Pdmi Preprint | 19/1998 Hard Formulas for Sat Local Search Algorithms

PDMI PREPRINT — 20/1998 Lifting formulas II

From Spin Glasses to Hard Satisfiable Formulas

We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably “glassy” behavior; that is, it has many local optima with large energy barriers between them, so that local search algorithms get stuck and have difficulty finding the true ground state, i.e., the unique satisfying assignment. ...

PDMI PREPRINT | 01/2000 ALGORITHMS FOR k-SAT BASED ON COVERING CODES

ALGORITHMS FOR k-SAT BASED ON COVERING CODES Evgeny DANTSIN1 Edward A. HIRSCH2 Russian A ademy of S ien es Russian A ademy of S ien es Steklov Mathemati al Institute Steklov Mathemati al Institute St. Petersburg Department St. Petersburg Department 27 Fontanka, St. Petersburg, 191011 27 Fontanka, St. Petersburg, 191011 Russia Russia E-mail: dantsin pdmi.ras.ru E-mail: hirs h pdmi.ras.ru January...

Single-solution Random 3-SAT Instances

We study a class of random 3-SAT instances having exactly one solution. The properties of this ensemble considerably differ from those of a random 3-SAT ensemble. It is numerically shown that the running time of several complete and stochastic local search algorithms monotonically increases as the clause density is decreased. Therefore, there is no easy-hard-easy pattern of hardness as for stan...

A Probability Distribution Strategy with Efficient Clause Selection for Hard Max-SAT Formulas

Many real-world problems involving constraints can be regarded as instances of the Max-SAT problem, which is the optimization variant of the classic satisfiability problem. In this paper, we propose a novel probabilistic approach for Max-SAT called ProMS. Our algorithm relies on a stochastic local search strategy using a novel probability distribution function with two strategies for picking va...