By Andreas Maletti
This publication constitutes the refereed lawsuits of the sixth overseas convention on Algebraic Informatics, CAI 2015, held in Stuttgart, Germany, in September 2015.
The 15 revised complete papers offered have been rigorously reviewed and chosen from 25 submissions. The papers hide subject matters akin to information versions and coding idea; primary elements of cryptography and defense; algebraic and stochastic types of computing; common sense 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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Extra resources for Algebraic Informatics: 6th International Conference, CAI 2015, Stuttgart, Germany, September 1-4, 2015. Proceedings
De Abstract. Geometry and Diophantine equations have been ever-present in mathematics. According to the existing literature the work of Diophantus of Alexandria was mentioned before 364 AD, but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justiﬁed at all. However, a Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation.
Soundness means that a guess can never transform a unsolvable system into a solvable one. Completeness means that for every solution x, there is some choice of correct guesses such that the procedure terminates with a system which has a trivial solution. So we begin by guessing a solution x ∈ Nn . First, we can check whether x = 0 is a solution by looking at c. Indeed, x = 0 is a solution if and only if c = 0. ) We deﬁne a vector b = c. The vector b (and the solution x) will be modiﬁed during the procedure.
1–15. , Heidelberg (2014) 8. : Word-mappings of level 2. Theory Comput. Syst. 54, 111–148 (2014) 9. : Satisﬁability of word equations with constants is in exponential space. In: Proc. 39th Ann. Symp. on Foundations of Computer Science (FOCS 1998), pp. 112–119. IEEE Computer Society Press, Los Alamitos (1998) 10. : Satisﬁability of equations in free groups is in PSPACE. In: Proceedings 32nd Annual ACM Symposium on Theory of Computing, STOC 2000, pp. 21–27. ACM Press (2000) 11. : Recompression: a simple and powerful technique for word equations.