On acceptance conditions for membrane systems: characterisations of L and NL

TL;DR

This paper explores how different acceptance conditions in membrane systems influence their computational power, showing that certain conditions characterize complexity classes NL and L through graph connectivity analysis.

Contribution

It provides a novel characterization of complexity classes NL and L based on acceptance conditions in membrane systems without dissolution.

Findings

Two acceptance conditions characterize NL.

Restricted acceptance conditions characterize L.

Connectivity properties of dependency graphs underpin these characterizations.

Abstract

In this paper we investigate the affect of various acceptance conditions on recogniser membrane systems without dissolution. We demonstrate that two particular acceptance conditions (one easier to program, the other easier to prove correctness) both characterise the same complexity class, NL. We also find that by restricting the acceptance conditions we obtain a characterisation of L. We obtain these results by investigating the connectivity properties of dependency graphs that model membrane system computations.