Related papers: Algorithmic Introduction of Quantified Cuts
We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
In order to generate prime implicants for a given cube (minterm), most of minimization methods increase the dimension of this cube by removing one literal from it at a time. But there are two problems of exponential complexity. One of them…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
$\Omega$-rule was introduced by W. Buchholz to give an ordinal-free cut-elimination proof for a subsystem of analysis with $\Pi^{1}_{1}$-comprehension. His proof provides cut-free derivations by familiar rules only for arithmetical…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We consider the problem of {\em restructuring} compressed texts without explicit decompression. We present algorithms which allow conversions from compressed representations of a string $T$ produced by any grammar-based compression…
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given. This algorithm is based on a combinatorial expression for a particular bijection among binary strings. The algorithm, which adheres to the…
Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…
We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
We consider quantum computation efficiency from a new perspective. The efficiency is reduced to its classical counterpart by imposing the semi-classical limit. We show that this reduction is caused by the fact that any elementary quantum…