A Characterization of a Dot-Depth Two Analogue of Generalized Definite Languages

The family of G-trivial languages is investigated. This family is a generalization of L-trivial and R-trivial languages, a relationship analogous to the one between generalized definite languages and the definite and reverse definite languages. Characterizations of G-trivial languages are given in terms of their syntactic monoids, various congruence relations, and the (finite) automata which recognize them. Finally, we examine noncounting languages and their connection to G-trivial languages.

[1]  J. Green,et al.  On semi-groups in which xr = x , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Janusz A. Brzozowski,et al.  Characterizations of locally testable events , 1973, Discret. Math..

[3]  Janusz A. Brzozowski,et al.  Dot-Depth of Star-Free Events , 1971, Journal of computer and system sciences (Print).

[4]  R. McNaughton,et al.  Counter-Free Automata , 1971 .

[5]  Magnus steinby.  On definite automata and related systems , 1969 .

[6]  Albert R. Meyer,et al.  A Note on Star-Free Events , 1969, JACM.

[7]  Janusz A. Brzozowski,et al.  A generalization of finiteness , 1976 .

[8]  Jean Françon.  Arbres Binaires de Recherche: Propriétés Combinatioires et Applications , 1976, RAIRO Theor. Informatics Appl..

[9]  Karel Culik,et al.  Classification of Noncounting Events , 1971, J. Comput. Syst. Sci..

[10]  Janusz A. Brzozowski,et al.  The Dot-Depth Hierarchy of Star-Free Languages is Infinite , 1978, J. Comput. Syst. Sci..

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

[12]  Marcel Paul Schützenberger,et al.  On Finite Monoids Having Only Trivial Subgroups , 1965, Inf. Control..

[13]  Janusz A. Brzozowski,et al.  Hierarchies of Aperiodic Languages , 1976, RAIRO Theor. Informatics Appl..

[14]  J. Brzozowski.  Canonical regular expressions and minimal state graphs for definite events , 1962 .

[15]  Faith Ellen,et al.  Languages of R-Trivial Monoids , 1980, J. Comput. Syst. Sci..

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

[17]  Imre Simon,et al.  Piecewise testable events , 1975, Automata Theory and Formal Languages.

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

[19]  S C Kleene,et al.  Representation of Events in Nerve Nets and Finite Automata , 1951 .