Event-State Duality: The Enriched Case
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
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A Chu space is a binary relation between two sets. In this thesis we show that Chu spaces form a non-interleaving model of concurrency which extends event structures while endowing them with an algebraic structure whose natural logic is linear logic. We provide several equivalent definitions of Chu spaces, including two pictorial representations. Chu spaces represent processes as automata or schedules, and Chu duality gives a simple way of converting between schedules and automata. We show that Chu spaces can represent various concurrency concepts like conflict, temporal precedence and internal and external choice, and they distinguish between causing and enabling events. We present a process algebra for Chu spaces including the standard combinators like parallel composition, sequential composition, choice, interaction, restriction, and show that the various operational identities between these hold for Chu spaces. The solution of recursive domain equations is possible for most of these operations, giving us an expressive specification and programming language. We define a history preserving equivalence between Chu spaces, and show that it preserves the causal structure of a process.