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Abstract: Context unification is a particular case of second-order unification, where all second-order variables are unary and only linear functions are sought for as solutions. Its decidability is an open problem. We present the simplest (currently known) undecidable quantified fragment of the theory of context unification by showing that for every signature containing a 2-ary symbol one can construct a context equation E [p; r; F ; w] with parameter p, first-order variables r, w, and context variables... (Update)
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BibTeX entry: (Update)
@misc{ vorobyov-equational,
author = "Sergei Vorobyov",
title = "Equational Theory of Context Unification is Hard",
url = "citeseer.ist.psu.edu/article/vorobyov98equational.html" }
Citations (may not include all citations):105 The problem of solvability of equations in a free semigroup (context) - Makanin - 1977
97 The undecidability of the second-order unification problem (context) - Goldfarb - 1981
23 On equality up-to constraints over finite trees (context) - Niehren, Pinkal et al. - 1997
20 Concatenation as a basis for arithmetic (context) - Quine - 1946
19 Unification of stratified second-order terms (context) - Schmidt-Schau - 1994
19 Simple second-order languages for which unification is undec.. (context) - Farmer - 1991
17 A unification algorithm for second-order monadic terms (context) - Farmer - 1988
7 Coding in the existential theory of concatenation (context) - Buchi, Senger - 1986
6 Studying algorithmic problems for free semi-groups and group.. (context) - Durnev - 1997
2 Positive theory of a free semigroup (context) - Durnev - 1973
1 Undecidability of the positive 89-theory of a free semigroup (context) - Marchenkov - 1982
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