Murphy, Niall and Woods, Damien (2014) Uniformity is weaker than semi-uniformity for some membrane systems. Fundamenta Informaticae, 134 (1-2). pp. 129-152. ISSN 1875-8681

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Abstract

We investigate computing models that are presented as families of finite computing devices with a uniformity condition on the entire family. Examples of such models include Boolean circuits, membrane systems, DNA computers, chemical reaction networks and tile assembly systems, and there are many others. However, in such models there are actually two distinct kinds of uniformity condition. The first is the most common and well-understood, where each input length is mapped to a single computing device (e.g. a Boolean circuit) that computes on the finite set of inputs of that length. The second, called semi-uniformity, is where each input is mapped to a computing device for that input (e.g. a circuit with the input encoded as constants). The former notion is well-known and used in Boolean circuit complexity, while the latter notion is frequently found in literature on nature-inspired computation from the past 20 years or so. Are these two notions distinct? For many models it has been found that these notions are in fact the same, in the sense that the choice of uniformity or semi-uniformity leads to characterisations of the same complexity classes. In other related work, we showed that these notions are actually distinct for certain classes of Boolean circuits. Here, we give analogous results for membrane systems by showing that certain classes of uniform membrane systems are strictly weaker than the analogous semi-uniform classes. This solves a known open problem in the theory of membrane systems. We then go on to present results towards characterising the power of these semi-uniform and uniform membrane models in terms of NL and languages reducible to the unary languages in NL, respectively.

Item Type:	Article
Keywords:	membranes systems; computational complexity; uniform families; semi-uniform families; tally languages;
Academic Unit:	Faculty of Science and Engineering > Computer Science Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	12407
Identification Number:	https://doi.org/10.3233/FI-2014-1095
Depositing User:	Damien Woods
Date Deposited:	10 Feb 2020 18:12
Journal or Publication Title:	Fundamenta Informaticae
Publisher:	IOS Press
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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