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Fair Equivalence Relations [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2003 Lecture Notes in Computer Science  
This hierarchy lies between the hierarchies of word and tree automata, and it collapses at Rabin conditions of index one, and Streett conditions of index two. § bisimulation [GL94], game-bisimulation [  ...  We consider three types of fair bisimulation studied in the literature: © bisimulation, game-bisimulation, and -bisimulation.  ...  The number of sets in a parity fairness condition or of pairs in a Rabin or Streett fairness condition is the index of 6 .  ... 
doi:10.1007/978-3-540-39910-0_30 fatcat:6c7kpqyb2vbhlmpbm43jbvbf5i

Fair Equivalence Relations [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2000 Lecture Notes in Computer Science  
This hierarchy lies between the hierarchies of word and tree automata, and it collapses at Rabin conditions of index one, and Streett conditions of index two. § bisimulation [GL94], game-bisimulation [  ...  We consider three types of fair bisimulation studied in the literature: © bisimulation, game-bisimulation, and -bisimulation.  ...  The number of sets in a parity fairness condition or of pairs in a Rabin or Streett fairness condition is the index of 6 .  ... 
doi:10.1007/3-540-44450-5_12 fatcat:dabexamcufepljiawgjdbs6psm

Parityizing Rabin and Streett

Udi Boker, Orna Kupferman, Avital Steinitz, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
Parityizing Rabin and Streett index of the automaton.  ...  The fact parity games are memoryless is of great importance in synthesis algorithms, where one wants to generate transducers for the winning strategies [4].  ...  The challenge has to do with the fact that reasoning about games one can abstract components of the game, whereas translations among automata must keep the exact same language -every letter counts.  ... 
doi:10.4230/lipics.fsttcs.2010.412 dblp:conf/fsttcs/BokerKS10 fatcat:q7l5cyskhfhojfwofcorhoesf4

Controller Synthesis for Probabilistic Systems (Extended Abstract) [chapter]

Christel Baier, Marcus Größer, Martin Leucker, Benedikt Bollig, Frank Ciesinski
IFIP International Federation for Information Processing  
Controller synthesis addresses the question of how to limit the internal behavior of a given implementation to meet its specification, regardless of the behavior enforced by the environment.  ...  We first consider probabilistic computation tree logic as specification formalism, discuss the role of strategy-types for the controller and show the NP-hardness of the controller synthesis problem.  ...  Reformulating as a parity winning condition, we may apply the reduction technique suggested in [Chatterjee et al., 2003] from qualitative stochastic parity games to (non-stochastic) 2-player parity games  ... 
doi:10.1007/1-4020-8141-3_38 dblp:conf/ifipTCS/BolligC04 fatcat:4gkdmzcejjatvoqn5esm2qm5pm

Fixpoints, games and the difference hierarchy

Julian C. Bradfield
2003 RAIRO - Theoretical Informatics and Applications  
This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory.  ...  Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference  ...  play. n is the Rabin index.  ... 
doi:10.1051/ita:2003011 fatcat:4hwj5rljynabbm7vc7af2y4kim

Determinising Parity Automata [chapter]

Sven Schewe, Thomas Varghese
2014 Lecture Notes in Computer Science  
As a side-result, this optimality extends to the determinisation of B\"uchi automata.  ...  Parity word automata and their determinisation play an important role in automata and game theory.  ...  with the parity index on the transitions from the states of the automata.  ... 
doi:10.1007/978-3-662-44522-8_41 fatcat:ktevnyi4dzeynhsrerisjjznza

Strategy construction in infinite games with Streett and Rabin chain winning conditions [chapter]

Nils Buhrke, Helmut Lescow, Jens Vöge
1996 Lecture Notes in Computer Science  
For the step from Rabin chain games to winning strategies examples are discussed, based on an implementation of the algorithm.  ...  We proceed in two steps: First, we give a reduction of Streett automata to automata with the Rabin chain (or parity) acceptance condition.  ...  For building Rabin chain games out of Streett games in our case we extend the \index appearance record", introduced by Muller and Schupp MS95], by two pointers as done by Safra Saf92] .  ... 
doi:10.1007/3-540-61042-1_46 fatcat:mjrj33qczvcj7ow5g4ecp4e2qq

A survey of stochastic ω-regular games

Krishnendu Chatterjee, Thomas A. Henzinger
2012 Journal of computer and system sciences (Print)  
We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems.  ...  Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not.  ...  together with an extended set R = R ∪ {(E d+1 , F d+1 )} of Rabin pairs.  ... 
doi:10.1016/j.jcss.2011.05.002 fatcat:267iudbahzf4tdef2fo573l3ie

