论文信息 - Un Algorithme Calculant le Cardinal, Fini ou Infini, des Demi-Groupes de Matrices

Un Algorithme Calculant le Cardinal, Fini ou Infini, des Demi-Groupes de Matrices

Abstract Let S be a finite set of matrices over a commutative field K . We give here an algorithm which decides whether the matrix semigroup H generated by S is finite; and in that case, our algorithm computes the cardinality of H . In other words, we can decide by an effective procedure whether a K -automaton is a finite automaton.

Gérard Jacob | G. Jacob

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

[2] Claudio Procesi,et al. The Burnside problem , 1966 .

[3] Gérard Jacob,et al. Decidabilite de la finitude des demi-groupes de matrices , 1977, Theoretical Computer Science.

[4] Yechezkel Zalcstein,et al. Finiteness conditions for matrix semigroups , 1973 .

[5] Gérard Jacob. La finitude des représentations linéaires des semi-groupes est décidable , 1978 .

[6] Marcel Paul Schützenberger,et al. Finite Counting Automata , 1962, Inf. Control..

[7] V. M. Kopytov,et al. Solvability of the problem of occurrence in finitely generated soluble groups of matrices over the field of algebraic numbers , 1968 .

[8] Imre Simon,et al. On Finite Semigroups of Matrices , 1977, Theor. Comput. Sci..

[9] Yechezkel Zalcstein. Syntactic Semigroups of Some Classes of Star-Free Languages , 1972, ICALP.

[10] Yechezkel Zalcstein,et al. The Burnside problem for semigroups , 1975 .

[11] Yechezkel Zalcstein,et al. Locally testable semigroups , 1972 .

[12] Frank Plumpton Ramsey,et al. On a Problem of Formal Logic , 1930 .

[13] Irving Kaplansky,et al. Fields and rings , 1969 .

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