Polynomial equality testing for terms with shared substructures

  • Sharing of substructures like subterms and subcontexts in terms is a common method for space-efficient representation of terms, which allows for example to represent exponentially large terms in polynomial space, or to represent terms with iterated substructures in a compact form. We present singleton tree grammars as a general formalism for the treatment of sharing in terms. Singleton tree grammars (STG) are recursion-free context-free tree grammars without alternatives for non-terminals and at most unary second-order nonterminals. STGs generalize Plandowski's singleton context free grammars to terms (trees). We show that the test, whether two different nonterminals in an STG generate the same term can be done in polynomial time, which implies that the equality test of terms with shared terms and contexts, where composition of contexts is permitted, can be done in polynomial time in the size of the representation. This will allow polynomial-time algorithms for terms exploiting sharing. We hope that this technique will lead to improved upper complexity bounds for variants of second order unification algorithms, in particular for variants of context unification and bounded second order unification.

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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 ; 21
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (21)
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:2005
Year of first Publication:2005
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/11/21
Tag:Baumgrammatiken; Polynomielles Wortproblem
polynomial word problem; sharing; tree grammars
GND Keyword:Wortproblem
Page Number:28
Last Page:28
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