By Jürgen Albert, German Tischler (auth.), Symeon Bozapalidis, George Rahonis (eds.)
This e-book constitutes the refereed lawsuits of the second one overseas convention on Algebraic Informatics, CAI 2007, held in Thessaloniki, Greece, in may perhaps 2007.
The 10 revised complete papers provided including 9 invited papers have been rigorously reviewed and chosen from 29 submissions. The papers hide subject matters akin to algebraic semantics on graphs and bushes, formal strength sequence, syntactic items, algebraic photograph processing, limitless computation, acceptors and transducers for strings, bushes, graphs, arrays, etc., and selection problems.
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Extra resources for Algebraic Informatics: Second International Conference, CAI 2007, Thessaloniki, Greece, May 21-25, 2007, Revised Selected and Invited Papers
The upper and lower Christoﬀel words are bxa = babaababaabaa and axb = aabaababaabab. Two standard words are associated with them, namely xab = abaababaabaab and xba = abaababaababa. The mechanical words sα,ρ and sα,ρ are purely periodic when α is rational. Moreover, if α = p/(p + q) for p⊥q, then sα,0 = wω and sα,0 = w ω where w and w are precisely the lower and upper Christoﬀel words deﬁned by p and q. It is easily checked that for 0 ≤ n < p + q, (n + 1) p p = n q q ⇐⇒ np mod p + q < (n + 1)p mod p + q .
Pw (n) < n 4 Thus in particular if cw (n) = O(n) then w has bounded palindromic complexity. This holds for Sturmian and episturmian words, for automatic words, and for words that are ﬁxed points of primitive morphisms. For uniformly recurrent 26 J. Berstel words, there is a more precise formula given in . They prove that, provided the set of factors F (w) is closed under reversal, pw (n) + pw (n + 1) ≤ 2 + cw (n + 1) − cw (n) . This is sharp for Sturmian words: these are characterized by the fact that pw (n) = 1 if n is even and pw (n) = 2 if n is odd , and also for AR-words over r > 2 letters: these words have palindrome complexity pw (n) = 1 if n is even and pw (n) = r if n is odd .
82(1), 71–84 (1991) 49. : A geometric proof of the enumeration formula for Sturmian words. Internat. J. Algebra Comput. 3(3), 349–355 (1993) Sturmian and Episturmian Words 47 50. : Random generation of ﬁnite Sturmian words. In: Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993), vol. 153, pp. 29–39 (1996) 51. : On the number of digital straight line segments. IEEE Trans. Pattern Anal. Mach. Intell. 10(6), 880–887 (1988) 52. : The number of digital straight lines on an n × n grid.