METHODS FOR SPECIFYING FAMILIES OF FORMAL LANGUAGES — PAST-PRESENT-FUTURE

Publisher Summary This chapter discusses the formal language theory. The methods for specifying the families of formal languages relate a number of diverse activities. The chapter discusses the different ways to describe the families of languages that are of interest to computer scientists. The formal languages arose from the study of natural languages. However, it was the work of the linguist Noam Chomsky in 1956 that is regarded as the starting point. In the paper, Chomsky presented the concept of a general phrase structure grammar. Therefore, one way to define a family of languages is by generative mechanisms, that is, by grammar. A family of languages that is not closed under intersection with regular sets should not be studied for its own right but only for other purposes. Thus, the Intersection theorem is an indication towards determining appropriate families of languages to study. Instead of concern to a scattering of linguists, logicians, and mathematicians, formal languages has become an object of study to the large group of individuals interested in the rapidly developing field of computers.

[1]  Friedrich L. Bauer,et al.  Report on the algorithmic language ALGOL 60 , 1960, Commun. ACM.

[2]  Dana S. Scott.  Some Definitional Suggestions for Automata Theory , 1967, J. Comput. Syst. Sci..

[3]  Alfred V. Aho,et al.  A Characterization of Two-Way Deterministic Classes of Languages , 1970, J. Comput. Syst. Sci..

[4]  S.-Y. Kuroda,et al.  Classes of Languages and Linear-Bounded Automata , 1964, Inf. Control..

[5]  Robert W. Floyd,et al.  On the nonexistence of a phrase structure grammar for ALGOL 60 , 1962, CACM.

[6]  Alfred V. Aho,et al.  Indexed Grammars—An Extension of Context-Free Grammars , 1967, SWAT.

[7]  Seymour Ginsburg,et al.  Studies In Abstract Families Of Languages , 1969 .

[8]  Robert McNaughton,et al.  Testing and Generating Infinite Sequences by a Finite Automaton , 1966, Inf. Control..

[9]  Ronald V. Book.  Simple Representations of Certain Classes of Languages , 1978, JACM.

[10]  A. Nerode,et al.  Linear automaton transformations , 1958 .

[11]  B. J. Mailloux,et al.  Report on the Algorithmic Language ALGOL 68 , 1969 .

[12]  Michael A. Harrison,et al.  A Grammatical Characterization of One-Way Nondeterministic Stack Languages , 1971, JACM.

[13]  Seymour Ginsburg,et al.  Two Families of Languages Related to ALGOL , 1962, JACM.

[14]  John E. Hopcroft,et al.  Scattered Context Grammars , 1969, J. Comput. Syst. Sci..

[15]  Seymour Ginsburg,et al.  Grammar Schemata , 1974, JACM.

[16]  Neil D. Jones,et al.  Classes of Automata and Transitive Closure , 1967, Inf. Control..

[17]  George A. Miller,et al.  Finite State Languages , 1958, Inf. Control..

[18]  Armin B. Cremers,et al.  Context-Free Grammar Forms , 1974, J. Comput. Syst. Sci..

[19]  Takumi Kasai,et al.  An Hierarchy Between Context-Free and Context-Sensitive Languages , 1970, J. Comput. Syst. Sci..

[20]  Celia Wrathall,et al.  Rudimentary Predicates and Relative Computation , 1978, SIAM J. Comput..

[21]  Rina S. Cohen,et al.  Theory of omega-Languages. I. Characterizations of omega-Context-Free Languages , 1977, J. Comput. Syst. Sci..

[22]  Seymour Ginsburg,et al.  Derivation-Bounded Languages , 1968, J. Comput. Syst. Sci..

[23]  Noam Chomsky,et al.  Three models for the description of language , 1956, IRE Trans. Inf. Theory.

[24]  Noam Chomsky,et al.  On Certain Formal Properties of Grammars , 1959, Inf. Control..

[25]  Ronald V. Book.  Polynomial Space and Transitive Closure , 1979, SIAM J. Comput..

[26]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[27]  Mary Katherine Yntema,et al.  Inclusion Relations Among Families Of Context-Free Languages , 1967, Inf. Control..