Sequence enumeration is a method for deriving a system model based on informal requirements. Under sequence enumeration, stimulus (input) sequences are considered in a breadth-first manner, with the expected system response to each sequence given. Not all sequences of stimuli are considered since a sequence need not be extended if either it is illegal (it cannot be applied in practice) or it ca...

An enumeration kernel as defined by Creignou et al. (2017) [11] for a parameterized problem consists of an algorithm that transforms each instance into one whose size is bounded the parameter plus solution-lifting efficiently enumerates all solutions from set kernel. We propose to consider two new versions kernels asking original can be enumerated in polynomial time or with delay solutions. Usi...

We prove sharp bounds on eigenvalues of the Laplacian that complement the Faber–Krahn and Luttinger inequalities. In particular, we prove that the ball maximizes the first eigenvalue and minimizes the spectral zeta function and heat trace. The normalization on the domain incorporates volume and a computable geometric factor that measures the deviation of the domain from roundness, in terms of m...

This note addresses the following problem posed by S . M. Ulam. Find a concise expression for the number of classes of sets of n indistinguishable elements . Here, a class of sets is a set whose members are subsets of a given finite set of n elements, and referring to the elements as indistinguishable means that two classes are identical if some permutation on the elements transforms one class ...

Functions are exhibited which interpolate the magnitude of a solution y of a linear, homogeneous, second-order differential equation at its critical points, \y'\ at the zeros of y, and \fi0y(t)Kt) àt\ at the zeros of y. Except for a normalization condition, the interpolating functions are independent of the specific solution v. A theorem similar in its conclusions to the Sonin-Pólya-Butlewski t...

We enumerate nonisomorphic lattice-square designs yielded by a conventional construction. Constructed designs are speci3ed by words composed from 3nite-3eld elements. These words are permuted by the isomorphism group in question. The latter group contains a direct-product subgroup, acting, respectively, upon the positions and identities of the 3nite-3eld elements. We review enumeration theory f...

12 Large singularities of analytic functions 113 12.1 The saddle point 13 Multivariate generating functions 128 14 Mellin and other integral transforms 134 15 Functional equations, recurrences, and combinations of methods 137 15.1 Implicit functions, graphical enumeration, and related

Degree theory studies mathematical structures, which arise from a formal notion of reducibility between sets of natural numbers based on their computational strength. In the past years many reducibilities, together with their induced degree structures have been investigated. One of the aspects in these investigations is always the characterization of the theory of the studied structure. One dis...

The purpose of this paper is to count the number of isomorphism types of reduced Witt rings of nondegenerate symmetric bilinear forms over fields with a fixed number of orderings. All of the background material necessary for understanding the situation in which this counting problem arises will be described in Section 1. Using results from [2], this problem is restated in Section 2 in terms of ...