Информационная система "Конференции"

Abstracts

Computability theory

We suggest new approaches to algorithmic problems in Algebra. These approaches have recently appeared due to the need of solving so called "Search" problems. Such a setup is motivated by the need to analyze the cryptosystems whose platforms are algebraic systems. Beside the classical worst-case complexity we consider on-average and generic complexity of particular algorithmic problems. Recent solution of Tarski problem in combinatorial group theory has given rise to numerous algorithms, which unfortunately are not very effective from the computational viewpoint. We suggest new approaches to these algorithmic problems, which use ideas of algebraic geometry and methods of infinite words. This should result more efficient algorithms in this domain.

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