Maximum satisfiability problem

About: Maximum satisfiability problem is a research topic. Over the lifetime, 2153 publications have been published within this topic receiving 46952 citations.

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Abstract: We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least.87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of 1/2 for MAX CUT and 3/4 or MAX 2SAT. Slight extensions of our analysis lead to a.79607-approximation algorithm for the maximum directed cut problem (MAX DICUT) and a.758-approximation algorithm for MAX SAT, where the best previously known approximation algorithms had performance guarantees of 1/4 and 3/4, respectively. Our algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.

Learning Decision Lists

Abstract: This paper introduces a new representation for Boolean functions, called decision lists, and shows that they are efficiently learnable from examples. More precisely, this result is established for k-;DL – the set of decision lists with conjunctive clauses of size k at each decision. Since k-DL properly includes other well-known techniques for representing Boolean functions such as k-CNF (formulae in conjunctive normal form with at most k literals per clause), k-DNF (formulae in disjunctive normal form with at most k literals per term), and decision trees of depth k, our result strictly increases the set of functions that are known to be polynomially learnable, in the sense of Valiant (1984). Our proof is constructive: we present an algorithm that can efficiently construct an element of k-DL consistent with a given set of examples, if one exists.

Test pattern generation using Boolean satisfiability

Abstract: The author describes the Boolean satisfiability method for generating test patterns for single stuck-at faults in combinational circuits. This new method generates test patterns in two steps: first, it constructs a formula expressing the Boolean difference between the unfaulted and faulted circuits, and second, it applies a Boolean satisfiability algorithm to the resulting formula. This approach differs from previous methods now in use, which search the circuit structure directly instead of constructing a formula from it. The new method is general and effective. It allows for the addition of heuristics used by structural search methods, and it has produced excellent results on popular test pattern generation benchmarks. >

Computational limitations on learning from examples

Abstract: The computational complexity of learning Boolean concepts from examples is investigated. It is shown for various classes of concept representations that these cannot be learned feasibly in a distribution-free sense unless R = NP. These classes include (a) disjunctions of two monomials, (b) Boolean threshold functions, and (c) Boolean formulas in which each variable occurs at most once. Relationships between learning of heuristics and finding approximate solutions to NP-hard optimization problems are given.