Treewidth and logical definability of graph products
نویسندگان
چکیده
منابع مشابه
On the Logical Definability of Certain Graph and Poset Languages
We show that it is equivalent, for certain sets of finite graphs, to be definable in CMS (counting monadic second-order, a natural extension of monoadic second-order logic), and to be recognizable in an algebraic framework induced by the notion of modular decomposition of a finite graph. More precisely, we consider the set F∞ of composition operations on graphs which occur in the modular decomp...
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The relationship between counting functions and logical expressibility is explored. The most well studied class of counting functions is #P, which consists of the functions counting the accepting computation paths of a nondeterministic polynomial-time Turing machine. For a logic L, #L is the class of functions on nite structures counting the tuples (T ; c) satisfying a given formula (T ; c) in ...
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We shall touch upon the theory of Graph Minors by Robertson and Seymour. This theory gives a very general condition under which a graph problem has a polynomial time algorithm (though the algorithms that come out of the theory are often not practical). We shall review a small part of this theory, and illustrate how dynamic programming can be used to solve some NP-hard problems on restricted cla...
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The family of rational subsets of a direct product of free monoids Σ∗ 1×. . .×Σ ∗ n (the rational relations) is not closed under Boolean operations, except when n = 1 or when all Σi’s are empty or singletons. In this paper we introduce the family of generalized rational subsets of an arbitrary monoid as the closure of the singletons under the Boolean operations, concatenation and Kleene star (j...
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We investigate here NP optimization problems from a logical deenability standpoint. We show that the class of optimization problems whose optimum is deenable using rst-order formulae coincides with the class of polynomially bounded NP optimization problems on nite structures. After this, we analyze the relative expressive power of various classes of optimization problems that arise in this fram...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2009
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2008.10.019