Abstract
This paper presents a formal framework for the automatic transformation of inefficient generate-and-test programs into equivalent programs by learning from the proofs of example queries. In the resulting program the search is guided by strategies based on abstracted proof traces obtained from the interpretation of example computations. Strategies are incrementally improved in an iterative process by a method for theory formation.
For the task of theory formation we developed a logic based method. It operates on a triple, consisting of a set of features augmented with taxonomic relations, a sequence of positive and negative facts and a set of hypotheses, which can also be the empty set. This triple is transformed into a set of hypotheses which implies all of the positive facts, but none of the negative facts and which is minimal in number of hypotheses. Hypotheses are constructed from facts by abstraction.
This method is embedded into a framework for program synthesis via constructive inductive proofs of input-output specifications. A prototypical implementation of the method was used in a mathematical application. The examples used in this paper are based on real problems that occurred during the generation of optimal mathematical algorithms.
This research was supported by the Deutsche Forschungsgemeinschaft under grant Bi:228/4-l.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Buntine. Generalized subsumption and its application to induction and redundancy. Artificial Intelligence, 36: 149–176, 1988.
I. Cicekli. Design and implementation of an abstract metaprolog engine for metaprolog. In H. Abramson and M. Rogers, editors, M eta-Programming in Logic Programming, pages 417-434. MIT Press, 1989.
S.L. Epstein and N.S. Sridharan. Knowledge representation for mathematical discovery: Three experiments in graph theory. Journal of Applied Intelligence, 1(1): 7–32, 1991.
J. Eusterbrock. Wissensbasierte Verfahren zur Synthese mathematischer Beweise: Eine kombinatorische Anwendung. PhD thesis, Institut für Informatik, Stuttgart, 1991.
A.M. Frisch and D.C. Page. Generalization with taxonomic information. In Proc. AAAI-90, Eigth Nat. Conf. on Artificial Intelligence, volume 2, pages 755-761. AAAI Press/ The MIT Press, 1990.
V. Harmelen and A. Bundy. Explanantion based generalization=partial evaluation. Artificial Intelligence, 36(3): 401–412, 1989.
J.L. Lassez and K. Marriot. Explicit representation of terms defined by counter examples. Journal of Automated Reasoning, 3: 301–317, 1987.
B. Meltzer. Proof, abstraction and semantics in mathematics and artificial intelligence. In A. Marzoilo, editor, Topics in Artificial Intelligence, pages 2–9. Springer Verlag, Wien New York, 1979.
T. M. Mitchell, P. E. Utgoff, B. Nudel, and R. Banerji. Learning problem solving heuristics through practice. In Proc. of International Joint Conference on Artificial Intelligence, pages 127-134, 1981.
T.M. et al Mitchell. Explanation-based-generalization. Machine Learning, 1: 47–80, 1985.
K.S. Murray. Multiple convergence: An approach to disjunctive concept acquisition. In Proc. Int. Joint Conf. on Artificial Intelligence, pages 297-300, 1987.
N. J. Nilsson. Principles of Artificial Intelligence. Tioga Publishing Company, Palo Alto, 1980.
G. D. Plotkin. A note on inductive generalization. In B. Meltzer and D. Michie, editors, Machine Intelligence 5, 1970.
E.Y. Shapiro. Algorithmic Program Debugging. ACM Distinguished Dissertations, The MIT Press, 1982.
E.Y. Shapiro, editor. Concurrent Prolog: Collected Papers. MIT Press Series in Logic Programming, 1987.
B. Silver. Meta Level Inference. North-Holland, Amsterdam, New York, Oxford, 1986.
Douglas R. Smith. Structure and design of global search algorithms. Technical report, KES.U.87.12, 1987.
D.R. Smith. Top-down synthesis of divide-and-conquer algorithms. Artificial Intelligence, 27: 43–96, 1985.
C.B. Suttner and W. Ertel. Automatic acquisition of search heuristics. In M. E. Stickel, editor, Proc. 10th International Conference on Automated Deduction, pages 470-484. Lecture Notes in Computer Science 449, Springer, 1990.
Vere. Induction concept in the predicate calculus. In Proc. IJCAI, 1975.
U. Yalcinalp and L. Sterling. An integrated interpreter for explaining prolog’s successes and failures. In H. Abramson and M. Rogers, editors, M eta-Programming in Logic Programming, pages 205-216. MIT Press, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag London
About this paper
Cite this paper
Eusterbrock, J. (1992). Speed-up Transformations of Logic Programs by Abstraction and Learning. In: Clement, T.P., Lau, KK. (eds) Logic Program Synthesis and Transformation. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3494-7_13
Download citation
DOI: https://doi.org/10.1007/978-1-4471-3494-7_13
Publisher Name: Springer, London
Print ISBN: 978-3-540-19742-3
Online ISBN: 978-1-4471-3494-7
eBook Packages: Springer Book Archive