Linear Process Algebra

Abstract

Abstract.A linear process is a system of events and states related by an inner product, on which are defined the behaviorally motivated operations of tensor product or orthocurrence, sum or concurrence, sequence, and choice. Linear process algebra or LPA is the theory of this framework. LPA resembles Girard's linear logic with the differences attributable to its focus on behavior instead of proof. As with MLL the multiplicative part can be construed via the Curry-Howard isomorphism as an enrichment of Boolean algebra. The additives cater for independent concurrency or parallel play. The traditional sequential operations of sequence and choice exploit process-specific state information catering for notions of transition and cancellation. BackgroundComputation itself, as distinct from its infrastructure (operating systems, programming languages, etc.) and applications (graphics, robotics, databases, etc.), has two main aspects, algorithmic and logical. The algorithmic aspect serves programmers by providing techniques for the design and analysis of programs. The logical aspect serves language designers, compiler writers, documentation writers, and program verification by proposing suitable concepts for the operations and constants of a language (abstract syntax), giving them meanings and names (semantics and concrete syntax), showing how to reason about them (logic), and studying their structure (abstract algebra).Originally computation was performed on a single computer under the control of a central processing unit. Parallel and distributed computing emerged from the infrastructure with the advent of multiprocessors and networking, enhancing the applications at the expense of complicating both the algorithmic and formal aspects of computation. This paper focuses on the latter.Formal methods divide broadly into logical and algebraic. On the logical side we find Amir Pnueli's temporal logic [45], which speaks of a single universal process from the point of view of a neutral observer. Pnueli has called this 1 More recent follow-up remarks and expansions on this paper may be found at