Process Algebra as Abstract Data Types
Ruqian Lu, Lixing Li, Yun Shang, Xiaoyu Li

TL;DR
This paper introduces an algebraic semantics for process algebra using seed algebras, establishing a novel way to characterize process bisimulation through deep isomorphisms of non-hidden closures.
Contribution
It develops seed algebras and hidden operations to model process behaviors, providing a new algebraic framework for understanding bisimulation in process algebra.
Findings
Bisimulation corresponds to deep isomorphism of seed algebras.
Introduces hidden operations to handle non-determinism.
Establishes relations among 10 different bisimulation types.
Abstract
In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type of algebra, the seed algebra, which describes exactly the behavior of a process within a labeled transition system. We have shown the possibility of characterizing the bisimulation of two processes with the isomorphism of their corresponding seed algebras. We pointed out that the traditional concept of isomorphism of algebra does not apply here, because there is even no one-one correspondence between the elements of two seed algebras. The lack of this one-one correspondence comes from the non-deterministic choice of transitions of a process. We introduce a technique of hidden operations to mask unwanted details of elements of a seed algebra, which only reflect non-determinism or other implicit control mechanism of process transition.…
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Taxonomy
TopicsFormal Methods in Verification · Cognitive Computing and Networks · Advanced Database Systems and Queries
