Linear process algebra

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, se-quence, and choice. Linear process algebra or LPA is the theory of this framework. LPA resembles Girard’s linear logic with the differences at-tributable 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 indepen-dent concurrency or parallel play. The traditional sequential operations of sequence and choice exploit process-specific state information catering for notions of transition and cancellation.