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Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in…

We review and possibly add some new variant to the existing derivations of the formula for the area of Jordan lattice polygons drawn on two-dimensional lattices. The formula is known as Pick's theorem and is related to the number theory…

We develop explicit formulas and algorithms for arithmetic in radical function fields K/k(x) over finite constant fields. First, we classify which places of k(x) whose local integral bases have an easy monogenic form, and give explicit…

An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…

We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…

This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems $Bx = b$ with positive definite $B$ for $x$. The goal is to replace the point estimates returned by existing methods with…

Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…

For an algebraic number $\alpha$ we consider the orders of the reductions of $\alpha$ in finite fields. In the case where $\alpha$ is an integer, it is known by the work on Artin's primitive root conjecture that the order is "almost always…

We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.

New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…

The unit cost model is both convenient and largely realistic for describing integer decision algorithms over (+,*). Additional operations like division with remainder or bitwise conjunction, although equally supported by computing hardware,…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Assuming the Generalized Riemann Hypothesis, we design a deterministic algorithm that, given a prime p and positive integer m=o(sqrt(p)/(log p)^4), outputs an elliptic curve E over the finite field F_p for which the cardinality of E(F_p) is…

We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…

Working with exhaustive search on large dataset is infeasible for several reasons. Recently, developed techniques that made pattern set mining feasible by a general solver with long execution time that supports heuristic search and are…

We compute the number of points over finite fields of some algebraic varieties related to cluster algebras of finite type. More precisely, these varieties are the fibers of the projection map from the cluster variety to the affine space of…

We present an algorithm, called Predict, for updating beliefs in causal networks quantified with order-of-magnitude probabilities. The algorithm takes advantage of both the structure and the quantification of the network and presents a…

Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…