Alternating refinement relations
 Rajeev Alur,
 Thomas A. Henzinger,
 Orna Kupferman,
 Moshe Y. Vardi
 … show all 4 hide
Abstract
Alternating transition systems are a general model for composite systems which allow the study of collaborative as well as adversarial relationships between individual system components. Unlike in labeled transition systems, where each transition corresponds to a possible step of the system (which may involve some or all components), in alternating transition systems, each transition corresponds to a possible move in a game between the components. In this paper, we study refinement relations between alternating transition systems, such as “Does the implementation refine the set A of specification components without constraining the components not in A?” In particular, we generalize the definitions of the simulation and trace containment preorders from labeled transition systems to alternating transition systems. The generalizations are called alternating simulation and alternating trace containment. Unlike existing refinement relations, they allow the refinement of individual components within the context of a composite system description. We show that, like ordinary simulation, alternating simulation can be checked in polynomial time using a fixpoint computation algorithm. While ordinary trace containment is PSPACEcomplete, we establish alternating trace containment to be EXPTIMEcomplete. Finally, we present logical characterizations for the two preorders in terms of ATL, a temporal logic capable of referring to games between system components.
 R. Alur, T.A. Henzinger, and O. Kupferman. Alternatingtime temporal logic. In Proc. 38th Symp. on Foundations of Computer Science, pp. 100–109. IEEE Computer Society, 1997. Full version in CompositionalityThe Significant Difference. SpringerVerlag Lecture Notes in Computer Science, 1998.
 J. Balcazar, J. Gabarro, and M. Santha. Deciding bisimilarity is Pcomplete. Formal Aspects of Computing, 4:638–648, 1992. CrossRef
 J.Y. Halpern and R. Fagin. Modeling knowledge and action in distributed systems. Distributed Computing, 3:159–179, 1989. CrossRef
 M.R. Henzinger, T.A. Henzinger, and P.W. Kopke. Computing simulations on finite and infinite graphs. In Proc. 36rd Symp. on Foundations of Computer Science, pp. 453–462. IEEE Computer Society, 1995.
 N. Immerman. Number of quantifiers is better than number of tape cells. J. Computer and System Sciences, 22:384–406, 1981. CrossRef
 O. Kupferman and M.Y. Vardi. Verification of fair transition systems. Chicago J. Theoretical Computer Science, 1998(2).
 R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd Int. Joint Conf. on Artificial Intelligence, pp. 481–489. British Computer Society, 1971.
 R. Milner. Operational and algebraic semantics of concurrent processes. In Handbook of Theoretical Computer Science, Vol. B, pp. 1201–1242. Elsevier, 1990.
 D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267–276, 1987. CrossRef
 D.E. Muller and P.E. Schupp. Simulating alternating tree automata by nondeterministic automata: new results and new proofs of theorems of Rabin, McNaughton, and Safra. Theoretical Computer Science, 141:69–107, 1995. CrossRef
 L.S. Shapley. Stochastic games. In Proc. National Academy of Science, 39:1095–1100, 1953. CrossRef
 M.Y. Vardi and P. Wolper. Automatatheoretic techniques for modal logics of programs. J. Computer and System Sciences, 32:182–221, 1986. CrossRef
 M.Y. Vardi and P. Wolper. Reasoning about infinite computations. Information and Computation, 115:1–37, 1994. CrossRef
 Title
 Alternating refinement relations
 Book Title
 CONCUR'98 Concurrency Theory
 Book Subtitle
 9th International Conference Nice, France, September 8–11, 1998 Proceedings
 Pages
 pp 163178
 Copyright
 1998
 DOI
 10.1007/BFb0055622
 Print ISBN
 9783540648963
 Online ISBN
 9783540684558
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1466
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors
 Authors

 Rajeev Alur ^{(1)}
 Thomas A. Henzinger ^{(2)}
 Orna Kupferman ^{(2)}
 Moshe Y. Vardi ^{(3)}
 Author Affiliations

 1. Department of Computer and Information Science, University of Pennsylvania, 19104, Philadelphia, PA, USA
 2. Department of Electrical Engineering and Computer Sciences, University of California, 947201770, Berkeley, CA, USA
 3. Department of Computer Science, Rice University, 770051892, Houston, TX, USA
Continue reading...
To view the rest of this content please follow the download PDF link above.