Abstract
Simplification orderings on terms play a crucial role in reducing the search space in paramodulation-based theorem proving. Such a use of orderings requires checking simple ordering constraints on substitutions as an essential part of many operations. Due to their frequency, such checks are costly and are a good target for optimisation. In this paper we present an efficient implementation technique for checking constraints in one of the most widely used simplification orderings, the Knuth-Bendix ordering. The technique is based on the idea of run-time algorithm specialisation, which is a close relative of partial evaluation.
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References
Hillenbrand, T., Löchner, B.: A Phytography of Waldmeister. AI Communications 15(2-3), 127–133 (2002)
Jones, N.D., Gomard, C.K., Sestoft, P.: Partial Evaluation and Automatic Program Generation. Prentice Hall International, Englewood Cliffs (1993)
Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford (1970)
Korovin, K., Voronkov, A.: Orienting rewrite rules with the Knuth-Bendix order. Information and Computation 183(2), 165–186 (2003)
Löchner, B., Schulz, S.: An Evaluation of Shared Rewriting. In: de Nivelle, H., Schulz, S. (eds.) Proc. of the 2nd International Workshop on the Implementation of Logics, MPI Preprint, Saarbrücken. Max-Planck-Institut für Informatik, pp. 33–48 (2001)
Nieuwenhuis, R., Rivero, J.M.: Practical algorithms for deciding path ordering constraint satisfaction. Information and Computation 178(2), 422–440 (2002)
Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 7. vol. I, pp. 371–443. Elsevier Science, Amsterdam (2001)
Riazanov, A., Voronkov, A.: Partially adaptive code trees. In: Brewka, G., Moniz Pereira, L., Ojeda-Aciego, M., de Guzmán, I.P. (eds.) JELIA 2000. LNCS (LNAI), vol. 1919, pp. 209–223. Springer, Heidelberg (2000)
Riazanov, A., Voronkov, A.: The design and implementation of Vampire. AI Communications 15(2-3), 91–110 (2002)
Riazanov, A., Voronkov, A.: Efficient instance retrieval with standard and relational path indexing. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 380–396. Springer, Heidelberg (2003)
Riazanov, A., Voronkov, A.: Limited resource strategy in resolution theorem proving. Journal of Symbolic Computations 36(1-2), 101–115 (2003)
Rivero, J.M.A.: Data Structures and Algorithms for Automated Deduction with Equality. Phd thesis, Universitat Politècnica de Catalunya, Barcelona (May 2000)
Schulz, S.: E - a braniac theorem prover. AI Communications 15(2-3), 111–126 (2002)
Sutcliffe, G., Suttner, C.: The TPTP problem library. tptp v. 2.4.1. Technical report, University of Miami (2001)
Tammet, T.: Gandalf. Journal of Automated Reasoning 18(2), 199–204 (1997)
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Riazanov, A., Voronkov, A. (2004). Efficient Checking of Term Ordering Constraints. In: Basin, D., Rusinowitch, M. (eds) Automated Reasoning. IJCAR 2004. Lecture Notes in Computer Science(), vol 3097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25984-8_3
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DOI: https://doi.org/10.1007/978-3-540-25984-8_3
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