condition to be satisfied with probability arbitrarily close to 1. We study the combination of two of these criteria for parity conditions, e.g., there are two parity conditions one of which must be won surely, and the other almost-surely. The problem has been studied recently by Berthon et al. for MDPs with combination of sure and almost-sure winning, under infinite-memory strategies, and the problem has been established to be in NP cap co-NP. Even in MDPs there is a difference between finite-memory and infinite-memory strategies. Our main results for combination of sure and almost-sure winning are as follows: (a) we show that for MDPs with finite-memory strategies the problem is in NP cap co-NP; (b) we show that for turn-based stochastic games the problem is co-NP-complete, both for finite-memory and infinite-memory strategies; and (c) we present algorithmic results for the finite-memory case, both for MDPs and turn-based stochastic games, by reduction to non-stochastic parity games. In addition we show that all the above complexity results also carry over to combination of sure and limit-sure winning, and results for all other combinations can be derived from existing results in the literature. Thus we present a complete picture for the study of combinations of two qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games.

Cite as

Krishnendu Chatterjee and Nir Piterman. Combinations of Qualitative Winning for Stochastic Parity Games. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{chatterjee_et_al:LIPIcs.CONCUR.2019.6,
  author =	{Chatterjee, Krishnendu and Piterman, Nir},
  title =	{{Combinations of Qualitative Winning for Stochastic Parity Games}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.6},
  URN =		{urn:nbn:de:0030-drops-109089},
  doi =		{10.4230/LIPIcs.CONCUR.2019.6},
  annote =	{Keywords: Two Player Games, Stochastic Games, Parity Winning Conditions}
}
Document
Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics

Authors: Pablo Castro, Cecilia Kilmurray, and Nir Piterman

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)


Abstract
We revisit a recently introduced probabilistic \mu-calculus and study an expressive fragment of it. By using the probabilistic quantification as an atomic operation of the calculus we establish a connection between the calculus and obligation games. The calculus we consider is strong enough to encode well-known logics such as pctl and pctl^*. Its game semantics is very similar to the game semantics of the classical mu-calculus (using parity obligation games instead of parity games). This leads to an optimal complexity of NP\cap co-NP for its finite model checking procedure. Furthermore, we investigate a (relatively) well-behaved fragment of this calculus: an extension of pctl with fixed points. An important feature of this extended version of pctl is that its model checking is only exponential w.r.t. the alternation depth of fixed points, one of the main characteristics of Kozen's mu-calculus.

Cite as

Pablo Castro, Cecilia Kilmurray, and Nir Piterman. Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 211-223, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


Copy BibTex To Clipboard

@InProceedings{castro_et_al:LIPIcs.STACS.2015.211,
  author =	{Castro, Pablo and Kilmurray, Cecilia and Piterman, Nir},
  title =	{{Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{211--223},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.211},
  URN =		{urn:nbn:de:0030-drops-49155},
  doi =		{10.4230/LIPIcs.STACS.2015.211},
  annote =	{Keywords: mu-calculus, probabilistic logics, model checking, game semantics}
}
  • Refine by Author
  • 2 Piterman, Nir
  • 1 Casares, Antonio
  • 1 Castro, Pablo
  • 1 Chatterjee, Krishnendu
  • 1 Kilmurray, Cecilia
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Automata over infinite objects
  • 1 Theory of computation → Formal languages and automata theory
  • 1 Theory of computation → Logic and verification

  • Refine by Keyword
  • 1 Arena-Independent Memory
  • 1 Automata on Infinite Words
  • 1 Complexity
  • 1 Games on Graphs
  • 1 History-determinism
  • Show More...

  • Refine by Type
  • 4 document

  • Refine by Publication Year
  • 1 2015
  • 1 2019
  • 1 2022
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail