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Solving the ST-Connectivity Problem with Pure Membrane Computing Techniques
Zsolt Gazdag,Miguel Ángel Gutiérrez Naranjo +1 more
- pp 207-219
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TLDR
In this article, the authors present three designs of uniform families of P systems that solve the decision problem STCON by using pure Membrane Computing strategies: P systems with membrane creation and active membranes with dissolution and without polarizations.Abstract:
In Membrane Computing, the solution of a decision problem \(X\) belonging to the complexity class P via a polynomially uniform family of recognizer P systems is trivial, since the polynomial encoding of the input can involve the solution of the problem. The design of such solution has one membrane, two objects, two rules and one computation step. Stricto sensu, it is a solution in the framework of Membrane Computing, but it does not use Membrane Computing strategies. In this paper, we present three designs of uniform families of P systems that solve the decision problem STCON by using Membrane Computing strategies (pure Membrane Computing techniques): P systems with membrane creation, P systems with active membranes with dissolution and without polarizations and P systems with active membranes without dissolution and with polarizations. Since STCON is NL-complete, such designs are constructive proofs of the inclusion of NL in \(\mathbf{PMC}_\mathcal{MC}\), \(\mathbf{PMC}_{\mathcal{AM}^0_{+d}}\) and \(\mathbf{PMC}_{\mathcal{AM}^+_{-d}}\).read more
Citations
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Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes
Zsolt Gazdag,Gábor Kolonits +1 more
TL;DR: In this article, the authors considered three restricted variants of P systems with active membranes: (1) P systems using send-out communication rules only, (2) P system using elementary membrane division and dissolution rules only and (3) polarizationless P system with dissolution and unit evolution rules only.
On acceptance conditions for membrane systems: characterisations of L and NL
Niall Murphy,Damien Woods +1 more
TL;DR: In this article, the authors investigate the affect of various acceptance conditions on membrane systems without dissolution and demonstrate that two particular acceptance conditions (one easier to program, the other easier to prove correctness) both characterise the same complexity class, NL.
References
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Book
The Oxford Handbook of Membrane Computing
TL;DR: This handbook provides both a comprehensive survey of available knowledge and established research topics, and a guide to recent developments in the field, covering the subject from theory to applications.
A Polynomial Complexity Class in P Systems Using Membrane Division.
TL;DR: The complexity class PMCF of all decision problems solvable in polynomial time by a family of P systems belonging to a given class of membrane systems with input, F, was introduced in this article.
Book ChapterDOI
Solving numerical NP-complete problems with spiking neural P systems
TL;DR: By using maximal parallelism, any given integer number can be converted from the usual binary notation to the unary form, and thus any given spiking neural P system can be initialized with the required (exponential) number of spikes in polynomial time.
Journal ArticleDOI
The computational power of membrane systems under tight uniformity conditions
Niall Murphy,Damien Woods +1 more
TL;DR: It turns out that the computational power of some systems is lowered from P to NL when using AC0-semi-uniformity, so it is argued that this is a more reasonable uniformity notion for these systems as well as others.
Journal ArticleDOI
A uniform solution to SAT using membrane creation
TL;DR: This paper provides the first uniform, efficient solution to the SAT problem in the framework of recogniser P systems with membrane creation using dissolution rules and shows the surprising role of the apparently ''innocent'' operation of membrane dissolution.