Abstract
We investigate the word and the subsumption problem for recurrent term schematizations, which are a special type of constraints based on iteration. By means of unification, we reduce these problems to a fragment of Presburger arithmetic. Our approach is applicable to all recurrent term schematizations having a finitary unification algorithm. Furthermore, we study a particular form of the complement problem. Given a finite set of terms, we ask whether its complement can be finitely represented by schematizations, using only the equality predicate without negation. The answer is negative as there are ground terms too complex to be represented by schematizations with limited resources.
Full version is at http://www.loria.fr/~hermann/publications/redelim.ps.gz. This work was done while the second author was visiting LORIA and was funded by Univeristé Henri Poincaré, Nancy 1.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Amaniss, M. Hermann, and D. Lugiez. Set operations for recurrent term schematizations. In M. Bidoit and M. Dauchet, editors, Proc. 7th TAPSOFT Conference, Lille (France), LNCS 1214, pages 333–344. Springer, 1997.
H. Chen and J. Hsiang. Recurrence domains: Their unification and application to logic programming. Information and Computation, 122:45–69, 1995.
H. Comon. On unification of terms with integer exponents. Mathematical Systems Theory, 28(1):67–88, 1995.
D.C. Cooper. Theorem proving in arithmetic without multiplication. In B. Meltzer and D. Mitchie, editors, Machine Intelligence, volume 7, pages 91–99. Edinburgh University Press, 1972.
M.R. Garey and D.S. Johnson. Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman and Co, 1979.
E. Grädel. Subclasses of Preburger arithmetic and the polynomial-time hierarchy. Theoretical Computer Science, 56(3):289–301, 1988.
M. Hermann and R. Galbavý. Unification of infinite sets of terms schematized by primal grammars. Theoretical Computer Science, 176(1–2):111–158, 1997.
J.-L. Lassez and K. Marriott. Explicit representation of terms defined by counter examples. J. Automated Reasoning, 3(3):301–317, 1987.
N. Peltier. Increasing model building capabilities by constraint solving on terms with integer exponents. J. Symbolic Computation, 24(1):59–101, 1997.
G. Salzer. Deductive generalization and meta-reasoning, or how to formalize Genesis. In österreichische Tagung für Künstliche Intelligenz, Informatik-Fachberichte 287, pages 103–115. Springer, 1991.
G. Salzer. The unification of infinite sets of terms and its applications. In A. Voronkov, editor, Proc. 3rd LPAR Conference, St. Petersburg (Russia), LNCS (LNAI) 624, pages 409–420. Springer, 1992.
G. Salzer. Primal grammars and unification modulo a binary clause. In A. Bundy, editor, Proc. 12th CADE Conference, Nancy (France), LNCS (LNAI) 814, pages 282–295. Springer, 1994.
U. Schöning. Complexity of Presburger arithmetic with fixed quantifier dimension. Theory of Computing Systems, 30(4):423–428, 1997.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hermann, M., Salzer, G. (1998). On the word, subsumption, and complement problem for recurrent term schematizations. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055775
Download citation
DOI: https://doi.org/10.1007/BFb0055775
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64827-7
Online ISBN: 978-3-540-68532-6
eBook Packages: Springer Book Archive