By Andreas Maletti
This publication 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 rigorously reviewed and chosen from 25 submissions. The papers hide subject matters corresponding to info types and coding thought; primary facets of cryptography and protection; algebraic and stochastic types of computing; common sense and software modelling.
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Additional info for Algebraic Informatics: 6th International Conference, CAI 2015, Stuttgart, Germany, September 1-4, 2015. Proceedings
Solution sets for equations over free groups are EDT0L languages. 03426 (2015) 5. : Makanin’s algorithm. ) Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications, vol. 90, chapter 12, pp. 387–442. Cambridge University Press (2002) 6. : The existential theory of equations with rational constraints in free groups is PSPACE-complete. Information and Computation 202, 105–40 (2005). Conference version in STACS 2001. LNCS 2010, pp. 170–182. Springer, Heidelberg (2001) 7.
Notice that c is the sum of two periodic conﬁgurations. Our results imply that any counter example must decompose into a sum of periodic components. In [KS15] we reported the following asymptotic result, using the approach discussed in the present paper. The detailed proof of the result will be published elsewhere. An Algebraic Geometric Approach to Multidimensional Words 41 Theorem 5 ([KS15]). Let c be a two-dimensional non-periodic configuration. Then |Pattm×n (c)| > mn for all but finitely many pairs m, n.
This idea gives the Decomposition theorem: 36 J. Kari and M. Szabados Theorem 3 (Decomposition theorem [KS15]). Let c be a finitary integral configuration with a non-trivial annihilator. Then there exist periodic integral configurations c1 , . . , cm such that c = c1 + · · · + cm . 5 An Example In this section we illustrate how the theory applies to a concrete example. Its properties were brieﬂy mentioned in [KS15], without proofs. Recall that conﬁgurations are not assumed to be ﬁnitary or integral unless explicitly stated so.