Bi-infinitary codes. (English) Zbl 0701.68061

Summary: The notion of bi-infinitary codes is introduced. For this purpose, the monoid \(^{\infty}A^{\infty}\) of finite, infinite and bi-infinite words over an alphabet A is defined. A necessary and sufficient condition for a set of words to be a bi-infinitary code is formulated. Conditions for a submonoid of \(^{\infty}A^{\infty}\) to have a minimal generator set are established. Using a specific kind of Thue system, the notion of bi-quasi free sub-monoids is introduced. An “algebraic” characterization of the submonoids generated by bi-infinitary codes is obtained. Finally, a “combinatorial” characterization of bi-quasi free submonoids is studied.


68Q45 Formal languages and automata
20M35 Semigroups in automata theory, linguistics, etc.
94A45 Prefix, length-variable, comma-free codes
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