Beyond half synchronized systems

Subject Areas : Majlesi Journal of Telecommunication Devices

Dawoud Ahmadi Dastjerdi ¹ , Manouchehr Shahamat ²

1 - University of Guilan, Faculty of Mathematical Science, Rasht, Iran
2 -

Received: 2019-04-02 Accepted : 2019-04-02 Published : 2019-06-01

Keywords: Fischer cover, Entropy, half synchronized, Kreiger graph,

Abstract :

In irreducible subshifts, a word m is synchronizing if whenever vm and mw are admissible words, then vmw is admissible as well. A word m is (left) half (resp. weak) synchronizing, when there is a left transitive ray (resp. a left ray) x− such that if x−m and mw are admissible, then x−mw is also admissible. The respective subshifts are called half (resp. weak) synchronized. K. Thomsen in [On the structure of a sofic shift space, American Mathematical Society, 356, Number 9, 3557-3619] considers a synchronized component of a general subshift and investigates the approximation of entropy from inside of this component by some certain SFTs. We, using a rather different approach, show how this result extends to weak synchronized systems.

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