Algebraic Informatics: 6th International Conference, CAI by Andreas Maletti

By Andreas Maletti

This e-book constitutes the refereed complaints of the sixth foreign convention on Algebraic Informatics, CAI 2015, held in Stuttgart, Germany, in September 2015.

The 15 revised complete papers awarded have been conscientiously reviewed and chosen from 25 submissions. The papers disguise issues similar to info versions and coding concept; basic features of cryptography and safety; algebraic and stochastic versions of computing; good judgment and software modelling.

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Extra resources for Algebraic Informatics: 6th International Conference, CAI 2015, Stuttgart, Germany, September 1-4, 2015. Proceedings

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Szabados The next lemma states that one-directed configurations in different directions are linearly independent. Lemma 5. Let c1 (X), . . , cn (X) be two-dimensional configurations that are one-directed and pairwise non-parallel. Then a1 , . . , an ∈ C satisfy a1 c1 (X) + · · · + an cn (X) = 0 if and only if a1 = · · · = an = 0. Proof. We prove the claim by induction on n. Case n = 1: since c1 (X) is onedirected, it is not the zero power series. Hence a1 c1 (X) = 0 if and only if a1 = 0. Suppose then the claim has been proved for n − 1, and let a1 , .

We have proved the following result: Theorem 4. Let α > 0 be irrational. The two-dimensional configuration s over the binary alphabet {0, 1} defined by sij = (i + j)α − iα − jα is a sum of three periodic integral configurations but not a sum of finitely many finitary periodic configurations. 6 Conclusions and Applications We have proved that multidimensional configurations of low local complexity can be expressed as a sum of periodic configurations. We have also demonstrated that sometimes the periodic components are necessarily non-finitary.

Inf. Control 16, 173–200 (1970) 7. : Forty years of formal power series in automata theory. , Yu, S. ) Half Century of Automata Theory, pp. 49–71. World Scientific (2001) 8. : Semirings, Automata, Languages. Springer (1986) 9. : Rational and recognisable power series. , Vogler, H. ) Handbook of Weighted Automata, Chapter 4, pp. 105–174. it Abstract. The notion of unbordered picture generalizes to two dimensions the notion of unbordered (or bifix-free) string. We extend to two dimensions Nielsen’s construction of unbordered strings ([23]) and describe an algorithm to construct the set U (m, n) of unbordered pictures of fixed size (m, n).

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