Reactive Turing Machines

TL;DR

This paper introduces reactive Turing machines (RTMs) that extend classical Turing machines with interaction, demonstrating their ability to simulate various transition systems and establishing their universality and correspondence with process calculus.

Contribution

It defines RTMs with interaction, proves their simulation capabilities for effective transition systems, and explores their universality and relationship with process calculi.

Findings

RTMs can simulate all computable transition systems with bounded branching.

Existence of universal RTMs modulo branching bisimilarity.

Parallel composition of RTMs can be simulated by a single RTM.

Abstract

We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system with a bounded branching degree is simulated modulo divergence-preserving branching bisimilarity by an RTM, and that every effective transition system is simulated modulo the variant of branching bisimilarity that does not require divergence preservation. We conclude from these results that the parallel composition of (communicating) RTMs can be simulated by a single RTM. We prove that there exist universal RTMs modulo branching bisimilarity, but these essentially employ divergence to be able to simulate an RTM of arbitrary branching degree. We also prove that modulo divergence-preserving branching bisimilarity there are RTMs that are universal up to their own branching degree. Finally, we establish a correspondence between executability and finite definability in a simple process calculus.