Satisfiability of word equations with constants is in PSPACE
Journal of the ACMPublished 1 May 2004
Wojciech Plandowski
Citations136
SJR quartileQ1
SJR score2.25
SNIP3.16
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Abstract
We prove that satisfiability problem for word equations is in PSPACE.
Keywords
Computer Science
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Two improvements of Makanin's algorithm are described which bring it nearer to the area of practical applicability and a simple pre-algorithm is suggested which decides the solvability of word equations with not more than two occurrences of each variable and which partially solves and simplifies the decision procedure for all other equations.
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The main result of this paper solves the complementary problem of generating the set of all solutions and generates, given a word equation, a minimal and complete set of unifiers.
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A new approach is introduced and the solvability can be tested in polynomial deterministic time if the lengths of all variables are given in binary and it is proved that each minimal solution of a word equation is highly compressible (exponentially compressible for long solutions) in terms of Lempel-Ziv encoding.
Finding patterns common to a set of strings (Extended Abstract)
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This problem is shown to be effectively solvable in the general case and to lead to correct inference in the limit of the pattern languages and a polynomial time algorithm for finding minimal one-variable pattern languages compatible with a given set of strings is given.
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This paper proves theorems which allow us to show that certain properties of words are not expressible as components of solutions of word equations.
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It is proved that the length of a shortest solution of a word equation of length n can bounded by a double exponential function in n and proves that the problem of solvability of word equations is in NEXPTIME.
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This paper proves the stronger fact that Makanin's algorithm (1977), a general procedure to decide if a word equation has a solution, is single exponential, while reducing it to triple exponential, and conjecturing that it could be brought down to double exponential.
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