Logarithmic SAT Solution with Membrane Computing

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