Stackelberg-Pareto Synthesis (Extended Version) [article]

Véronique Bruyère, Baptiste Fievet, Jean-François Raskin, Clément Tamines
2022 arXiv   pre-print
We show that this problem is fixed-parameter tractable for games in which objectives are all reachability, safety, Büchi, co-Büchi, Boolean Büchi, parity, Muller, Streett or Rabin objectives.  ...  We study the framework of two-player Stackelberg games played on graphs in which Player 0 announces a strategy and Player 1 responds rationally with a strategy that is an optimal response.  ...  ACKNOWLEDGMENTS This work is partially supported by the PDR project Subgame perfection in graph games (F.R.S.  ... 
arXiv:2203.01285v1 fatcat:6ff7ej2cqzaxvbhnwcsigrfzwe

From Spot 2.0 to Spot 2.10: What's New? [article]

Alexandre Duret-Lutz, Jérôme Dubois, Clément Gillard, Henrich Lauko
2022 arXiv   pre-print
Since then, Spot has been extended with several features such as acceptance transformations, alternating automata, games, LTL synthesis, and more.  ...  This paper summarizes its evolution over the past six years, since the release of Spot 2.0, which was the first version to support ω-automata with arbitrary acceptance conditions, and the last version  ...  Currently, Spot has solvers for safety games and for games with parity max odd acceptance, but we plan to at least generalize the latter to any kind of parity condition.  ... 
arXiv:2206.11366v1 fatcat:ukei6ijbtvhjtozbuwb7kcxiyi

The Complexity of Nash Equilibria in Stochastic Multiplayer Games

Michael Ummels, Dominik Wojtczak, Wolfgang Thomas
2011 Logical Methods in Computer Science  
is given by a parity condition with a bounded number of priorities.  ...  We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives.  ...  strategy τ i of the coalition Π \ {i} in the coalition game G i .  ... 
doi:10.2168/lmcs-7(3:20)2011 fatcat:i4ggd6mxyfcoljokr2s7y3mtgq

Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness [article]

Tamajit Banerjee, Rupak Majumdar, Kaushik Mallik, Anne-Kathrin Schmuck, Sadegh Soudjani
2022 arXiv   pre-print
For Rabin games with k pairs, the complexity of the new algorithm is O(n^k+2k!) symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption.  ...  We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic  ...  Acknowledgments: We thank Daniel Hausmann and Nir Piterman for valuable comments on an earlier version of this manuscript, in particular for the observation that the parity fixpoint does not allow for  ... 
arXiv:2202.07480v2 fatcat:zqzb5nuwevalbesjl66v4ltjbu

Finitary Winning in ω-Regular Games [chapter]

Krishnendu Chatterjee, Thomas A. Henzinger
2006 Lecture Notes in Computer Science  
In this work we study games with finitary parity and Streett (fairness) objectives.  ...  Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds).  ...  The index appearance record (IAR) construction [13] translates games with player 1 Streett objectives into games with parity objectives, preserving the abilities of both players to win.  ... 
doi:10.1007/11691372_17 fatcat:r5jtenvybrhb5lwb6st3axwyfy

Collapsible Pushdown Parity Games [article]

Christopher H. Broadbent, Arnaud Carayol, Matthew Hague, Andrzej S. Murawski, C.-H. Luke Ong, Olivier Serre
2020 arXiv   pre-print
Our main result is to establish the decidability of such games and to provide an effective representation of the winning region as well as of a winning strategy.  ...  This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata.  ...  Finally, an abstract pushdown parity game is a parity game played on such an abstract pushdown arena where the colouring function is defined as above.  ... 
arXiv:2010.06361v1 fatcat:zit3yx6ti5bvljehpympuwklka

Relational semantics of linear logic and higher-order model-checking [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
We show how to extend this result to alternating parity automata (APT) by introducing a parametric version of the exponential modality of linear logic, capturing the formal properties of colors (or priorities  ...  Moreover, the interaction between the relational interpretations of the HORS and of the ATA identifies the set of accepting states of the tree automaton against the infinite tree generated by the recursion  ...  strategy for Eve in the parity game defined in [15] .  ... 
arXiv:1501.04789v3 fatcat:4yd3ryhkpzgzfhpy52fctlmglq
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