Sublinear P system solutions to NP-complete problems

Many membrane systems (e.g. P System), including cP systems (P Systems with compound terms), have been used to solve efficiently many NP-hard problems, often in linear time. However, these solutions have been independent of each other and have not utilised the theory of reductions. This work presents a sublinear solution to k-SAT and demonstrates that k-colouring can be reduced to k-SAT in constant time. This work demonstrates that traditional reductions are efficient in cP systems and that they can sometimes produce more efficient solutions than the previous problem-specific solutions

Logarithmic SAT Solution with Membrane Computing

P systems have been known to provide efficient polynomial (often linear) deterministic solutions to hard problems. In particular, cP systems have been shown to provide very crisp and efficient solutions to such problems, which are typically linear with small coefficients. Building on a recent result by Henderson et al., which solves SAT in square-root-sublinear time, this paper proposes an orders-of-magnitude-faster solution, running in logarithmic time, and using a small fixed-sized alphabet and ruleset (25 rules). To the best of our knowledge, this is the fastest deterministic solution across all extant P system variants. Like all other cP solutions, it is a complete solution that is not a member of a uniform family (and thus does not require any preprocessing). Consequently, according to another reduction result by Henderson et al., cP systems can also solve k-colouring and several other NP-complete problems in logarithmic time

Cube-and-Conquer approach for SAT solving on grids

Our goal is to develop techniques for using distributed computing re- sources to efficiently solve instances of the propositional satisfiability problem (SAT). We claim that computational grids provide a distributed computing environment suitable for SAT solving. In this paper we apply the Cube and Conquer approach to SAT solving on grids and present our parallel SAT solver CCGrid (Cube and Conquer on Grid) on computational grid infrastructure. Our solver consists of two major components. The master application runs march_cc, which applies a lookahead SAT solver, in order to partition the input SAT instance into work units distributed on the grid. The client application executes an iLingeling instance, which is a multi-threaded CDCL SAT solver. We use BOINC middleware, which is part of the SZTAKI Desktop Grid package and supports the Distributed Computing Application Programming Interface (DC-API). Our preliminary results suggest that our approach can gain significant speedup and shows a potential for future investigation and development. Keywords: grid, SAT, parallel SAT solving, lookahead, march_cc, iLingeling, SZTAKI Desktop Grid, BOINC, DC-AP

In Memoriam, Solomon Marcus

This book commemorates Solomon Marcus’s fifth death anniversary with a selection of articles in mathematics, theoretical computer science, and physics written by authors who work in Marcus’s research fields, some of whom have been influenced by his results and/or have collaborated with him