Abstract
We present a new algorithm ICGE for incremental learning of extended Mealy automata computing over abstract data types. Our approach extends and refines our previous research on congruence generator extension (CGE) as an algebraic approach to automaton learning. In the congruence generator approach, confluent terminating string rewriting systems (SRS) are used to represent hypothesis automata. We show how an approximating sequence R 0 , R 1 , … of confluent terminating SRS can be directly and incrementally generated from observations about the loop structure of an unknown automaton A. Such an approximating sequence converges finitely if A is finite state, and converges in the limit if A is an infinite state automaton.
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
Angluin, D.: A note on the number of queries needed to identify regular languages. Information and Control 51(1), 76–87 (1981)
Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75(1), 87–106 (1987)
Balcazar, J.L., Diaz, J., Gavalda, R.: Algorithms for learning finite automata from queries. In: Advances in Algorithms, Languages and Complexity, pp. 53–72. Kluwer (1997)
de la Higuera, C.: Grammatical Inference. Cambridge University Press (2010)
Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: Handbook of Theoretical Computer Science. North-Holland (1990)
Dupont, P.: Incremental Regular Inference. In: Miclet, L., de la Higuera, C. (eds.) ICGI 1996. LNCS (LNAI), vol. 1147, pp. 222–237. Springer, Heidelberg (1996)
Gold, E.M.: Language identification in the limit. Information and Control 10(5), 447–474 (1967)
Goguen, J.A., Meseguer, J.: Initiality, induction and computability. In: Algebraic Methods in Semantics, pp. 460–541. Cambridge University Press (1985)
Klop, J.W.: Term rewriting systems. In: Handbook of Logic in Computer Science, vol. 2, pp. 2–117. Oxford University Press (1992)
Knuth, D.E., Bendix, P.: Simple word problems in universal algebras. In: Computational Problems in Abstract Algebra, pp. 263–269. Pergamon Press (1970)
Lang, K.J.: Random dfa’s can be approximately learned from sparse uniform examples. In: Fifth ACM Workshop on Computational Learning Theory, pp. 45–52. ACM Press (1992)
Lloyd, J.W.: Foundations of Logic Programming. Springer (1993)
Meinke, K.: CGE: A Sequential Learning Algorithm for Mealy Automata. In: Sempere, J.M., García, P. (eds.) ICGI 2010. LNCS (LNAI), vol. 6339, pp. 148–162. Springer, Heidelberg (2010)
Meinke, K., Niu, F.: Learning-Based Testing for Reactive Systems Using Term Rewriting Technology. In: Wolff, B., Zaïdi, F. (eds.) ICTSS 2011. LNCS, vol. 7019, pp. 97–114. Springer, Heidelberg (2011)
Meinke, K., Niu, F., Sindhu, M.: Learning-based software testing: a tutorial. In: Proc. Int. ISoLA Workshop on Machine Learning for Software Construction. CCIS. Springer (2012)
Meinke, K., Sindhu, M.A.: Incremental Learning-Based Testing for Reactive Systems. In: Gogolla, M., Wolff, B. (eds.) TAP 2011. LNCS, vol. 6706, pp. 134–151. Springer, Heidelberg (2011)
Meinke, K., Tucker, J.V.: Universal algebra. In: Handbook of Logic in Computer Science, vol. 1, pp. 189–411. Oxford University Press (1993)
Oncina, J., Garcia, P.: Inferring regular languages in polynomial update time. In: Pattern Recognition and Image Analysis. Series in Machine Perception and Artificial Intelligence. World Scientific (1992)
Parekh, R., Honavar, V.: Grammar inference, automata induction and language acquisition. In: Handbook of Natural Language Processing, Marcel Dekker (2000)
Parekh, R.G., Nichitiu, C., Honavar, V.G.: A Polynomial Time Incremental Algorithm for Learning DFA. In: Honavar, V.G., Slutzki, G. (eds.) ICGI 1998. LNCS (LNAI), vol. 1433, pp. 37–49. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meinke, K., Niu, F. (2012). An Incremental Learning Algorithm for Extended Mealy Automata. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Technologies for Mastering Change. ISoLA 2012. Lecture Notes in Computer Science, vol 7609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34026-0_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-34026-0_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34025-3
Online ISBN: 978-3-642-34026-0
eBook Packages: Computer ScienceComputer Science (R0)