Abstract
Context unification is a generalisation of string unification where words are generalized to terms with one hole. Though decidability of string unification was proved by Makanin, the decidability of context unification is currently an open question. This paper provides a step in understanding the complexity of context unification and the structure of unifiers. It is shown, that if a context unification problem of size d is unifiable, then there is also a unifier with an exponent of periodicity smaller than O(21.07d). We also prove NP-hardness for restricted cases of the context unification problem and compare the complexity of general context unification with that of general string unification.
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References
F. Baader and K. U. Schulz. Unification in the union of disjoint equational theories: Combining decision procedures. J. Symbolic Computation, 21:211–243, 1996.
V. Bulitko. Equations and inequalities in a free group and free semigroup. Tul. Gos. Ped. Inst. Ucen. Zap. Mat. Kafedr. Vyp 2 Geometr. i Algebra, pages 242–252, 1970. in Russian.
H. Comon. Completion of rewrite systems with membership constraints, part I: Deduction rules and part II: Constraint solving. Technical report, CNRS and LRI, Université de Paris Sud, 1993. to appear in JSC.
W. Farmer. A unification algorithm for second order monadic terms. Annals of Pure and Applied Logic, 39:131–174, 1988.
W. Farmer. Simple second-order languages for which unification is undecidable. Theoretical Computer Science, 87:173–214, 1991.
M. Garey and D. Johnson. “Computers and Intractability”: A guide to the theory of NP-completeness. W.H. Freeman and Co., San Francisco, 1979.
W. Goldfarb. The undecidability of the second-order unification problem. Theoretical Computer Science, 13:225–230, 1981.
G. Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1:27–57, 1975.
A. Koscielski and L. Pacholski. Complexity of Makanin's algorithms. Journal of the Association for Computing Machinery, 43:670–684, 1996.
J. Levy. Linear second order unification. In Proc. of the 7th Int. Conf. on Rewriting Techniques and Applications, volume 1103 of LNCS, pages 332–346, 1996.
G. Makanin. The problem of solvability of equations in a free semigroup. Math. USSR Sbornik, 32(2): 129–198, 1977.
J. Niehren, M. Pinkal, and P. Ruhrberg. On equality up-to constraints over finite trees, context unification, and one-step rewriting. In Proc. of the Int. Conf. on Automated Deduction, volume 1249 of LNCS, pages 34–48, 1997.
T. Pietrzykowski. A complete mechanization of second-order type theory. J. ACM, 20:333–364, 1973.
M. Schmidt-Schauß. Unification of stratified second-order terms. Internal Report 12/94, Fachbereich Informatik, Universität Frankfurt, Germany, 1994.
M. Schmidt-Schauß. An algorithm for distributive unification. In Proc. of the 7th Int. Conf. on Rewriting Techniques and Applications, volume 1103 of LNCS, pages 287–301, 1996.
W. Snyder and J. Gallier. Higher-order unification revisited: Complete sets of transformations. J. Symbolic Computation, 8:101–140, 1989.
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© 1998 Springer-Verlag
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Schmidt-Schauß, M., Schulz, K.U. (1998). On the exponent of periodicity of minimal solutions of context equations. In: Nipkow, T. (eds) Rewriting Techniques and Applications. RTA 1998. Lecture Notes in Computer Science, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052361
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DOI: https://doi.org/10.1007/BFb0052361
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