Model Counting Using the Inclusion-Exclusion Principle
نویسندگان
چکیده
The inclusion-exclusion principle is a well-known mathematical principle used to count the number of elements in the union of a collection of sets in terms of intersections of sub-collections. We present an algorithm for counting the number of solutions of a given k-SAT formula using the inclusion-exclusion principle. The key contribution of our work consists of a novel subsumption pruning technique. Subsumption pruning exploits the alternating structure of the terms involved in the inclusion-exclusion principle to discover term cancellations that can account for the individual contributions of a large number of terms in a single step.
منابع مشابه
The Inclusion-Exclusion Principle for IF-States
Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...
متن کاملCounting Models using Extension Rules
In recent years we have viewed tremendous improvements in the field of Propositional satisfiability (SAT). Many NPcomplete problems from a variety of domains, such as classic planning problems (Kautz 1999), have been compiled into SAT instances, and solved effectively by SAT solvers (Zhang et al 2001). On the other hand, the problem of counting the number of models of a prepositional formula (#...
متن کاملCounting Problems and the Inclusion-Exclusion Principle
In this paper, we present improved techniques for computing and getting bounds on the cardinality of a union of sets using the inclusion-exclusion principle and Bonferroni inequalities. We organize the terms involved in the inclusionexclusion sum as a tree, showing that a set inclusion between a parent and its children yields a cancellation, where we may prune an entire subtree. Next, we provid...
متن کاملPower-Law Based Estimation of Set Similarity Join Size
We propose a novel technique for estimating the size of set similarity join. The proposed technique relies on a succinct representation of sets using Min-Hash signatures. We exploit frequent patterns in the signatures for the Set Similarity Join (SSJoin) size estimation by counting their support. However, there are overlaps among the counts of signature patterns and we need to use the set Inclu...
متن کاملCounting occurrences for a finite set of words: an inclusion-exclusion approach
In this paper, we give the multivariate generating function counting texts according to their length and to the number of occurrences of words from a finite set. The application of the inclusion-exclusion principle to word counting due to Goulden and Jackson (1979, 1983) is used to derive the result. Unlike some other techniques which suppose that the set of words is reduced (i.e., where no two...
متن کامل