Related papers: Quantifier Elimination for Statistical Problems
We give a quantifier elimination procedures for the extension of Presburger arithmetic with a unary threshold counting quantifier $\exists^{\ge c} y$ that determines whether the number of different $y$ satisfying some formula is at least $c…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
Elimination of unknowns in systems of equations, starting with Gaussian elimination, is a problem of general interest. The problem of finding an a priori upper bound for the number of differentiations in elimination of unknowns in a system…
Qualitative numerical planning is classical planning extended with non-negative real variables that can be increased or decreased "qualitatively", i.e., by positive indeterminate amounts. While deterministic planning with numerical…
Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the…
By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…
Inference in graphical models consists of repeatedly multiplying and summing out potentials. It is generally intractable because the derived potentials obtained in this way can be exponentially large. Approximate inference techniques such…
We apply verified numerics to the Nirenberg problem, proving that a genuine solution exists near two given computer-generated approximate solutions. This proves existence of a solution for a particular prescribed curvature that was…
This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
Second-order quantifier elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
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…
Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical…
First principles approaches have revolutionized our ability in using computers to predict, explore and design materials. A major advantage commonly associated with these approaches is that they are fully parameter free. However, numerically…
We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with…
Quantification is the machine learning task of estimating test-data class proportions that are not necessarily similar to those in training. Apart from its intrinsic value as an aggregate statistic, quantification output can also be used to…
In 1985, van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretic argument, which provides no…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…