Inference of Reversible Languages

A famdy of efficient algorithms for referring certain subclasses of the regular languages from fmtte posttwe samples is presented These subclasses are the k-reversible languages, for k = 0, 1, 2, . . . . For each k there is an algorithm for finding the smallest k-reversible language containing any fimte posluve sample. It ts shown how to use this algorithm to do correct identification m the ILmlt of the kreversible languages from posmve data A reversible language is one that Is k-reverstble for some k __ 0. An efficient algonthrn is presented for mfernng reversible languages from posmve and negative examples, and it is shown that it leads to correct identification m the hmlt of the class of reversible languages. Numerous examples are gtven to dlustrate the algorithms and their behawor

[1]  Journal of the Association for Computing Machinery , 1961, Nature.

[2]  Micha A. Perles,et al.  The Theory of Definite Automata , 1963, IEEE Trans. Electron. Comput..

[3]  Abraham Ginzburg,et al.  About Some Properties of Definite, Reverse-Definite and Related Automata , 1966, IEEE Trans. Electron. Comput..

[4]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[5]  Robert McNaughton,et al.  Parenthesis Grammars , 1967, JACM.

[6]  Robert McNaughton,et al.  The Loop Complexity of Pure-Group Events , 1967, Inf. Control..

[7]  S. Reder,et al.  Grammatical complexity and inference , 1969 .

[8]  Janusz A. Brzozowski,et al.  General Properties of Star Height of Regular Events , 1970, J. Comput. Syst. Sci..

[9]  Robert McNaughton,et al.  Counter-Free Automata (M.I.T. research monograph no. 65) , 1971 .

[10]  Stefano Crespi-Reghizzi,et al.  An Effective Model for Grammar Interference , 1971, IFIP Congress.

[11]  Yechezkel Zalcstein,et al.  Locally Testable Languages , 1972, J. Comput. Syst. Sci..

[12]  Jerome A. Feldman,et al.  On the Synthesis of Finite-State Machines from Samples of Their Behavior , 1972, IEEE Transactions on Computers.

[13]  Jerome A. Feldman,et al.  Some Decidability Results on Grammatical Inference and Complexity , 1972, Inf. Control..

[14]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[15]  Robert E. Tarjan,et al.  Efficiency of a Good But Not Linear Set Union Algorithm , 1972, JACM.

[16]  Manuel Blum,et al.  Toward a Mathematical Theory of Inductive Inference , 1975, Inf. Control..

[17]  John Case,et al.  Anomaly hierarchies of mechanized inductive inference , 1978, STOC.

[18]  Giovanni Guida,et al.  Noncounting Context-Free Languages , 1978, JACM.

[19]  Van Nam Tran,et al.  Syntactic pattern recognition , 1978 .

[20]  E. Mark Gold,et al.  Complexity of Automaton Identification from Given Data , 1978, Inf. Control..

[21]  DANA ANGLUIN,et al.  On the Complexity of Minimum Inference of Regular Sets , 1978, Inf. Control..

[22]  Michael A. Harrison,et al.  Introduction to formal language theory , 1978 .

[23]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[24]  Dana Angluin,et al.  Inductive Inference of Formal Languages from Positive Data , 1980, Inf. Control..

[25]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

[26]  Dana Angluin,et al.  Finding Patterns Common to a Set of Strings , 1980, J. Comput. Syst. Sci..

[27]  Laurent Miclet.  Regular Inference with a Tail-Clustering Method , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[28]  Michael G. Thomason,et al.  Syntactic Pattern Recognition, An Introduction , 1978, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Stephen Y. Itoga.  A New Heuristic for Inferring Regular Grammars , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.