Suguru Tamaki

A Satisfiability Algorithm and Average-Case Hardness for Formulas over the Full Binary Basis

We present a moderately exponential time algorithm for the satisfiability of Boolean formulas over the full binary basis. For formulas of size at most

Improved Randomized Algorithms for 3-SAT

cn

On the boolean connectivity problem for horn relations

, our algorithm runs in time

On the Boolean connectivity problem for Horn relations

2^{(1-\mu_c)n}

Beating brute force for systems of polynomial equations over finite fields

for some constant

Circuit Size Lower Bounds and #SAT Upper Bounds Through a General Framework

\mu_c>0

Bounded Depth Circuits with Weighted Symmetric Gates: Satisfiability, Lower Bounds and Compression

. As a byproduct of the running time analysis of our algorithm, we get strong average-case hardness of affine extractors for linear-sized formulas over the full binary basis.

Improved Exact Algorithms for Mildly Sparse Instances of Max SAT

This pager gives a new randomized algorithm which solves 3-SAT in time O(1.32113 n ). The previous best bound is O(1.32216 n ) due to Rolf (J. SAT, 2006). The new algorithm uses the same approach as Iwama and Tamaki (SODA 2004), but exploits the non-uniform initial assignment due to Hofmeister et al. (STACS 2002) against the Schoning’s local search (FOCS 1999).

Solving Sparse Instances of Max SAT via Width Reduction and Greedy Restriction

Gopalan et al. studied in ICALP06 [17] connectivity properties of the solution-space of Boolean formulas, and investigated complexity issues on the connectivity problems in Schaefers framework. A set S of logical relations is Schaefer if all relations in S are either bijunctive, Horn, dual Horn, or affine. They conjectured that the connectivity problem for Schaefer is in P. We disprove their conjecture by showing that there exists a set S of Horn relations such that the connectivity problem for S is coNP-complete. We also show that the connectivity problem for bijunctive relations can be solved in O(min{n|φ|, T(n)}) time, where n denotes the number of variables, φ denotes the corresponding 2-CNF formula, and T(n) denotes the time needed to compute the transitive closure of a directed graph of n vertices. Furthermore, we investigate a tractable aspect of Horn and dual Horn relations with respect to characteristic sets.

The complexity of the Hajós calculus for planar graphs

Gopalan et al. studied in [P. Gopalan, P.G. Kolaitis, E.N. Maneva, C.H. Papadimitriou, The connectivity of Boolean satisfiability: computational and structural dichotomies, in: Proceedings of the 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006, 2006, pp. 346-357] and [P. Gopalan, P.G. Kolaitis, E.N. Maneva, C.H. Papadimitriou, The connectivity of Boolean satisfiability: computational and structural dichotomies, SIAM J. Comput. 38 (6) (2009) 2330-2355] connectivity properties of the solution-space of Boolean formulas, and investigated complexity issues on the connectivity problems in Schaefers framework. A set S of logical relations is Schaefer if all relations in S are either bijunctive, Horn, dual Horn, or affine. They first conjectured that the connectivity problem for Schaefer is in P. We disprove their conjecture by showing that there exists a set S of Horn relations such that the connectivity problem for S is coNP-complete. We also investigate a tractable aspect of Horn and dual Horn relations with respect to characteristic sets.