P Systems Computing the Period of Irreducible Markov Chains

Mónica Cardona-Roca, M. Ángels Colomer-Cugat, Agustín Riscos-Núñez, Miquel Rius-Font


It is well known that any irreducible and aperiodic Markov chain has exactly one stationary distribution, and for any arbitrary initial distribution, the se- quence of distributions at time n converges to the stationary distribution, that is, the Markov chain is approaching equilibrium as n→∞.
In this paper, a characterization of the aperiodicity in existential terms of some state is given. At the same time, a P system with external output is associated with any irre- ducible Markov chain. The designed system provides the aperiodicity of that Markov chain and spends a polynomial amount of resources with respect to the size of the in- put. A comparative analysis with respect to another known solution is described.


Markov chain, P Sytems, Membrane Computing

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DOI: https://doi.org/10.15837/ijccc.2009.3.2437

Copyright (c) 2017 Mónica Cardona-Roca, M. Ángels Colomer-Cugat, Agustín Riscos-Núñez, Miquel Rius-Font

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