Related papers: Quantifier Elimination for Statistical Problems

We propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier…

We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. QE dates back to Tarski's work in the 1940s with software to perform it dating to the 1970s. There is a great body of work considering its…

We consider existential problems over the reals. Extended quantifier elimination generalizes the concept of regular quantifier elimination by providing in addition answers, which are descriptions of possible assignments for the quantified…

This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…

We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers. Furthermore, we argue that quantifier elimination theory…

We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…

All known quantifier elimination procedures for Presburger arithmetic require doubly exponential time for eliminating a single block of existentially quantified variables. It has even been claimed in the literature that this upper bound is…

We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically…

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite…

We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…

We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…

Quantifier elimination over the reals is a central problem in computational real algebraic geometry, polynomial system solving and symbolic computation. Given a semi-algebraic formula (whose atoms are polynomial constraints) with…

Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.

Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining what we call almost free algebras. One of…

We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…

We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition…

Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations. In this work, we supply logical foundations to this practice,…

We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding…

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…

We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a…