Abstract not found

We discuss a well-known binary sequence called the Thue-Morse sequence, or the Prouhet-Thue-Morse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences.

A new block code is introduced which is capable of correcting multiple insertion, deletion and substitution errors. The code consists of non-linear inner codes, which we call `watermark' codes, concatenated with low-density parity-check codes over non-binary elds. The inner code allows probabilistic resynchronisation and provides soft outputs for the outer decoder, which then completes decoding. We present codes of rate 0.7 and transmitted length 5000 bits that can correct 30 insertion/deletion errors per block. We also present codes of rate 3/14 and length 4600 bits that can correct 450 insertion/deletion errors per block.

this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund.

The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.

We introduce an equivalence relation ' between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the '-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of soc systems we prove that the '-equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having \dierent slope" are not conjugate. Classication: Symbolic Dynamics, Combinatoric on words, Automata and Formal Languages. 1 Introduction In this paper we present a new topological invariant for Symbolic Dynamics. The techniques we use and some complementary results are from Combinatorics on words and from the theory of Automata and Formal Languages. Indeed there...

ively 1) if the sum of the binary digits of n is even (respectively odd). This number q can be then obtained as the unique positive solution of 1 = P 1 n=1 ffi n q \Gamman . It is equal to 1:787231650::: In the electronic abstract of [4], the authors ask whether the number q = 1:787231650::: in Theorem 1 above is irrational. The purpose of this note is to prove, as a simple consequence of a result of Mahler, that q is transcendental. Theorem 2 The number q = 1:787231650::: defined as the smallest number in (1; 2) for which there exists a unique expansion of 1 as 1 = P 1 n=1 ffi n q<F1

We investigate the density of critical positions, that is, the ratio between the number of critical positions and the number of all positions of a word, in in nite sequences of words of index one, that is, the period of which is longer than half of the length of the word.

this paper, it is shown that the subword complexity of a D0L language is bounded by cn (resp. cn log n, cn) if the morphism that generates the languages is arbitrary (resp. growing, uniform). This result was extended in [Pan84a]: Theorem 6.7. The subword complexity of an in nite word generated by iterating a morphism is of one of the following types: (n), (n log n), (n log n log n), (n ), or (1)

Abstract. This paper describes the cutting sequences of geodesic flow on the modular surface H/PSL(2, Z) with respect to the standard fundamental domain F = {z = x+iy: −1 1 2 ≤ x ≤