Murphy, Niall and Woods, Damien
(2009)
The Computational Complexity of Uniformity
and Semiuniformity in Membrane Systems.
In: Seventh Brainstorming Week on Membrane Computing, 2 – 6 February 2009, Seville.
(Unpublished)
Abstract
We investigate computing models that are presented as families of finite
computing devices with a uniformity condition on the entire family. Examples include
circuits, membrane systems, DNA computers, cellular automata, tile assembly systems,
and so on. However, in this list there are actually two distinct kinds of uniformity conditions.
The first is the most common and wellunderstood, where each input length is mapped
to a single computing device that computes on the finite set of inputs of that length. The
second, called semiuniformity, is where each input is mapped to a computing device for
that input. The former notion is wellknown and used in circuit complexity, while the
latter notion is frequently found in literature on natureinspired computing models, from
the past 20 years or so.
Are these two notions distinct or not? For many models it has been found that these
notion are in fact the same, in the sense that the choice of uniformity or semiuniformity
leads to characterisations of the same complexity classes. Here, we buck this trend and
show that these notions are actually distinct: we give classes of uniform membrane systems
that are strictly weaker than their semiuniform counterparts. This solves a known
open problem in the theory of membrane systems.
Item Type: 
Conference or Workshop Item
(Paper)

Additional Information: 
Niall Murphy is funded by the Irish Research Council for Science, Engineering
and Technology. Damien Woods is supported by a Project of Excellence from the
Junta de Andaluca, grant number TIC581. 
Keywords: 
Computational Complexity; Uniformity; Semiuniformity; Membrane Systems; 
Academic Unit: 
Faculty of Science and Engineering > Computer Science 
Item ID: 
2497 
Depositing User: 
CS Editor

Date Deposited: 
13 Apr 2011 15:49 
Refereed: 
No 
URI: 

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