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