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The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…

An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…

Prime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved…

Polynomial factorization is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different variants of this problem. In parallel, algebraic complexity…

Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…

We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision…

We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…

Based on the well-known algorithm of W. Penney we determine the set of lengths of the canonical representation of integers with respect to the trinomial X^2m + 2X^m + 2.

We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…

While efficient randomized algorithms for factorization of polynomials given by algebraic circuits have been known for decades, obtaining an even slightly non-trivial deterministic algorithm for this problem has remained an open question of…

We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…

We compute the free energy of the planar monomer-dimer model. Unlike the classical planar dimer model, an exact solution is not known in this case. Even the computation of the low-density power series expansion requires heavy and nontrivial…

Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…

The power of real-time Turing machines using sublinear space is investigated. In contrast to a claim appearing in the literature, such machines can accept non-regular languages, even if working in deterministic mode. While maintaining a…

Bellantoni and Cook have given a function-algebra characterization of the polynomial-time computable functions via an unbounded recursion scheme which is called safe recursion. Inspired by their work, we characterize the exponential-time…

We prove that centralizers of elements in [f.g. free]-by-cyclic groups are computable. As a corollary we get that, given two conjugate elements in a [f.g. free]-by-cyclic group, the set of conjugators can be computed and that the conjugacy…

We show how polynomial path orders can be employed efficiently in conjunction with weak innermost dependency pairs to automatically certify polynomial runtime complexity of term rewrite systems and the polytime computability of the…

Character polynomials are used to study the restriction of a polynomial representation of a general linear group to its subgroup of permutation matrices. A simple formula is obtained for computing inner products of class functions given by…

We say a power series $a_0+a_1q+a_2q^2+\cdots$ is \emph{multiplicative} if $n\mapsto a_n/a_1$ for positive integers $n$ is a multiplicative function. Given the Eisenstein series $E_{2k}(q)$, we consider formal multiplicative power series…

Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…