Related papers: Partial Quantifier Elimination
Programming-by-Example (PBE) systems synthesize an intended program in some (relatively constrained) domain-specific language from a small number of input-output examples provided by the user. In this paper, we motivate and define the…
We describe a method of model checking called Computing Range Reduction (CRR). The CRR method is based on derivation of clauses that reduce the set of traces of reachable states in such a way that at least one counterexample remains (if…
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…
We consider the problem of existential quantifier elimination for Boolean formulas in Conjunctive Normal Form (CNF). We present a new method for solving this problem called Derivation of Dependency-Sequents (DDS). A Dependency-sequent…
We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. There is a great body of work considering QE applications in science and engineering but we demonstrate here that it also has use in the…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
Quantities are essential in documents to describe factual information. They are ubiquitous in application domains such as finance, business, medicine, and science in general. Compared to other information extraction approaches,…
Advances in the field of Machine Learning and Deep Neural Networks (DNNs) has enabled rapid development of sophisticated and autonomous systems. However, the inherent complexity to rigorously assure the safe operation of such systems…
This report presents an elementary theory of unification for positive conjunctive queries. A positive conjunctive query is a formula constructed from propositional constants, equations and atoms using the conjunction $\wedge$ and the…
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…
Determining the validity of a quantified Boolean formula (QBF) is a PSPACE-complete problem with rich expressive power. Despite interest in efficient solvers, there is, compared to problems in NP, a lack of positive theoretical results, and…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…
Cylindrical Algebraic Decomposition (CAD) was the first practical means for doing real quantifier elimination (QE), and is still a major method, with many improvements since Collins' original method. Nevertheless, its complexity is…
Generative quantum eigensolver (GQE) is a hybrid quantum-classical algorithm that iteratively trains a classical generative machine learning model such that the model can generate quantum circuits with desired properties such as…
Determination of molecular energetics and properties is one of the core challenges in the near-term quantum computing. To this end, hybrid quantum-classical algorithms are preferred for Noisy Intermediate Scale Quantum (NISQ) architectures.…
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…