Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in O(dm · (n/⌈d/2⌉) ⌈d/2⌉) time, and requires a rerun of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning str...

out, R will represent an associative ring with center Z(R). As usual the commutator xy−yx will be denoted by [x,y]. We will use basic commutator identities [xy,z] = [x,z]y+x[y,z] and [x,yz]= [x,y]z+y[x,z]. Recall that a ring R is prime if aRb = (0) implies that a = 0 or b = 0, and is semiprime if aRa = (0) implies a = 0. An additive mapping x x∗ on a ring R is called involution in case (xy)∗ = ...

For any fixed integer d≥ 1, let ud(N) denote the number of permutations in the symmetric group S(N)which have no decreasing subsequence of length d+1.Regev determined the asymptotic form of ud(N) in the N→ ∞ limit; his argument relies on Selberg’s integral formula. In this article we give an elementary derivation of Regev’s formula via an asymptotic bijection with standard Young tableaux of rec...

We summarize recent progress in the understanding of minimal string theory, focusing on the worldsheet description of physical operators and D-branes. We review how a geometric interpretation of minimal string theory emerges naturally from the study of the D-branes. This simple geometric picture ties together many otherwise unrelated features of minimal string theory, and it leads directly to a...

In the papers [1, 2, 4–6, 8] the similarities and differences between systems of sequents and systems of natural deduction for some fragments of intuitionistic logic were presented. The main goal of almost all of these papers was to study the connection between cut-free derivations and normal derivations. It is a well-known property that the natural deduction image of a cut-free derivation is a...

This paper presents techniques to reason about the composition of configurable components and to automatically derive consistent compositions. The reasoning is achieved by describing components in a formal component description language, that allows the description of component variability, dependencies and configuration actions. It also enables the automatic, configuration-driven, derivation o...

In this paper we study planar polynomial differential systems of this form: dX dt = Ẋ = A(X, Y ), dY dt = Ẏ = B(X, Y ), where A, B ∈ Z[X, Y ] and degA ≤ d, degB ≤ d, ‖A‖∞ ≤ H and ‖B‖∞ ≤ H. A lot of properties of planar polynomial differential systems are related to irreducible Darboux polynomials of the corresponding derivation: D = A(X, Y )∂X + B(X, Y )∂Y . Darboux polynomials are usually comp...

Let A be an integral k-algebra of finite type over a field k of characteristic zero. Let F be a family of k-derivations on A and MF the A-module spanned by F . In this paper, we generalise a result due to A. Nowicki and construct an element ∂ of MF such that ker ∂ = ∩d∈Fker d. Such a derivation is called F-minimal. Then we establish a density theorem for F-minimal derivations in MF .

Let k[X]:= k[x 0 , x 1 ,. .. , x n ] be a polynomial algebra over a field k of characteristic zero. We offer an algorithm for calculation of kernel of Weitzenbök derivation d(x i) = x i−1 ,. .. , d(x 0) = 0, i = 1. .. n that is based on an analogue of the well known Casimir elements of finite dimensional Lie algebras. By using this algorithm, the kernel is calculated in the case n < 7.

A rule of thumb derivation of the Dirac-Born-Infeld action for D-branes is studied à la Fradkin and Tseytlin, by simply integrating out of the superstring coordinates in a narrow strip attached to the D-branes. In case of superstrings, the coupling of Ramond-Ramond fields as well as the Dirac-Born-Infeld type coupling of the Neveu Schwarz-Neveu Schwarz fields come out in this way.