Bisimulations, games and logic

In a recent paper by Joyal, Nielsen, and Winskel, bisimulation is defined in an abstract and uniform way across a wide range of di#erent models for concurrency . In this paper, following a recent trend in theoretical computer science, we characterize their abstract definition game-theoretically and logically in a non-interleaving model. Our characterizations appear as surprisingly simple extensions of corresponding characterizations of interleaving bisimulation. # Basic Research in Computer Science, Centre of the Danish National Research Foundation i Contents 1 Introduction 1 2 An Abstract Equivalence 4 3 Game Characterizations 8 3.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 A Characteristic Game for Interleaving Bisimulation . . . . . . 10 3.3 Allowing Opponent to Backtrack . . . . . . . . . . . . . . . . 12 4 A Path Logic 16 5 Conclusion 19 A Every Game Has a Winner 22 B Proofs From Section 3 22 B.1 From #-bisimilarity to #-equivalence . . . . . ..

Bisimulations, Games and Logic

In a recent paper by Joyal, Nielsen, and Winskel, bisimulation is defined in an abstract and uniform way across a wide range of different models for concurrency. In this paper, following a recent trend in theoretical computer science, we characterize their abstract definition game-theoretically and logically in a non-interleaving model. Our characterizations appear as surprisingly simple extensions of corresponding characterizations of interleaving bisimulation