Related papers: Automating Equational Proofs in Dirac Notation
The dynamical equations which are basic for the description of the dynamics of quantum felds in arbitrary space--time geometries, can be derived from the requirements of a unique deterministic evolution of the quantum fields, the…
Fermi-Dirac machines were proposed recently as an approach to solving semidefinite optimization problems on quantum computers. Here, we reinterpret them as canonical quantizations of classical neurons. By viewing a classical neuron as an…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is…
Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose…
Classically, in saturation-based proof systems, unification has been considered atomic. However, it is also possible to move unification to the calculus level, turning the steps of the unification algorithm into inferences. For calculi that…
Parikh's Theorem is a fundamental result in automata theory with numerous applications in computer science: software verification (e.g. infinite-state verification, string constraints, and theory of arrays), verification of cryptographic…
We analyse the behaviour of the Dirac equation in $d=1+1$ with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
The ordered structures of natural, integer, rational and real numbers are studied here. It is known that the theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language…
We propose a new evaluation for automatic solvers for algebra word problems, which can identify mistakes that existing evaluations overlook. Our proposal is to evaluate such solvers using derivations, which reflect how an equation system…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well…