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**1 - 3**of**3**### Zeta functions of finite-type-Dyck shifts are N-algebraic

"... Abstract—Constrained coding is a technique for converting unrestricted sequences of symbols into constrained sequences, i.e. sequences with a predefined set of properties. Regular constraints are described by finite-state automata and the set of bi-infinite constrained sequences are finite-type or s ..."

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Abstract—Constrained coding is a technique for converting unrestricted sequences of symbols into constrained sequences, i.e. sequences with a predefined set of properties. Regular constraints are described by finite-state automata and the set of bi-infinite constrained sequences are finite-type or sofic shifts. A larger class of constraints, described by sofic-Dyck automata, are the visibly pushdown constraints whose corresponding set of bi-infinite sequences are the sofic-Dyck shifts. An algebraic formula for the zeta function, which counts the periodic sequences of these shifts, can be obtained for sofic-Dyck shifts having a right-resolving presentation. We extend the formula to all sofic-Dyck shifts. This proves that the zeta function of all sofic-Dyck shifts is a computable Z-algebraic series. We prove that the zeta function of a finite-type-Dyck shift is a computable N-algebraic series, i.e. is the generating series of some unambiguous context-free language. We conjecture that the result holds for all sofic-Dyck shifts. I.

### Entropy of a bit-shift channel

, 2006

"... Abstract: We consider a simple transformation (coding) of an iid source called a bit-shift channel. This simple transformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. We discuss methods of computing the entropy of the transformed proces ..."

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Abstract: We consider a simple transformation (coding) of an iid source called a bit-shift channel. This simple transformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. We discuss methods of computing the entropy of the transformed process, and study some of its properties. Results presented in this paper originate from the discussions we had at the “Coding Club ” – the weekly seminar on coding theory at the Philips Research Laboratories in Eindhoven. Mike Keane, when his active travelling schedule permits, is also attending this seminar. We would like to use this opportunity to thank Mike for his active participation, pleasant and fruitful discussions, his inspiration which we had a pleasure to share. 1. Bit-shift channel In this paper we consider a simplified model for errors occurring in the readout of digital information stored on an optical recording medium like the Compact Disk (CD) or the Digital Versatile Disk (DVD). For more detailed information on optical

### ON A CERTAIN CLASS OF g-FUNCTIONS FOR SUBSHIFTS

, 2006

"... Abstract. A property (D) of subshifts was defined in: Wolfgang Krieger, On g-functions for subshifts, IMS Lecture Notes- Monograph Series, Vol. 48, Dynamics & Stochastics (2006) 306- 316, arXiv:math.DS/0608259. With a view towards a theory of g-fnctions beyond the case of finte type subshifts pa ..."

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Abstract. A property (D) of subshifts was defined in: Wolfgang Krieger, On g-functions for subshifts, IMS Lecture Notes- Monograph Series, Vol. 48, Dynamics & Stochastics (2006) 306- 316, arXiv:math.DS/0608259. With a view towards a theory of g-fnctions beyond the case of finte type subshifts partially defined continuous g-functions of property (D) subshifts are studied.