Incremental Learning of Cellular Automata for Parallel Recognition of Formal Languages

• Published in: Discovery Science Vol. 6332; pp. 117 - 131
• Main Authors: Nakamura, Katsuhiko, Imada, Keita
• Format: Book Chapter
• Language: English; Japanese
• Published: Germany Springer Berlin / Heidelberg 2010; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Cellular Automaton; Context Free Grammar; Formal Language; Incremental Learning; Negative Sample
• ISBN: 3642161839; 9783642161834
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-16184-1_9

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 {anbncn | n ≥ 1}.