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

By Andreas Maletti

ISBN-10: 3319230204

ISBN-13: 9783319230207

ISBN-10: 3319230212

ISBN-13: 9783319230214

This publication constitutes the refereed lawsuits of the sixth foreign convention on Algebraic Informatics, CAI 2015, held in Stuttgart, Germany, in September 2015.

The 15 revised complete papers provided have been conscientiously reviewed and chosen from 25 submissions. The papers hide themes akin to information types and coding conception; primary elements of cryptography and defense; algebraic and stochastic versions of computing; common sense and software modelling.

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

Example text

Then there exists an integer r such that for every positive integer n relatively prime to r we have f (X n ) ∈ Ann(c). Proof. Denote f (X) = av X v . First we prove the claim for the case when n is a large enough prime. Let p be a prime, then we have f p (X) ≡ f (X p ) (mod p). Because f annihilates c, multiplying both sides by c(X) results in 0 ≡ f (X p )c(X) (mod p). The coefficients in f (X p )c(X) are bounded in absolute value by s = cmax |av |, where cmax is the maximum absolute value of coefficients in c.

3. Define bi = bi /2 and xi = xi /2. We obtain a new system AX = b with solution Ax = b . 4. Rename b and x as b and x. end while. The clue is that, since b 1 ≤ A 1 by Equation (1), we obtain by Equation (2) and the third step an invariant: b 1 = b 1 /2 ≤ b 1 /2 + A 1 /2 ≤ A 1 . The procedure is obviously sound. It is complete because in each round x 1 decreases and therefore termination is guaranteed for every solution as long as we make correct guesses. The final observation is that the procedure defines a More Than 1700 Years of Word Equations 27 finite graph.

1007/978-3-319-23021-4 5 46 M. Anselmo et al. called a cross-bifix-free code. Constructive methods for cross-bifix-free codes are investigated in [7,10,13]. The increasing interest for pattern recognition and image processing has motivated the research on two-dimensional languages of pictures. A two dimensional string is called picture and it is given by a rectangular array of symbols taken from a finite alphabet Σ. The set of all pictures over Σ is usually denoted by Σ ∗∗ . Extending results from the formal (string) languages theory to two dimensions is a very challenging task.

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Algebraic Informatics: 6th International Conference, CAI 2015, Stuttgart, Germany, September 1-4, 2015. Proceedings by Andreas Maletti

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