Nondeterministic finite automata based on star cellular nonlinear networks

Oscillatory networks represent the most appropriate paradigm for modeling almost all physical, biological and chemical systems that exhibit periodic collective behavior. Under the assumption that the entities composing the system interact weakly, it has been shown that such weakly connected oscillatory networks (WCONs) can be exploited for dynamic pattern recognition. In this manuscript we have considered WCONs, composed by nonlinear oscillators that admit of a Lurpsilae model, having the star topology. We have shown that, the finite sequences of binary patterns explored by the WCON can be identified by exploiting the approximate expression of the phase equation obtained by using a technique based on the describing function technique and of Malkinpsilas Theorem. This is due to the fact that the finite binary sequences are in one-to-one correspondence with the equilibria of the phase equation. Finally, we have shown that such finite sequences of binary patterns can be meant as epsiv-closure sets in NFAs-epsiv. Such results open the possibility to implement regular languages through WCONs by developing algorithms for designing the nonlinear couplings among the oscillators.