Abstract
Parallel language recognition by cellular automata (CAs) is currently an important subject in computation theory. This paper describes incremental learning of one-dimensional, bounded, one-way, cellular automata (OCAs) that recognize formal languages from positive and negative sample strings. The objectives of this work are to develop automatic synthesis of parallel systems and to contribute to the theory of real-time recognition by cellular automata. We implemented methods to learn the rules of OCAs in the Occam system, which is based on grammatical inference of context-free grammars (CFGs) implemented in Synapse. An important feature of Occam is incremental learning by a rule generation mechanism called bridging and the search for rule sets. The bridging looks for and fills gaps in incomplete space-time transition diagrams for positive samples. Another feature of our approach is that the system synthesizes minimal or semi-minimal rule sets of CAs. This paper reports experimental results on learning several OCAs for fundamental formal languages including sets of balanced parentheses and palindromes as well as the set {a n b n c n | nāā„ā1}.
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
Balzer, R.: An 8-State Minimal Time Solution to the Firing Squad Synchronization Problem. Information and ControlĀ 10, 22ā42 (1967)
Choffrut, C., Culik II, K.: On real-time cellular automata and trellis automata. Acta InformaticaĀ 21, 393ā407 (1984)
Dyer, C.: One-way bounded cellular automata. Inform. and ControlĀ 44, 54ā69 (1980)
Hopcroft, J.E., Ullman, J.E.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)
Fisher, P.C.: Generation of primes by a one-dimensional real-time iterative array. Jour. of ACMĀ 12, 388ā394 (1965)
Ibarra, O.H., Palis, M.P., Kim, S.M.: Fast parallel language recognition by cellular automata. Theoret. Comput. Sci.Ā 41, 231ā246 (1985)
Ibarra, O.H., Jiang, T.: Relating the power of cellular arrays to their closure properties. Theoret. Comput. Sci.Ā 57, 225ā238 (1988)
Imada, K., Nakamura, K.: Towards Machine Learning of Grammars and Compilers of Programming Languages. In: Daelemans, W., Goethals, B., Morik, K. (eds.) ECML PKDD 2008, Part II. LNCS (LNAI), vol.Ā 5212, pp. 98ā112. Springer, Heidelberg (2008)
Imada, K., Nakamura, K.: Learning Context Free Grammars by SAT Solvers, Internat. Conf. on Machine Learning and Applications, IEEE DOI 10.1109/ICMLA, 28 267, 267-272 (2009)
JuillĆ©, H., Pollack, J.B.: Coevolving the āidealā trainer: Application to the discovery of cellular automata rules. In: Koza, J.R., et al. (eds.) Proceedings of the Third Annual Conference on Genetic Programming 1998, pp. 519ā527. Morgan Kaufmann, San Francisco (1998)
Kasami, T., Fujii, M.: Some results on capabilities of one-dimensional iterative logical networks. Electrical and CommunicationĀ 51-C, 167ā176 (1968)
Mitchell, M.: Crutchfield, J. P. and Hraber, P. T., Evolving cellular automata to perform computations: mechanism and impediments. Physica DĀ 75, 361ā391 (1994)
Nakamura, K., Matsumoto, M.: Incremental Learning of Context Free Grammars Based on Bottom-up Parsing and Search. Pattern RecognitionĀ 38, 1384ā1392 (2005)
Nakamura, K.: Incremental Learning of Context Free Grammars by Bridging Rule Generation and Semi-Optimal Rule Sets. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds.) ICGI 2006. LNCS (LNAI), vol.Ā 4201, pp. 72ā83. Springer, Heidelberg (2006)
Nakamura, K.: Real-time recognition of cyclic strings by one-way and two-way cellular automata. IEICE Trans. of Information and SystemsĀ E88-D, 171ā177 (2005)
Richards, F.C., Meyer, T.P., Packard, N.H.: Extracting cellular automaton rules from experimental data. Physica DĀ 45, 189ā202 (1990)
Smith III, A.R.: Real-time language recognition by one-dimensional cellular automata. Jour. Comput. and System Sci.Ā 6, 233ā253 (1972)
Smith III, A.R.: Cellular automata complexity trade-offs. Inform. and ControlĀ 18, 466ā482 (1971)
Terrier, V.: On real time one-way cellular array. Theoret. Comput. Sci.Ā 141, 331ā335 (1995)
Terrier, V.: Languages not recognizable in real time by one-way cellular automata. Theoret. Comput. Sci.Ā 156, 281ā287 (1996)
Umeo, H., Morita, K., Sugata, K.: Deterministic one-way simulation of two-way real-time cellular automata and its related problems. Information Process. Lett.Ā 14, 159ā161 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nakamura, K., Imada, K. (2010). Incremental Learning of Cellular Automata for Parallel Recognition of Formal Languages. In: Pfahringer, B., Holmes, G., Hoffmann, A. (eds) Discovery Science. DS 2010. Lecture Notes in Computer Science(), vol 6332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16184-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-16184-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16183-4
Online ISBN: 978-3-642-16184-1
eBook Packages: Computer ScienceComputer Science (R0)