On Distributed Solution to SAT by Membrane Computing

Abstract

Tissue P systems with evolutional communication rules and cell division (TPec, for short) are a class of bio-inspired parallel computational models, which can solve NP-complete problems in a feasible time. In this work, a variant of TPec, called $k$-distributed tissue P systems with evolutional communication and cell division ($k\text{-}\Delta_{TP_{ec}}$, for short) is proposed. A uniform solution to the SAT problem by $k\text{-}\Delta_{TP_{ec}}$ under balanced fixed-partition is presented. The solution provides not only the precise satisfying truth assignments for all Boolean formulas, but also a precise amount of possible such satisfying truth assignments. It is shown that the communication resource for one-way and two-way uniform $k$-P protocols are increased with respect to $k$; while a single communication is shown to be possible for bi-directional uniform $k$-P protocols for any $k$. We further show that if the number of clauses is at least equal to the square of the number of variables of the given boolean formula, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem are more efficient than TPec as show in \cite{bosheng2017}; if the number of clauses is equal to the number of variables, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem work no much faster than TPec.

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Published
2018-05-27
How to Cite
ADORNA, Henry N.; PAN, Linqiang; SONG, Bosheng. On Distributed Solution to SAT by Membrane Computing. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 13, n. 3, p. 303-320, may 2018. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/3217>. Date accessed: 09 july 2020. doi: https://doi.org/10.15837/ijccc.2018.3.3217.