Distributed Games and Distributed Control for Asynchronous Systems

We introduce distributed games over asynchronous transition systems to model a distributed controller synthesis problem. A game involves two teams and is not turn-based: several players of both teams may simultaneously be enabled. We define distributed strategies based on the causal view that players have of the system. We reduce the problem of finding a winning distributed strategy with a given memory to finding a memoryless winning distributed strategy in a larger distributed game. We reduce the latter problem to finding a strategy in a classical 2-players game. This allows to transfer results from the sequential case to this distributed setting.

[1]  O. Kupermann,et al.  Synthesizing distributed systems , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[2]  Amir Pnueli,et al.  Distributed reactive systems are hard to synthesize , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[3]  Igor Walukiewicz,et al.  Distributed Games , 2003, FSTTCS.

[4]  P. S. Thiagarajan,et al.  A Decidable Class of Asynchronous Distributed Controllers , 2002, CONCUR.

[5]  Wojciech Zielonka,et al.  The Book of Traces , 1995 .

[6]  W. M. Wonham,et al.  The control of discrete event systems , 1989 .

[7]  Madhavan Mukund.  Hereditary History Preserving Bisimulation Is Decidable for Trace-Labelled Systems , 2002, FSTTCS.

[8]  Jean-Eric Pin,et al.  Infinite words - automata, semigroups, logic and games , 2004, Pure and applied mathematics series.

[9]  Marcin Jurdzinski,et al.  A Discrete Strategy Improvement Algorithm for Solving Parity Games , 2000, CAV.

[10]  Wieslaw Zielonka,et al.  Notes on Finite Asynchronous Automata , 1987, RAIRO Theor. Informatics Appl..

[11]  Wieslaw Zielonka.  Asynchronous Automata , 1995, The Book of Traces.

[12]  Wieslaw Zielonka,et al.  Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees , 1998, Theor. Comput. Sci..

[13]  P. S. Thiagarajan,et al.  Distributed Controller Synthesis for Local Specifications , 2001, ICALP.

[14]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains , 1979, Semantics of Concurrent Computation.

[15]  Yves Métivier,et al.  Asynchronous Mappings and Asynchronous Cellular Automata , 1993, Inf. Comput..

[16]  Moshe Tennenholtz,et al.  Distributed Games , 1998, TARK.

[17]  Wolfgang Thomas,et al.  Infinite Games and Verification (Extended Abstract of a Tutorial) , 2002, CAV.

[18]  Mogens Nielsen,et al.  Hereditary History Preserving Bisimilarity Is Undecidable , 1999, STACS.

[19]  Yves Métivier,et al.  Partial Commutation and Traces , 1997, Handbook of Formal Languages.

[20]  LogicsMarek A. Bednarczyk.  Hereditary History Preserving Bisimulations , 1991 .

[21]  Mogens Nielsen,et al.  Games and Logics for a Noninterleaving Bisimulation , 1995, Nord. J. Comput..