Related papers: Borel computation of names in template iterations
We present a simple iteration for the Lebesgue identity on partitions, which leads to a refinement involving the alternating sums of partitions.
In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…
We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
In this paper, a computably definable predicate is defined and characterized. Then, it is proved that every separable infinite-dimensional Hilbert structure in an effectively presented language is computable. Moreover, every definable…
A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded…
In this paper we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The…
In this paper we give an Immerman's Theorem for real-valued computation. We define circuits operating over real numbers and show that families of such circuits of polynomial size and constant depth decide exactly those sets of vectors of…
We refine the complexity landscape for enumeration problems by introducing very low classes defined by using Boolean circuits as enumerators. We locate well-known enumeration problems, e.g., from graph theory, Gray code enumeration, and…
Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from…
In this paper, we propose a new algebraic winding number and prove that it computes the number of complex roots of a polynomial in a rectangle, including roots on edges or vertices with appropriate counting. The definition makes sense for…
We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the…
We establish a simple recurrence formula for the number $Q_g^n$ of rooted orientable maps counted by edges and genus. We also give a weighted variant for the generating polynomial $Q_g^n(x)$ where $x$ is a parameter taking the number of…
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual…
The number of ad-nilpotent ideals of the Borel subalgebra of the classical Lie algebra of type B_n is determined using combinatorial arguments involving a generalization of Dyck-paths. We also solve a similar problem for the untwisted…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
By establishing an interesting connection between ordinary Bell polynomials and rational convolution powers, some composition and inverse relations of Bell polynomials as well as explicit expressions for convolution roots of sequences are…
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…