Related papers: Polygraphic programs and polynomial-time functions
We study the problem of automatically computing the time complexity of concurrent object-oriented programs. To determine this complexity we use intermediate abstract descriptions that record relevant information for the time analysis (cost…
Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
In our previous paper, Real Polynomials with a Complex Twist [see http://archives.math.utk.edu/ICTCM/VOL28/A040/paper.pdf], we used advancements in computer graphics that allow us to easily illustrate more complete graphs of polynomial…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
Polymorphic types are an important feature in most strongly typed programming languages. They allow functions to be written in a way that can be used with different data types, while still enforcing the relationship and constraints between…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Euler diagrams are a tool for the graphical representation of set relations. Due to their simple way of visualizing elements in the sets by geometric containment, they are easily readable by an inexperienced reader. Euler diagrams where the…
This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of…
We discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time). We discover that all these claims…
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…
We investigate the expressive power of a Turing-complete logic based on game-theoretic semantics. By defining suitable fragments and variants of the logic, we obtain a range of natural characterizations for some fundamental families of…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
The computational complexity of polynomial ideals and Gr\"obner bases has been studied since the 1980s. In recent years, the related notions of polynomial subalgebras and SAGBI bases have gained more and more attention in computational…