Evolving MultiAlgebras unify all usual sequential computation models

TL;DR

This paper introduces Evolving MultiAlgebras (EMAs), a semantic extension of Abstract State Machines, unifying various sequential computation models by replacing syntactic programs with simple, definable functionals.

Contribution

It proposes EMAs, a modified ASM framework that naturally unifies different sequential computation models through semantic definitions, improving upon the simulation limitations of traditional ASMs.

Findings

EMAs correspond to extended machine models and grammar models.

EMAs maintain the computation approach despite model modifications.

The framework unifies all sequential computation paradigms.

Abstract

It is well-known that Abstract State Machines (ASMs) can simulate "step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some type do not constitute a natural class among all ASMs. We modify Gurevich's notion of ASM to that of EMA ("Evolving MultiAlgebra") by replacing the program (which is a syntactic object) by a semantic object: a functional which has to be very simply definable over the static part of the ASM. We prove that very natural classes of EMAs correspond via "literal identifications" to slight extensions of the usual machine models and also to grammar models. Though we modify these models, we keep their computation approach: only some contingencies are modified. Thus, EMAs appear as the mathematical model unifying all kinds of sequential computation paradigms.