P Systems Computing the Period of Irreducible Markov Chains

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. Ministerio de Educación y Ciencia TIN2006–13425 Junta de Andalucía P08-TIC-04200