By Jürgen Albert, German Tischler (auth.), Symeon Bozapalidis, George Rahonis (eds.)
This ebook constitutes the refereed complaints of the second one overseas convention on Algebraic Informatics, CAI 2007, held in Thessaloniki, Greece, in could 2007.
The 10 revised complete papers offered including 9 invited papers have been conscientiously reviewed and chosen from 29 submissions. The papers disguise themes comparable to algebraic semantics on graphs and timber, formal energy sequence, syntactic items, algebraic photo processing, limitless computation, acceptors and transducers for strings, timber, graphs, arrays, etc., and choice problems.
Read or Download Algebraic Informatics: Second International Conference, CAI 2007, Thessaloniki, Greece, May 21-25, 2007, Revised Selected and Invited Papers PDF
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Extra info for Algebraic Informatics: Second International Conference, CAI 2007, Thessaloniki, Greece, May 21-25, 2007, Revised Selected and Invited Papers
Heinis provided independently in  a lower bound, and Tarannikov  shows that π n g (n) = Θ(n2 (2 cos ) ) +2 which is better for ≥ 3. On the other hand, the number of factors of length n of strict episturmian words (or equivalently of Arnoux-Rauzy words) has been considered. A bispecial factor is a word that is both a left and a right special factor of the same ArnouxRauzy word. Sturmian and Episturmian Words 37 Proposition 33.  The number of factors of length n of strict episturmian words over a k-letter alphabet is n−2 k + (n − 1)k(k − 1) + (k − 1)2 (n − i − 1)b(i) i=1 where b(m) is the number of bispecial factors of length m of Arnoux-Rauzy words.
In fact, the authors give the exact expression for the arithmetical complexity of Sturmian words for 1/3 < α < 1/2 (note that exchanging the two letters in a Sturmian words replaces the slope α by 1 − α without changing the complexity, so the result holds also for 1/2 < α < 2/3). Denote by (rk ) the decreasing sequence of rational numbers given by rk = k/(3k − 1), for k ≥ 2. Thus r2 = 2/3, r3 = 3/8. Theorem 3.  For any irrational α with 1/3 < α < 1/2, one has aα (n) = h(n) − 8 h(n) − 9 if n is odd otherwise for n ≥ 3k, where k is such that rk−1 > α > rk .
Proposition 11.  A word is central if and only if it is a palindrome preﬁx of a characteristic Sturmian word. Proposition 12.  A word is central if and only if it is a binary right iterated palindrome. Proposition 13.  A word w is central if and only if wab or wba is a standard Sturmian word. Proposition 14.  A word w is central if and only if it is a palindrome and wab (or wba) is a product of two palindromes. 34 J. Berstel Proposition 15.  A word w is a conjugate of a standard Sturmian word if and only if it is primitive and all its conjugates are balanced.