相关论文: Better Answers to Real Questions
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF…
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…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
The recently introduced framework of Graded Quantitative Rewriting is an innovative extension of traditional rewriting systems, in which rules are annotated with degrees drawn from a quantale. This framework provides a robust foundation for…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
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…
<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…
This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…
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 build on our previous paper \cite{constructive} by using the general method introduced there in conjunction with invariant theory. This yields quantifier elimination results for the classical quaternions, octonions, as well as other…
We present a knowledge compilation approach for existential and universal quantification in alternating automata. Knowledge compilation transforms formulas into normal forms with special properties that enable efficient answering of…
Quantum metrology stands as a leading application of quantum science and technology, yet noise often constrains its precision and sensitivity. In near-term quantum metrology, existing protocols largely depend on virtual state purification,…
While the body of research directed towards constructing and generating clarifying questions in mixed-initiative conversational search systems is vast, research aimed at processing and comprehending users' answers to such questions is…
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real…
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…