Search results for "Programming"
showing 10 items of 3090 documents
Semigroups of composition operators and integral operators in spaces of analytic functions
2013
We study the maximal spaces of strong continuity on BMOA and the Bloch space B for semigroups of composition operators. Characterizations are given for the cases when these maximal spaces are V MOA or the little Bloch B0. These characterizations are in terms of the weak compactness of the resolvent function or in terms of a specially chosen symbol g of an integral operator Tg. For the second characterization we prove and use an independent result, namely that the operators Tg are weakly compact on the above mentioned spaces if and only if they are compact.
New spaces of matrices with operator entries
2019
In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a finite number of diagonals. We will use the Schur product with Toeplitz matrices generated by summability kernels to describe such a class and show that in the case of Toeplitz matrices it can be identified with the space of continuous functions with values in $\mathcal B(H)$. We shall also introduce matriceal versions with operator entries of classical spaces of holomorphic functions such as $H^\infty(\mathbb{D})$ and $A(\mathbb{D})$ when dealing with upper t…
Padding and the expressive power of existential second-order logics
1998
Padding techniques are well-known from Computational Complexity Theory. Here, an analogous concept is considered in the context of existential second-order logics. Informally, a graph H is a padded version of a graph G, if H consists of an isomorphic copy of G and some isolated vertices. A set A of graphs is called weakly expressible by a formula ϕ in the presence of padding, if ϕ is able to distinguish between (sufficiently) padded versions of graphs from A and padded versions of graphs that are not in A.
On the Power of Tree-Walking Automata
2000
Tree-walking automata (TWAs) recently received new attention in the fields of formal languages and databases. Towards a better understanding of their expressiveness, we characterize them in terms of transitive closure logic formulas in normal form. It is conjectured by Engelfriet and Hoogeboom that TWAs cannot define all regular tree languages, or equivalently, all of monadic second-order logic. We prove this conjecture for a restricted, but powerful, class of TWAs. In particular, we show that 1-bounded TWAs, that is TWAs that are only allowed to traverse every edge of the input tree at most once in every direction, cannot define all regular languages. We then extend this result to a class …
Polyhedral results for a vehicle routing problem
1991
Abstract The Vehicle Routing Problem is a well known, and hard, combinatorial problem, whose polyhedral structure has deserved little attention. In this paper we consider the particular case in which all the demands are equal (since in the general case the associated polytope may be empty). From a known formulation of the problem we obtain the dimension of the corresponding polytope and we study the facetial properties of every inequality in it.
ON THE STAR HEIGHT OF RATIONAL LANGUAGES
1994
Two problems concerning the star height of a rational language are investigated: the star height one problem and the relationships between the unambiguity of an expression and its star height. For this purpose we consider the class of factorial, transitive and rational (FTR) languages. From the algebraic point of view a FTR language is the set of factors of a rational submonoid M. Two subclasses of FTR languages are introduced: renewal languages, corresponding to the case of M finitely generated, and unambiguous renewal languages, corresponding to the case of M finitely generated and free. We prove that a FTR language has star height one if and only if it is renewal. This gives a simple de…
Nondeterministic operations on finite relational structures
1998
Abstract This article builds on a tutorial introduction to universal algebra for language theory (Courcelle, Theoret. Comput. Sci. 163 (1996) 1–54) and extends it in two directions. First, nondeterministic operations are considered, i.e., operations which give a set of results instead of a single one. Most of their properties concerning recognizability and equational definability carry over from the ordinary case with minor modifications. Second, inductive sets of evaluations are studied in greater detail. It seems that they are handled most naturally in the framework presented here. We consider the analogues of top-down and bottom-up tree transducers. Again, most of their closure propertie…
On block pumpable languages
2016
Ehrenfeucht, Parikh and Rozenberg gave an interesting characterisation of the regular languages called the block pumping property. When requiring this property only with respect to members of the language but not with respect to nonmembers, one gets the notion of block pumpable languages. It is shown that these block pumpable are a more general concept than regular languages and that they are an interesting notion of their own: they are closed under intersection, union and homomorphism by transducers; they admit multiple pumping; they have either polynomial or exponential growth.
Branch and bound for the cutwidth minimization problem
2013
The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solu…
Optimization procedures for the bipartite unconstrained 0-1 quadratic programming problem
2014
The bipartite unconstrained 0-1 quadratic programming problem (BQP) is a difficult combinatorial problem defined on a complete graph that consists of selecting a subgraph that maximizes the sum of the weights associated with the chosen vertices and the edges that connect them. The problem has appeared under several different names in the literature, including maximum weight induced subgraph, maximum weight biclique, matrix factorization and maximum cut on bipartite graphs. There are only two unpublished works (technical reports) where heuristic approaches are tested on BQP instances. Our goal is to combine straightforward search elements to balance diversification and intensification in bot…