Characterizing Tractability by Tissue-Like P Systems

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In the framework of recognizer cell–like membrane systems it is well known that the construction of exponential number of objects in polynomial time is not enough to efficiently solve NP–complete problems. Nonetheless, it may be sufficient to create an exponential number of membranes in polynomial time.

In this paper, we study the computational efficiency of recognizer tissue P systems with communication (symport/antiport) rules and division rules. Some results have been already obtained in this direction: (a) using communication rules and making no use of division rules, only tractable problems can be efficiently solved; (b) using communication rules with length three and division rules, NP–complete problems can be efficiently solved. In this paper, we show that the length of communication rules plays a relevant role from the efficiency point of view for this kind of P systems.