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Codes engendrant certains systèmes sofiques. (Codes generating certain sofic systems). (French) Zbl 0683.28009

The author defines the terms “local code” and “local code with finite splitting to the left and right” and shows that a sofic system is of finite type (respectively almost finite type) if and only if all first return codes are local (respectively local with unique splitting to the right and left).
A. Restivo [Inf. Control 25, 93-101 (1974; Zbl 0279.68054)] proved that finite circular codes generate subshifts of finite type. The author proves the following: (i) local codes are circular, (ii) finite local codes are identical to finite circular codes, (iii) finite codes with unique splitting are identical to finite codes with finite deciphering delay to the same side.
The paper finishes by showing that finite codes with unique splitting to the left and right generate almost finite type subshifts. This does not happen when the finiteness condition is dropped.
Reviewer: G.R.Goodson

MSC:

28D05 Measure-preserving transformations
94B05 Linear codes (general theory)

Citations:

Zbl 0279.68054
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Full Text: DOI

References:

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