Following are the two main results of this paper, that the Radius and the Covering Radius of a code are hard to compute. Proof: First, note that this problem is in NP, as a center of a k-radius sphere which contains C is a linear time veriiable witness to the fact that R(C) k. To show that the problem is NP hard, we reduce 3SAT to MR. Given a 3CNF formula = ! 1 ^ : : : ^ ! t ; we deene the foll...

Assuming 3-SAT formulas are hard to refute on average, Feige showed some approximation hardness results for several problems like min bisection, dense k-subgraph, max bipartite clique and the 2-catalog segmentation problem. We show a similar result for max bipartite clique, but under the assumption, 4-SAT formulas are hard to refute on average. As falsity of the 4-SAT assumption implies falsity...

The last few years have seen significant advances in Boolean satisfiability (SAT) solving. This has lead to the successful deployment of SAT solvers in a wide range of problems in Engineering and Computer Science. In general, most SAT solvers are applied to Boolean decision problems that are expressed in conjunctive normal form (CNF). While this input format is applicable to some engineering ta...

Car sequencing is a well known NP-complete problem. This paper introduces encodings of this problem into CNF based on sequential counters. We demonstrate that SAT solvers are powerful in this domain and report new lower bounds for the benchmark set in the CSPLib.

We present a compiler that translates a problem speciica-tion into a propositional satissability test (SAT). Problems are speciied in a logic-based language, called np-spec, which allows the deenition of complex problems in a highly declarative way, and whose expressive power is such to capture exactly all problems which belong to the complexity class NP. The target SAT instance is solved using...

Given a Boolean function as input, a fundamental problem is to find a Boolean circuit with the least number of elementary gates (AND, OR, NOT) that computes the function. The problem generalises naturally to the setting of multiple Boolean functions: find the smallest Boolean circuit that computes all the functions simultaneously. We study an NP-complete variant of this problem titled Ensemble ...

Boolean satisfiability (SAT) is of central importance in many areas of Operations Research and Computer Science. In its general (conjunctive normal) form, the problem can be stated as follows. There is a number of Boolean (binary) variables generically called “literals,” and a number of covertype constraints implicitly defined over these variables, called “clauses.” Pairs of the literals may be...

In this paper, we are interested in the Maximum Satisfiability Problem (MAX-SAT) which is an optimization variant of the Boolean satisfiability problem (SAT). SAT is of a central importance in various areas of computer science, including theoretical computer science, algorithmic, artificial intelligence, hardware design and verification. Formally, given a set of m clauses C = {C1;C2 . . . Cm} i...

We perform a comprehensive study of mappings between constraint satisfaction problems (CSPs) and propositional satissability (SAT). We analyse four diierent mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, we compare the impact of achieving arc-consistency on the CSP with unit propagation on the SAT problem. We then extend these results to CSP algorithms ...

We present schemes to reduce the compilation time of conngurable hardware that solves Boolean Satiss-ability. The SAT solver presented by Zhong in last year's FCCM conference has a large compilation time overhead mainly due to placement and routing of many FPGAs. We attack the problem on 3 fronts. First, we partitioning the SAT solver into instance-speciic and instance non-speciic components. S...