By Andreas Maletti
This booklet constitutes the refereed court cases 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 disguise issues reminiscent of information versions and coding concept; basic features of cryptography and safeguard; algebraic and stochastic versions of computing; good judgment and software modelling.
Read or Download Algebraic Informatics: 6th International Conference, CAI 2015, Stuttgart, Germany, September 1-4, 2015. Proceedings PDF
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Additional resources for Algebraic Informatics: 6th International Conference, CAI 2015, Stuttgart, Germany, September 1-4, 2015. Proceedings
Recompression: a simple and powerful technique for word equations. , Wilke, T. ) STACS. LIPIcs, vol. 20, pp. 233–244. Schloss DagstuhlLeibniz-Zentrum f¨ ur Informatik. To appear in JACM, Dagstuhl, Germany (2013) 28 V. Diekert 12. : Eﬃcient randomized pattern-matching algorithms. IBM Journal of Research and Development 31, 249–260 (1987) 13. : Elementary theory of free non-abelian groups. J. of Algebra 302, 451–552 (2006) 14. : Complexity of Makanin’s algorithm. Journal of the Association for Computing Machinery 43(4), 670–684 (1996) 15.
The border of p will be the subpicture corresponding to the portion where p and p match. The two dimensions of the structure allow several possibilities to specialize this notion. The simplest one is when the matching is checked only by sliding the two picture copies with a horizontal or a vertical move: in this case we allow only borders with the same number of columns or rows of the picture p itself. Notice that this case is not really interesting, since pictures can be handled as they were thick strings on the alphabet either of the columns or of the rows: then the string algorithm by Nielsen can be directly applied to calculate all unbordered pictures.
M − 1} the vectors on the right side span the whole Cm . Therefore the left side must be the zero vector, and especially for α such that v0 ∈ Sα we have av Z v . 0 = fα (Z) = v∈Sα Because Z does not have zero coordinates, each term on the right hand side is non-zero. But the sum is zero, therefore there are at least two vectors v0 , v ∈ Sα . From the deﬁnition of Sα we have Z rv = Z rv0 = α, so Z is a root of X rv −X rv0 . Now we are ready to apply the Nullstellensatz to obtain a simple annihilator: Theorem 2.