On models of a nondeterministic computation

TL;DR

This paper explores models of nondeterministic computation using deterministic multi-head 2-way automata with auxiliary memory, characterizing standard complexity classes without relying on alternation.

Contribution

It introduces a novel automata-based framework for nondeterministic computation that characterizes classical complexity classes without the use of alternation.

Findings

Standard complexity classes like L, NL, P, NP, PSPACE are characterized by these automata models.

The models differ from traditional ones by the absence of alternation in their definitions.

Restricted guesses with constraints are also considered in the characterization.

Abstract

In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is successful for some memory content. Also we consider the case of restricted guesses in which a guess should satisfy some constraint. We show that the standard complexity classes such as L, NL, P, NP, PSPACE can be characterized in terms of these models of nondeterministic computation. These characterizations differ from the well-known ones by absence of alternation.