Abstract
We consider finite-state games as a model of nonterminating reactive computations. A natural type of specification is given by games with Streett winning condition (corresponding to automata accepting by conjunctions of fairness conditions). We present an algorithm which solves the problem of program synthesis for these specifications. We proceed in two steps: First, we give a reduction of Streett automata to automata with the Rabin chain (or parity) acceptance condition. Secondly, we develop an inductive strategy construction over Rabin chain automata which yields finite automata that realize winning strategies. For the step from Rabin chain games to winning strategies examples are discussed, based on an implementation of the algorithm.
Supported by Deutsche Forschungsgemeinschaft, projects Th 352/3-2 and Th 352/5-1.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
M. Abadi, L. Lamport, and P. Wolper. Realizable and unrealizable specifications of reactive systems. In G. Ausiello et al., editor, Automata, Languages, and Programming, volume 372 of LNCS, pages 1–17, Berlin, Heidelberg, New York, 1989. Springer-Verlag.
E. Asarin, O. Maler, and A. Pnueli. Symbolic controller synthesis for discrete and timed systems. In P. Antsaklis et al., editor, Hybrid Systems II, volume 999 of LNCS, pages 1–20, Berlin, Heidelberg, New-York, 1995. Springer-Verlag.
J. R. Büchi and L. H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295–311, 1969.
J. R. Büchi. State strategies for games in F σδ ∩ G δσ . J. Symb. Logic, 48:1171–1198, 1983.
E.A. Emerson and C.S. Jutla. Tree automata, mu-calculus and determinacy. In Proc. 32nd IEEE Symp. on the Foundations of Computing, pages 368–377, 1991.
Y. Gurevich and L. Harrington. Trees, automata, and games. In Proc 14th ACM Symp. on the Theory of computing, pages 60–65, San Fancisco, 1982.
D. Gale and F. M. Stewart. Infinite games with perfect information. Annals of Mathematical Studies, 28:245–266, 1953.
R. Kumar and V. K. Garg. Modeling and Control of Logical Discrete Event Systems. Kluwer Academic Publishers, Norwell, MA, USA, 1995.
R. McNaughton. Infinite games played on finite graphs. Ann. Pure Appl Logic, 65:149–184, 1993.
A.W. Mostowski. Games with forbidden positions. Technical Report Preprint No. 78, Uniwersytet Gdański, Instytyt Matematyki, 1991.
D.E. Muller and P.E. Schupp. Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of Rabin, McNaughton and Safra. Theoretical Computer Science, 141:69–107, 1995.
A. Muchnik. Games on infinite trees and automata with deadends: A new proof for the decidability of the monadic second order theory of two successors. Bulletin of the European Association for Theoretical Computer Science, 48:220–267, 1992.
A. Nerode, A. Yakhnis, and V. Yakhnis. Concurrent programs as strategies in games. In Moschovakis Y., editor, Logic from Computer Science. Springer, 1992.
A. Pnueli and R. Rosner. On the systhesis of a reactive module. In Proc. 16th ACM Sympos. on Principles of Prog. Lang., pages 179–190, Austin, 1989.
M. O. Rabin. Decidability of second-order theories and automata on infinite trees. Transactions of the American Mathematical Society, 141:1–35, 1969.
P. J. G. Ramadge and W. M. Wonham. The control of discrete event systems. Proceedings of the IEEE, 77, 1:81–98, 1989.
S. Safra. Exponential determinization for Ω-automata with strong-fairness acceptance condition. In Proc. 24th ACM Symposium on Theory of Computing (STOC), pages 275–282, 1992.
R.S. Streett. Propositional dynamic logic of looping and converse. Information and Control, 54: 121–141, 1982.
W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 4, pages 131–191. North-Holland, Amsterdam, 1990.
W. Thomas. On the synthesis of strategies in infinite games. In Ernst W. Mayr and Claude Puech, editors, STACS 95, volume 900 of LNCS, pages 1–13, Berlin, Heidelberg, New-York, 1995. Springer-Verlag.
J.G. Thistle and W.M. Wonham. Control of infinite behaviour of finite automata. SIAM J. of Control and Optimization, 32(4):1075–1097, 1994.
A. Yakhnis and V. Yakhnis. Gurevich — Harrington's games defined by finite automata. Ann. Pure Appl Logic, 62:265–294, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Buhrke, N., Lescow, H., Vöge, J. (1996). Strategy construction in infinite games with Streett and Rabin chain winning conditions. In: Margaria, T., Steffen, B. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 1996. Lecture Notes in Computer Science, vol 1055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61042-1_46
Download citation
DOI: https://doi.org/10.1007/3-540-61042-1_46
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61042-7
Online ISBN: 978-3-540-49874-2
eBook Packages: Springer Book Archive