Related papers: A probabilistic algorithm to test local algebraic …
A right [left] locally testable language S is a language with the property that for some non negative integer k two words u and v in alphabet S are equal in the semi group if (1) the prefix and suffix of the words of length k coincide, (2)…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
Marginal problems naturally arise in a variety of different fields: basically, the question is whether some marginal/partial information is compatible with a joint probability distribution. To this aim, the characterization of marginal sets…
This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove…
A locally testable semigroup S is a semigroup with the property that for some nonnegative integer k, called the order or level of local testability, two words u and v in some set of generators for semigroup S are equal in the semigroup if…
The \emph{Orbit Problem} consists of determining, given a linear transformation $A$ on $\mathbb{Q}^d$, together with vectors $x$ and $y$, whether the orbit of $x$ under repeated applications of $A$ can ever reach $y$. This problem was…
Autonomous systems are often required to operate in partially observable environments. They must reliably execute a specified objective even with incomplete information about the state of the environment. We propose a methodology to…
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…
This paper is our second step towards developing a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by an arithmetic circuit has some types of monomials in its…
We present a heuristic strategy for marginal MAP (MMAP) queries in graphical models. The algorithm is based on a reduction of the task to a polynomial number of marginal inference computations. Given an input evidence, the marginals mass…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
The study of semifeasible algorithms was initiated by Selman's work a quarter of century ago [Sel79,Sel81,Sel82]. Informally put, this research stream studies the power of those sets L for which there is a deterministic (or in some cases,…
Partially Observable Markov Decision Processes (POMDPs) are a natural and general model in reinforcement learning that take into account the agent's uncertainty about its current state. In the literature on POMDPs, it is customary to assume…
An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system…
Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a small portion of the input. The most typical situation where sublinear time algorithms are…