Search results for "PROGRAM"
showing 10 items of 5938 documents
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…
Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations
1999
Let X be either the class of all transitive groups of finitary permutations, or the class of all periodic irreducible finitary linear groups. We show that almost primitive X-groups are countably recognizable, while totally imprimitive X-groups are in general not countably recognizable. In addition we derive a structure theorem for groups all of whose countable subsets are contained in totally imprimitive X-subgroups. It turns out that totally imprimitive p-groups in the class X are countably recognizable.
Classification of n-dimensional subvarieties of G(1, 2n) that can be projected to G(1, n + 1)
2005
A structure theorem is given for n-dimensional smooth subvarieties of the Grassmannian G(1, N); with N >= n + 3, that can be isomorphically projected to G(1, n + 1). A complete classification in the cases N = 2n + 1 and N = 2n follows, as a corollary.
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.
Minimal forbidden words and symbolic dynamics
1996
We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system defined by L.
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.