Step Automata

TL;DR

This paper introduces step automata and step Turing machines, extending traditional automata and Turing machines to incorporate atomic step execution, bridging the gap between classical computation models and concurrency.

Contribution

It proposes the novel concepts of step automata and step Turing machines, enabling atomic step execution in automata and Turing machines, linking classical models with concurrent computation.

Findings

Defines step automata and step Turing machines.

Establishes the theoretical framework for atomic step execution.

Bridges classical automata theory with concurrent computation models.

Abstract

For computation, there existed Turing machine and later-matured automata theory. For low-level parallel computation, there existed variants of Turing machine, such as two-tapes Turing machine and multi-tapes Turing machine. In the literature, the combination of computation and concurrency is still active, such the combination of automata and processes, and the introduction of concurrency into automata: the so-called pomset automata and branch automata. But the linkage of Turing machine and concurrent automaton is still absent. In this paper, we propose the concepts of step automaton and step Turing machine (STM), which a natural extension to traditional automaton and classical Turing machine just allowing an automaton or Turing machine to execute a step of atomic actions (without partial orders pairwise).