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Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 281 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
On Equality Upto Constraints over Finite Trees, Context Unification, and OneStep Rewriting
"... We introduce equality upto constraints over finite trees and investigate their expressiveness. Equality upto constraints subsume equality constraints, subtree constraints, and onestep rewriting constraints. ..."
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Cited by 27 (7 self)
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We introduce equality upto constraints over finite trees and investigate their expressiveness. Equality upto constraints subsume equality constraints, subtree constraints, and onestep rewriting constraints.
Solvability of context equations with two context variables is decidable
 THE JOURNAL OF SYMBOLIC COMPUTATION
, 1999
"... Context unification is a natural variant of second order unification that represents a generalization of word unification at the same time. While second order unification is wellknown to be undecidable and word unification is decidable it is currently open if solvability of context equations is deci ..."
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Cited by 25 (2 self)
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Context unification is a natural variant of second order unification that represents a generalization of word unification at the same time. While second order unification is wellknown to be undecidable and word unification is decidable it is currently open if solvability of context equations is decidable. We show that solvability of systems of context equations with two context variables is decidable. The context variables may have an arbitrary number of occurrences, and the equations may contain an arbitrary number of individual variables as well. The result holds under the assumption that the first order background signature is finite.
The existential theory of equations with rational constraints in free groups is PSPACEcomplete
, 2001
"... ..."
A decision algorithm for stratified context unification
 FACHBEREICH INFORMATIK, J.W. GOETHEUNIVERSITAT
, 1999
"... Context unification is a variant of second order unification and also a generalization of string unification. Currently it is not known whether context unification is decidable. A specialization of context unification is stratified context unification. Recently, it turned out that stratified context ..."
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Cited by 17 (1 self)
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Context unification is a variant of second order unification and also a generalization of string unification. Currently it is not known whether context unification is decidable. A specialization of context unification is stratified context unification. Recently, it turned out that stratified context unification and onestep rewrite constraints are equivalent. This paper contains a description of a decision algorithm SCU for stratified context unification, which shows decidability of stratified context unification as well as of satisfiability of onestep rewrite constraints.
Application of LempelZiv Encodings to the Solution of Word Equations
 Proc. of 25th International Colloquium on Automata, Languages, and Programming
, 1998
"... 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 define various properties of strings, e.g. general ..."
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Cited by 16 (4 self)
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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 define various properties of strings, e.g. general versions of patternmatching with variables. This paper is devoted to introduce a new approach and to study relations between LempelZiv compressions and word equations. Instead of dealing with very long solutions we propose to deal with their LempelZiv encodings. As our first main result we prove that each minimal solution of a word equation is highly compressible (exponentially compressible for long solutions) in terms of LempelZiv encoding. A simple algorithm for solving word equations is derived. If the length of minimal solution is bounded by a singly exponential function (which is believed to be always true) then LZ encoding of each minimal solution is of a polynomial size (though th...
The Expressibility of Languages and Relations By Word Equations
, 1997
"... Classically, several properties and relations of words, such as "being a power of a same word", can be expressed by using word equations. This paper is devoted to study in general the expressive power of word equations. As main results we prove theorems which allow us to show that certain properties ..."
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Cited by 13 (5 self)
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Classically, several properties and relations of words, such as "being a power of a same word", can be expressed by using word equations. This paper is devoted to study in general the expressive power of word equations. As main results we prove theorems which allow us to show that certain properties of words are not expressible as components of solutions of word equations. In particular, "the primitiveness" and "the equal length" are such properties, as well as being "any word over a proper subalphabet".
Satisfiability of Word Equations with Constants is in Exponential Space
, 1998
"... In this paper we study solvability of equations over free semigroups, known as word equations, particularly Makanin's algorithm, a general procedure to decide if a word equation has a solution. The upper bound timecomplexity of Makanin's original decision procedure (1977) was quadruple exponential ..."
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Cited by 12 (3 self)
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In this paper we study solvability of equations over free semigroups, known as word equations, particularly Makanin's algorithm, a general procedure to decide if a word equation has a solution. The upper bound timecomplexity of Makanin's original decision procedure (1977) was quadruple exponential in the length of the equation, as shown by Jaffar. In 1990 Ko'scielski and Pacholski reduced it to triple exponential, and conjectured that it could be brought down to double exponential. The present paper proves this conjecture. In fact we prove the stronger fact that its spacecomplexity is single exponential. Introduction Solving equations in equationally defined free algebras (Unification) is a widely used technique in Computer Science, see e.g. [3]. In particular, solving equations in free semigroups, i.e. word equations, is of great interest in e.g. associative rewriting and completion, string unification in PROLOG3, extensions of string rewrite systems, unification in some theories...