Abstract
Context unification is a natural variant of second order unification that represents a generalization of word unification at the same time. While second order unification is wellknown to be undecidable and word unification is decidable it is currently open if solvability of context equations is decidable. We show that solvability of systems of context equations with two context variables is decidable. The context variables may have an arbitrary number of occurrences, and the equations may contain an arbitrary number of individual variables as well. The result holds under the assumption that the first-order background signature is finite
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References
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. Simple second-order languages for which unification is undecidable. Theoretical Computer Science, 87:173–214, 1991.
H. Ganzinger, F. Jacquemard, and M. Veanes. Rigid reachability. In J. Hsiang and A. Ohori, editors, Advances in Computing Science-ASIAN’98, Springer LNCS 1538, pages 4–21, 1998.
W. Goldfarb. The undecidability of the second-order unification problem. Theoretical Computer Science, 13:225–230, 1981.
A. Kościelski 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, Springer LNCS 1103, pages 332–346, 1996.
J. Levy and M. Veanes. On the undecidability of second-order unification. Submitted to Information and Computation, 1999.
G. Makanin. The problem of solvability of equations in a free semigroup. Math. USSR Sbornik, 32(2):129–198, 1977.
J. Marcinkowski. Undecidability of the first order theory of one-step right ground rewriting. In H. Comon, editor, International Conference on Rewriting Techniques and Applications, Springer LNCS 1232, pages 241–253, 1997.
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, Springer LNCS 1249, pages 34–48, 1997.
J. Niehren, M. Pinkal, and P. Ruhrberg. A uniform approach to underspecification and parallelism. Technical Report, 1997.
J. Niehren, S. Tison, and R. Treinen. On stratified context unification and rewriting constraints. Talk at CCL’98 Workshop, 1998.
M. Schmidt-Schauß. Unification of stratified second-order terms. Internal Report 12/94, Fachb. Informatik, J.W. Goethe-Universität Frankfurt, Germany, 1994.
M. Schmidt-Schauß. An algorithm for distributive unification. Theoretical Computer Science, 208:111–148, 1998.
M. Schmidt-Schauß. Decidability of bounded second order unification. Draft, Fachbereich Informatik, J.W. Goethe-Universität Frankfurt, Germany, 1998.
M. Schmidt-Schauß and K. U. Schulz. On the exponent of periodicity of minimal solutions of context equations. In Rewriting Techniques and Applications, Proc. RTA’98, volume 1379 of LNCS, pages 61–75. Springer-Verlag, 1998.
M. Schmidt-Schauß and K. U. Schulz. Solvability of context equations with two context variables is decidable. CIS-Report 98-114, CIS, University of Munich, Germany, 1999. available under ftp://ftp.cis.uni-muenchen.de/pub/cis-berichte/CIS-Bericht-98-114.ps.
K. U. Schulz. Makanin’s algorithm-two improvements and a generalization. In Proc. of IWWERT 1990, Springer LNCS 572, pages 85–150, 1990.
K. U. Schulz. Word unification and transformation of generalized equations. J. Automated Reasoning, pages 149–184, 1993.
R. Treinen. The first-order theory of one-step rewriting is undecidable. In H. Ganzinger, editor, 7th International Conference on Rewriting Techniques and Applications, Springer LNCS 1103, pages 276–286,Rutgers University, NJ, USA, 1996.
S. Vorobyov. The first-order theory of one step rewriting in linear noetherian systems is undecidable. In H. Comon, editor, International Conference on Rewriting Techniques and Applications, Springer LNCS 1232, pages 254–268, 1997.
S. Vorobyov. The 898-equational theory of context unification is co-recursively enumerable hard. Talk at CCL’98 Workshop, 1998.
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Schmidt-Schauß, M., Schulz, K.U. (1999). Solvability of Context Equations with Two Context Variables Is Decidable. In: Automated Deduction — CADE-16. CADE 1999. Lecture Notes in Computer Science(), vol 1632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48660-7_5
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DOI: https://doi.org/10.1007/3-540-48660-7_5
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