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Limits on the number of satisfying assignments for CNS instances with n variables and m clauses are derived from various inequalities. Some bounds can be calculated in polynomial time, sharper bounds demand information about the distribution of the number of unsatisfied clauses. Quite generally, the number of satisfying assignments involve variance and mean of this distribution. For large formulae, m>>1, bounds vary with 2**n/n, so they may be of use only for instances with a large number of satisfying assignments.
We introduce a new algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not ha
A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in polynomial t
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is introduced
We present a (full) derandomization of HSSW algorithm for 3-SAT, proposed by Hofmeister, Schoning, Schuler, and Watanabe in [STACS02]. Thereby, we obtain an O(1.3303^n)-time deterministic algorithm for 3-SAT, which is currently fastest.
The notion of compliance in Multiset Rewriting Models (MSR) has been introduced for untimed models and for models with discrete time. In this paper we revisit the notion of compliance and adapt it to fit with additional nondeterminism specific for de