1,643 research outputs found
Boolean Satisfiability in Electronic Design Automation
Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks
An Overview of Backtrack Search Satisfiability Algorithms
Propositional Satisfiability (SAT) is often used as the underlying model for a significan
On the Computational Complexity of Non-dictatorial Aggregation
We investigate when non-dictatorial aggregation is possible from an
algorithmic perspective, where non-dictatorial aggregation means that the votes
cast by the members of a society can be aggregated in such a way that the
collective outcome is not simply the choices made by a single member of the
society. We consider the setting in which the members of a society take a
position on a fixed collection of issues, where for each issue several
different alternatives are possible, but the combination of choices must belong
to a given set of allowable voting patterns. Such a set is called a
possibility domain if there is an aggregator that is non-dictatorial, operates
separately on each issue, and returns values among those cast by the society on
each issue. We design a polynomial-time algorithm that decides, given a set
of voting patterns, whether or not is a possibility domain. Furthermore, if
is a possibility domain, then the algorithm constructs in polynomial time
such a non-dictatorial aggregator for . We then show that the question of
whether a Boolean domain is a possibility domain is in NLOGSPACE. We also
design a polynomial-time algorithm that decides whether is a uniform
possibility domain, that is, whether admits an aggregator that is
non-dictatorial even when restricted to any two positions for each issue. As in
the case of possibility domains, the algorithm also constructs in polynomial
time a uniform non-dictatorial aggregator, if one exists. Then, we turn our
attention to the case where is given implicitly, either as the set of
assignments satisfying a propositional formula, or as a set of consistent
evaluations of an sequence of propositional formulas. In both cases, we provide
bounds to the complexity of deciding if is a (uniform) possibility domain.Comment: 21 page
Statistical mechanics of the random K-SAT model
The Random K-Satisfiability Problem, consisting in verifying the existence of
an assignment of N Boolean variables that satisfy a set of M=alpha N random
logical clauses containing K variables each, is studied using the replica
symmetric framework of diluted disordered systems. We present an exact
iterative scheme for the replica symmetric functional order parameter together
for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the
number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to
predict a first order jump at the threshold where the Boolean expressions
become unsatisfiable with probability one, is thoroughly displayed. In the case
K=2, the (rigorously known) critical value (alpha=1) of the number of clauses
per Boolean variable is recovered while for K>=3 we show that the system
exhibits a replica symmetry breaking transition. The annealed approximation is
proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section
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