Computability in Europe 2008
Logic and Theory of Algorithms

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Regular Talk:
Algorithmic Properties of Structures for Languages with Two Unary Functional Symbols

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Speaker: Ekaterina Fokina


When studying algorithmic properties of structures with
interesting  algebraic and model--theoretic  properties, one often
uses known structural properties of the structures. However, it is
often the case that results on particular kinds of structures can
be transferred to structures from many other interesting classes.
One of the ways of such generalization involves coding of the
original structure into a structure from the given class in a way
that is effective enough to preserve interesting algorithmic
properties. There are several constructions that allow us to
reduce algorithmic questions for arbitrary structures to graphs.
They also show that if we have a result for a graph, we also have
it for a structure for any language containing at least one
$n$--ary relational symbol, where $n\geq 2$. We prove that it is
possible to generalize this approach and get the same results for
structures for a language with two unary functional symbols. Thus,
we get the results for structures for so--called rich languages.

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