Abstract
We propose a method for constructing test sets for deciding whether a term is ground reducible w.r.t. an arbitrary, many-sorted, unconditional term rewriting system. Our approach is based on a suitable characterization of such test sets using a certain notion of transnormality. It generates very small test sets and shows some promise to be an important step towards a practicable implementation.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
B. Bogaert and S. Tison. Equality and disequality constraints on direct subterms in tree automata. In Proc. 9 th STACS, volume 577 of LNCS, pages 161–171. Springer, 1992.
R. Bündgen. Term completion versus algebraic completion. Ph.D. thesis, Fakultät für Informatik, Eberhard-Karls-Universität, Tübingen, Germany, May 1991.
H. Comon and F. Jacquemard. Ground reducibility and automata with disequality constraints. In Proc. 11 th STACS, LNCS 775, pages 151–162. Springer, 1994.
H. Comon and J.-L. Remy. How to characterize the language of ground normal forms. Rapports de Recherche 676, INRIA, 1987.
N. Dershowitz and J.-P. Jouannaud. Notations for rewriting. Bulletin EATCS, No. 43, pages 162–172, Feb 1991.
D. Hofbauer and M. Huber. Linearizing term rewriting systems using test sets. Journal of Symbolic Computation, 17:91–129, 1994.
J. Jouannaud and E. Kounalis. Automatic proofs by induction in theories without constructors. Information and Computation, 82:1–33, July 1989. An earlier version of this paper appeared in Bulletin EATCS, No. 27, 1985, pages 49–55.
D. Kapur, P. Narendran, and H. Zhang. On sufficient completeness and related properties of term rewriting systems. Acta Informatica, 24:395–415, 1987.
D. Kapur, P. Narendran, and H. Zhang. Automating inductionless induction using test sets. Journal of Symbolic Computation, 11:83–111, 1991.
E. Kounalis. Testing for inductive (co)-reducibility. In CAAP'90, Copenhagen, Denmark, volume 431 of LNCS, pages 221–238, 1990.
E. Kounalis. Testing for the ground (co)-reducibility property in term-rewriting systems. Theoretical Computer Science, Elsevier, 106:87–117, 1992.
G. Kucherov and M. Tajine. Decidability of regularity and related properties of ground normal form languages. In 3rd CTRS, LNCS 656, pages 272–286, 1992.
D. Plaisted. Semantic confluence tests and completion methods. Information and Control, 65:182–215, 1985.
S. Vágvölgyi and R. Gilleron. For a rewriting system it is decidable whether the set of irreducible ground terms is recognizable. Bulletin EATCS, No. 48, pages 197–200, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schmid, K., Fettig, R. (1995). Towards an efficient construction of test sets for deciding ground reducibility. In: Hsiang, J. (eds) Rewriting Techniques and Applications. RTA 1995. Lecture Notes in Computer Science, vol 914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59200-8_49
Download citation
DOI: https://doi.org/10.1007/3-540-59200-8_49
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59200-6
Online ISBN: 978-3-540-49223-8
eBook Packages: Springer Book Archive