Takahisa Toda

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A pattern occurs in a permutation if there is a subsequence of the permutation with the same relative order as the pattern. For mathematical analysis of permutation patterns, strong Wilf-equivalence has been defined as the equivalence between permutation patterns based on the number of occurrences of a pattern. In this paper, we present an algorithm for(More)
We improve an existing OBDD-based method of computing all total satisfying assignments of a Boolean formula, where an OBDD means an ordered binary decision diagram that is not necessarily reduced. To do this, we introduce lazy caching and finer caching by effectively using unit propagation. We implement our methods on top of a modern SAT solver, and show by(More)
All solutions SAT (AllSAT for short) is a variant of the propositional satisfiability problem. AllSAT has been relatively unexplored compared to other variants despite its significance. We thus survey and discuss major techniques of AllSAT solvers. We accurately implemented them and conducted comprehensive experiments using a large number of instances and(More)
  • Takahisa Toda
  • Annals of Mathematics and Artificial Intelligence
  • 2014
Dualization of Boolean functions is a fundamental problem that appears in various fields such as artificial intelligence, logic, data mining, etc. For monotone Boolean functions, many empirical researches that focus on practical efficiency have recently been done. We extend our previous work for monotone dualization and present a novel method for(More)
A zero-suppressed binary decision diagram (ZDD) is a graph representation suitable for handling sparse set families. Given a ZDD representing a set family, we present an efficient algorithm to discover a hidden structure, called a co-occurrence relation, on the ground set. This computation can be done in time complexity that is related not to the number of(More)
We focus on families of bipartitions, i.e. set partitions consisting of atmost two components. A family of bipartitions is a separating family for a set if every two elements in the set are separated by some bipartition. In this paper we enumerate separating families of arbitrary size. We furthermore enumerate inclusion-wise minimal separating families of(More)