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On codes concerning bi-infinite words. (English) Zbl 0816.94012

Summary: The authors consider a subclass of circular codes called \(Z\)-codes. Some tests of Sardinas-Patterson type [the first two authors, RAIRO, Inf. Théor. Appl. 24, 441-458 (1990; Zbl 0704.68066)] for \(Z\)-codes are given when they are finite or regular languages. As consequences they prove again the results of A. Restivo [Theor. Comput. Sci. 1, 95- 101 (1975; Zbl 0381.94017)] relating regular \(Z\)-codes to circular codes and codes with finite synchronization delay. Furthermore, the structure of two-element \(Z\)-codes is described.

MSC:

94A45 Prefix, length-variable, comma-free codes
68R15 Combinatorics on words
68Q45 Formal languages and automata
20M35 Semigroups in automata theory, linguistics, etc.
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