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Abstract: We review known results and improve known boundaries between the decidable and the undecidable cases of second-order unification with various restrictions on second-order variables. As a key tool we prove an undecidability result that provides a partial solution to an open problem about simultaneous rigid E-unification. (Update)
Context of citations to this paper: More
.... separated decidable from undecidable unification problems by introducing several restrictions of a unification expression [1, 6, 7, 8, 11, 12, 15, 16, 17]. It is also well known that the second order matching problem is NP complete [2] Huet and Lang [14] have designed a...
...problems, like unification, become undecidable. The unification problem is crucial for applying resolution techniques. We proved [61, 65, 66] that the problem is undecidable even for unification problems with only one second order variable, and where this variable occurs only...
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BibTeX entry: (Update)
J. Levy and M. Veanes. On unification problems in restricted second-order languages. In Annual Conference of the European Association for Computer Science Logic, CSL'98, LNCS, Brno, Czech Republic, 1998. http://citeseer.ist.psu.edu/levy98unification.html More
@inproceedings{ levy98on-unification,
author = "Jordi Levy and Margus Veanes",
title = "On Unification Problems in Restricted Second-Order Languages",
year = 1998,
booktitle = "Annual Conf. of the European Assotiation of Computer Sciece Logic",
address = "Brno, Czech Republic",
url = "citeseer.ist.psu.edu/levy98unification.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
97 The undecidability of the second-order unification problem (context) - Goldfarb - 1981
75 Completion of rewrite systems with membership constraints Pa.. - Comon - 1997
36 Unification of simply typed lambda-terms as logic programmin.. (context) - Miller - 1991
33 Theorem proving using rigid E-unification: Equational mating.. (context) - Gallier, Raatz et al. - 1987
28 unification is NPcomplete (context) - Gallier, Narendran et al. - 1988
25 The undecidability of simultaneous rigid E-unification - Degtyarev, Voronkov - 1996
21 Bi-rewrite systems - Levy, Agust'i - 1996
19 Unification of stratified second-order terms (context) - Schmidt-Schauss - 1995
19 the exponent of periodicity of minimal solutions of context .. (context) - Schmidt-Schauss, Schulz - 1998
19 The undecidability of unification in third order logic (context) - Huet - 1973
19 Simple second-order languages for which unification is undec.. (context) - Farmer - 1991
19 Linear second-order unification - Levy - 1996
19 Proof search in intuitionistic logic with equality - Voronkov - 1996
19 Special cases and substitutes for rigid E-unification - Plaisted - 1995
17 A unification algorithm for second-order monadic terms (context) - Farmer - 1988
12 Computing Science Department (context) - Veanes, Rigid et al. - 1997
10 The decidability of simultaneous rigid E-unification with on.. - Degtyarev, Gurevich et al. - 1998
10 An algorithm for distributive unification (context) - Schmidt-Schauss - 1996
9 Decidable and undecidable second-order unification problems - Levy - 1998
8 Second-order unification and type inference for Church-style.. - Schubert - 1998
6 The undecidability of simultaneous rigid E-unification with .. (context) - Veanes - 1997
4 Some undecidable problems related to the Herbrand theorem - Gurevich, Veanes - 1997
4 Personal communication (context) - Comon - 1998
3 The relation between second-order unification and simultaneo.. (context) - Veanes - 1998
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