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

By Andreas Maletti

This booklet constitutes the refereed complaints of the sixth overseas 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 hide issues resembling information types and coding idea; primary points of cryptography and safety; algebraic and stochastic types of computing; good judgment and application modelling.

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

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The set of annihilating polynomials is an ideal of the polynomial ring. Using Hilbert’s Nullstellensatz we show that the annihilator ideal contains polynomials of simple form. In particular, we show that the configuration can be annihilated by a product of difference filters (X v − 1) that subtract from a configuration its translated copy. This in turn implies a decomposition of the configuration into a sum of periodic components. The result reported here have been presented in [KS15], except for the proofs related to the example in Section 5.

On power series over a graded monoid. , Kazuo, I. ) Gruska Festschrift. LNCS, vol. 8808, pp. 49–55. Springer, Heidelberg (2014) 4. : Ambiguity and transcendence. In: Brauer, W. ) Automata, Languages and Programming. LNCS, pp. 179–188. Springer, Heidelberg (1985) 5. : The equivalence problem of multitape finite automata. Theoretical Computer Science 78, 347–355 (1991) 6. : On the entropy of context-free languages. Inf. Control 16, 173–200 (1970) 7. : Forty years of formal power series in automata theory.

Xvdd . vd =−∞ As usual, we abbreviate the vector (x1 , . . , xd ) of variables as X, and write monomial xv11 . . xvdd as X v for v = (v1 , . . , vd ) ∈ Zd . Configuration c can now be expressed compactly as cv X v . c(X) = (1) v∈Zd Usually we let A ⊆ Z so that configurations are power series with integer coefficients, but to use Nullstellensatz we need an algebraically closed field, so that An Algebraic Geometric Approach to Multidimensional Words 31 frequently we consider multivariate power series and polynomials over C.

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