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Journals and Conferences
We prove that satisfiability problem for word equations is in PSPACE.
We show how to speed up two string-matching algorithms: the Boyer-Moore algorithm (BM algorithm), and its version called here the reverse factor algorithm (RF algorithm). The RF algorithm is based on factor graphs for the reverse of the pattern. The main feature of both algorithms is that they scan the text right-to-left from the supposed right position of… (More)
We consider the complexity of problems related to 2-dimensional texts (2d-texts) described succinctly. In a succinct description, larger rectangular sub-texts are deened in terms of smaller parts in a way similar to that of Lempel-Ziv compression for 1-dimensional texts, or in shortly described strings as in 9], or in hierarchical graphs described by… (More)
We present the first DEXPTIME algorithm which solves word equations i.e. finds a finite representation of all solutions of an equation in a free semigroup. We show how to use our approach to solve two new problems in PSPACE which deal with properties of the solution set of a word equation:<ul><li>deciding finiteness of the solution set,</li><li>deciding… (More)
One of the most intricate algorithms related to words is Makanin's algorithm solving word equations. The algorithm is very complicated and the complexity of the problem of solving word equations is not well understood. Word equations can be used to deene various properties of strings, e.g. general versions of pattern-matching with variables. This paper is… (More)
The multi-pattern matching problem consists in finding all occurrences of the patterns from a finite set X in a given text T of length n. We present a new and simple algorithm combining the ideas of the Aho–Corasick algorithm and the directed acyclic word graphs. The algorithm has time complexity which is linear in the worst case (it makes at most 2n symbol… (More)
We prove that the length of a shortest solution of a word equation of length n can bounded by a double exponential function in n. This applied to the algorithm in  proves that the problem of solvability of word equations is in NEXPTIME. The best previously known bound for the problem was EXPSPACE 131.