Abstract
A method to infer a subclass of linear languages from positive structural information (i.e. skeletons) is presented. The characterization of the class and the analysis of the time and space complexity of the algorithm is exposed too. The new class, Terminal and Structural Distinguishable Linear Languages (TSDLL), is defined through an algebraic characterization and a pumping lemma. We prove that the proposed algorithm correctly identifies any TSDL language in the limit if structural information is presented. Furthermore, we give a definition of a characteristic structural set for any target grammar. Finally we present the conclusions of the work and some guidelines for future works.
Part of this work was carried out during a visit of J. Sempere to Prof. G. Nagaraja at IIT, Mumbai. The visit was granted by the área de Programas Internacionales (API) of the Universidad Politécnica de Valencia
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References
V. Amar, G. PutzoluOn a Family of Linear Grammars. Information and Control 7 (1964) 283–291.
P. García Learning k-Testable Tree Sets from positive data. Departamento de Sistemas Informáticos y Computación. Universidad Politécnica de Valencia. Technical report DSIC-II/46/93. 1993.
E. Mark GoldLanguage Identification in the Limit. Information and Control,10 (1969) 447–474.
M. Harrison Introduction to Formal Language Theory. Addison-Wesley Publishing Company. 1978.
C. de la HigueraCharacteristic Sets for Polynomial Grammatical Inference. Machine Learning 27 (1997) 125–138.
T. Koshiba, E. MÄkinen, Y. TakadaLearning deterministic even linear languages from positive examples. Theoretical Computer Science 185 (1997) 63–97.
E. MÄkinenThe grammatical inference problem for the Szilard languages of Linear Grammars. Information Processing Letters 36 (1990) 203–206.
E. MÄkinenOn the structural grammatical inference problem for some classes of context-free grammars. Information Processing Letters 42 (1992) 1–5.
E. MÄkinenRemarks on the structural grammatical inference problem for context-free grammars. Information Processing Letters 44 (1992) 125–127.
E. MÄkinenA note on the grammatical inference problem for even linear languages. Fundamenta Informaticae 25, No. 2 (1996) 175–181.
V. RadhakrishnanGrammatical Inference from Positive Data: An Effective Integrated Approach. Ph.D. Thesis. Department of Computer Science and Engineering. HT Bombay. 1987.
V. Radhakrishnan and G. NagarajaInference of Regular Grammars via Skeletons. IEEE Trans. on Systems, Man and Cybernetics, 17, No. 6 (1987) 982–992.
V. Radhakrishnan and G. NagarajaInference of Even Linear Languages and Its Application to Picture Description Languages. Pattern Recognition,21, No. 1 (1988) 55–62.
G. RozenbergDirect Proofs of the Undecidability of the Equivalence Problem for Sentential Forms of Linear Context-Free Grammars and the Equivalence Problem for 0L Systems. Information Processing Letters 1 (1972) 233–235.
J. Ruiz and P. GarcíaThe algorithms RT and k-TTI: A first comparison. Proceedings of the Second International Colloquium, ICGI-94. LNAI Vol. 862, pp 180–188. 1994.
Y. SakakibaraLearning context-free grammars from structural data in polynomial time. Theoretical Computer Science 76 (1990) 223–242.
Y. SakakibaraEfficient Learning of Context-Free Grammars from Positive Structural Examples. Information and Computation 97 (1992) 23–60.
J.M. Sempere and P. García A Characterization of Even Linear Languages and its Application to the Learning Problem. Proceedings of the Second International Colloquium, ICGI-94. LNAI Vol. 862, pp 38–44. Springer-Verlag. 1994.
José M. Sempere and Antonio FosLearning linear grammars from Structural Information. Proceedings of the Third International Colloquium, ICGI-96. LNAI Vol. 1147, pp 126–133. Springer-Verlag. 1996.
Y. TakadaInferring Parenthesis Linear Grammars Based on Control Sets. Journal of Information Processing, 12, No. 1 (1988) 27–33.
Y. TakadaGrammatical Inference for Even Linear Languages based on Control Sets. Information Processing Letters. 28, No. 4 (1988) 193–199.
Y. TakadaA hierarchy of languages families learnable by regular language learning. Information and Computation, 123(1) (1995) 138–145.
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Sempere, J.M., Nagaraja, G. (1998). Learning a subclass of linear languages from positive structural information. In: Honavar, V., Slutzki, G. (eds) Grammatical Inference. ICGI 1998. Lecture Notes in Computer Science, vol 1433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054073
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DOI: https://doi.org/10.1007/BFb0054073
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