Journal of Advances in Mathematics and Computer Science

Generalizing the Asymmetric Run-length-limited Systems

D. Ahmadi Dastjerdi *

Faculty of Mathematics, University of Guilan, Iran.

S. Jangjooye Shaldehi

Faculty of Mathematics, University of Guilan, Iran.

*Author to whom correspondence should be addressed.

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Abstract

For i = 1; 2, if Xi is a synchronized system generated by Vi = {uⁱ ∝_I : ∝_{I u}ⁱ  ∝_I  ∈ B (Xi), ∝_I  uⁱ }  where _i is a synchronizing word for Xi, then a natural generalization of an asymmetric-RLL(d1; k1; d0; k0) systems is a coded system Z generated by   We investigate the dynamical properties of Z. We show that Z is sofic or has specification with variable gap length (SVGL) if and only if X1 and X2 are so. Also, if Z is SFT or AFT, then X and Y are SFT or AFT respectively and sufficient conditions for the converse will be given.

Keywords: Shift of finite type, sofic, almost-finite-type, synchronized, coded system.

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