Unconventional complexity classes in unconventional computing (extended abstract)

TL;DR

This paper explores unconventional computing models that transcend traditional complexity classes like P and PSPACE, characterizing intermediate complexity classes through variants of cellular automata and membrane systems.

Contribution

It introduces variants of cellular automata and membrane systems that characterize intermediate complexity classes beyond the usual P and PSPACE.

Findings

Unconventional models can characterize intermediate complexity classes.

Some models escape the P vs. PSPACE dichotomy.

Discussion of reasons behind these complexity characterizations.

Abstract

Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial time (and in the maximally parallel way, where this applies). We discuss variants of cellular automata and membrane systems that escape this dichotomy and characterise intermediate complexity classes, usually defined in terms of Turing machines with oracles, as well as some possible reasons why this happens.