Abstract
We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to solve the PSPACE-complete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved by the same P system) and uses only communication rules: evolution rules, as well as membrane division and dissolution rules, are not used. Our result shows that, as it happens with Turing machines, this model of P systems can solve in exponential time and polynomial space problems that cannot be solved in polynomial time, unless P = SPACE.
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Notes
An alternative definition, where the size of a configuration is given by the sum of the number of membranes and the number of bits required to store the objects they contain, has been considered in Porreca et al. (2009). However, the choice between the two definitions is irrelevant as far as the results of this paper are concerned.
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Acknowledgements
We would like to thank Damien Woods for the suggestion to avoid object evolution rules in our solution to Q3SAT. This work was partially supported by the Italian project FIAR 2007 “Modelli di calcolo naturale e applicazioni alla Systems Biology”.
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Porreca, A.E., Leporati, A., Mauri, G. et al. P systems with active membranes: trading time for space. Nat Comput 10, 167–182 (2011). https://doi.org/10.1007/s11047-010-9189-x
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DOI: https://doi.org/10.1007/s11047-010-9189-x