Abstract
We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to provide a full proof of correctness of the answer. To guarantee correctness we use proof planning techniques, which construct proofs in a human-oriented reasoning style. This gives the human mathematician the necessary insight into the computed solution, as well as making it feasible to check the solution for relatively large groups.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bundy, A.: The Use of Explicit Plans to Guide Inductive Proofs. In: Lusk, E., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310. Springer, Heidelberg (1988)
Caprotti, O., Oostdijk, M.: Formal and efficient primality proofs by use of computer algebra oracles. J. of Symbolic Computation 32(1/2) (2001)
Cohen, A., Murray, S.: An automated proof theory approach to computation with permutation groups. Tech. report, Dept. of Mathematics, TUEindhoven (2002)
Siekmann, J., et al.: Proof development with Omega. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, p. 144. Springer, Heidelberg (2002)
Fiedler, A.: P.rex: An interactive proof explainer. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, p. 416. Springer, Heidelberg (2001)
The GAP Group, Aachen, St Andrews. GAP – Groups, Algorithms, and Programming, Version 4 (1998), http://www-gap.dcs.st-and.ac.uk/~gap
Harrison, J., Théry, L.: A Skeptic’s Approach to Combining HOL and Maple. J. of Automated Reasoning 21(3) (1998)
Kapur, D., Wang, D. (eds.): J. of Automated Reasoning— Special Issue on the Integration of Deduction and Symbolic Computation Systems 21(3) (1998)
Kerber, M., Kohlhase, M., Sorge, V.: Integrating Computer Algebra Into Proof Planning. J. of Automated Reasoning 21(3) (1998)
Kraan, I., Basin, D., Bundy, A.: Middle-Out Reasoning for Logic Program Synthesis. Technical Report MPI-I-93-214, Max-Planck-Institut, Germany (1993)
Meier, A., Pollet, M., Sorge, V.: Comparing Approaches to the Exploration of the Domain of Residue Classes. J. of Symbolic Computation 34(4) (2002)
Melis, E., Siekmann, J.: Knowledge-Based Proof Planning. Artificial Intelligence 115(1) (1999)
Sorge, V.: Non-Trivial Symbolic Computations in Proof Planning. In: Kirchner, H. (ed.) FroCos 2000. LNCS, vol. 1794. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cohen, A., Murray, S.H., Pollet, M., Sorge, V. (2003). Certifying Solutions to Permutation Group Problems. In: Baader, F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science(), vol 2741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45085-6_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-45085-6_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40559-7
Online ISBN: 978-3-540-45085-6
eBook Packages: Springer Book Archive