Finitary codes for biinfinite words. (English) Zbl 0754.68066

Summary: The aim of decoding, or factorizing a single way, biinfinite words with a finitary language leads to define, according to the definition of factorizations, two distinct notions of finitary codes for biinfinite words we call “\(bi\omega\)-codes” and “\(\mathbb{Z}\)-codes”. These codes are respectively close to the precircular codes and to the circular codes. The notion of \(bi\omega\)-code is weaker but seems to be more suitable for biinfinite words. Indeed, \(bi\omega\)-codes are characterized using coding morphisms, as are usual codes and codes for infinite words. \(\mathbb{Z}\)-codes are rather codes for \(\mathbb{Z}\)-words. The relationships between all these finitary codes are studied, and characteristic properties of \(bi\omega\)- codes and \(\mathbb{Z}\)-codes are given.


68Q45 Formal languages and automata
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