Groups in the syntactic monoid of a composed code
Copyright policy )Groups in the syntactic monoid of a composed code
It is proved: Let Y and Z be codes (with Z finite) and let \(X=Y\circ Z\). Then every group in \(M(X^*)\), the syntactic monoid of \(X^*\), divides a generalized wreath product \((G_ 1\times...\times G_ n)\square H\), where \(G_ 1,...,G_ n\) are groups dividing \(M(Y^*)\) and H is a group dividing \(M(Z^*)\). For the convenience of the reader all definitions and results needed are summarized and most of the results are proved.
Algebraic theory of languages and automata, Algebra and Number Theory, Semigroups in automata theory, linguistics, etc., syntactic monoid, Other types of codes, codes, generalized wreath product, unambiguous automaton
Algebraic theory of languages and automata, Algebra and Number Theory, Semigroups in automata theory, linguistics, etc., syntactic monoid, Other types of codes, codes, generalized wreath product, unambiguous automaton
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