Decidability of bounded second order unification

  • It is well known that first order uni cation is decidable, whereas second order and higher order unification is undecidable. Bounded second order unification (BSOU) is second order unification under the restriction that only a bounded number of holes in the instantiating terms for second order variables is permitted, however, the size of the instantiation is not restricted. In this paper, a decision algorithm for bounded second order unification is described. This is the fist non-trivial decidability result for second order unification, where the (finite) signature is not restricted and there are no restrictions on the occurrences of variables. We show that the monadic second order unification (MSOU), a specialization of BSOU is in sum p s. Since MSOU is related to word unification, this is compares favourably to the best known upper bound NEXPTIME (and also to the announced upper bound PSPACE) for word unification. This supports the claim that bounded second order unification is easier than context unification, whose decidability is currently an open question.

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Author:Manfred Schmidt-SchaußORCiDGND
Parent Title (German):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik ; 11
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (11)
Publisher:Johann Wolfgang Goethe-Univ., Fachbereich Informatik und Mathematik, Inst. für Informatik, Research group for Artificial Intelligence and Software Technology
Place of publication:Frankfurt [am Main]
Document Type:Working Paper
Year of Completion:1997
Year of first Publication:1997
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/05/12
Tag:automated deduction; context unification; logics in artificial intelligence; rewriting; second order unification; unification
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoDeutsches Urheberrecht