Sofic systems

Constant-to-one and onto global maps of homomorphisms between strongly connected graphs

“…Since h 2 is regular (because h 2 is 0 bundle-mergible (remark 5.2)) and any two distinct maximal b-compatible sets for h 2 are disjoint, it follows from lemma 5.8 that g is biregular. Since h 2 is p b-bundlemergible, it follows from lemma 5.5 and theorem 1.5 that there exists an isomorphism p" of (tl (H), a) [3], and extensions of them to finite-to-one and onto homomorphisms between TPPD sofic systems were mentioned in [4].) Many of Hedlund's discussions on a block map /: A" -» A, where A is a non-empty finite set of symbols and n is a positive integer, and the mapping f x : il A -» Cl A defined by…”

Zeta functions of formal languages

“…0 This proposition, together with Theorem 1, shows that the zeta function of a sofic system is rational, and gives an effective procedure for computing it. Actually, the rationality of the zeta function of a sofic system was quoted without proof by Coven and Paul [9], who claimed that Manning's argument [22] could be adapted. The latter was confirmed to us by Mike Boyle, especially in the light of a recent work of D. Fried [12]; moreover, Manning's argument is constructive, and so is another procedure given without proof by R. Bowen [6] and a recent one of M. Boyle [7].…”

Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems

“…If X is finite, if X is another alphabet, and if 6 : X -► X, then 6 extends a NJ coordinate-wise to a map from £2^ to S , and ilAe = {9(co):coeQA} is a sofic system (see [Coven/Paul, 1975]). As in [Krieger, 1984] it is easy to show that 3 is finite.…”

“…The zeta function of a sofic system is rational, and its inverse need not be a polynomial (see [Coven/Paul, 1975]). 4.9.…”

“…From his work I learned how to use the theory of nuclear operators for investigating dynamical systems. The results presented here apply to a much broader class of subshifts including sofic systems (see [Coven/Paul, 1975], [Weiss, 1973]) and many coded systems (see [Blanchard/Hansel, 1986]). …”