Imperative process algebra and models of computation

TL;DR

This paper explores the use of an imperative process algebra based on ACP to precisely model various computational models, including sequential and parallel machines, and extends it to probabilistic variants with complexity measures.

Contribution

It demonstrates that the imperative process algebra can accurately describe different models of computation and their complexity, including probabilistic models, advancing formal methods in computational theory.

Findings

Process algebra effectively models sequential and parallel computation.

It provides a formal framework for complexity measures.

Probabilistic models are incorporated with complexity analysis.

Abstract

Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an imperative process algebra based on ACP (Algebra of Communicating Processes). In this paper, it is investigated whether the imperative process algebra concerned can play a role in the field of models of computation.It is demonstrated that the process algebra is suitable to describe in a mathematically precise way models of computation corresponding to existing models based on sequential, asynchronous parallel, and synchronous parallel random access machines as well as time and work complexity measures for those models. A probabilistic variant of the model based on sequential random access machines and complexity measures for it are also described.