Related papers: Multi types and reasonable space
We consider a Celestial Mechanics model: the spin-orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to compute quasi-periodic…
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…
While extensive research on query evaluation has achieved consistent improvements in the time complexity of algorithms, the space complexity of query evaluation has been largely ignored. This is a particular challenge in settings with…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
We study increasingly expressive type systems, from $F^\mu$ -- an extension of the polymorphic lambda calculus with equirecursive types -- to $F^{\mu;}_\omega$ -- the higher-order polymorphic lambda calculus with equirecursive types and…
In this paper, we investigate space-time tradeoffs for answering conjunctive queries with access patterns (CQAPs). The goal is to create a space-efficient data structure in an initial preprocessing phase and use it for answering (multiple)…
We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications we give a new interpretation of arithmetic Laplacians and we discuss the de Rham cohomology of some…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
This is part II of our book on KAM theory. We start by defining functorial analysis and then switch to the particular case of Kolmogorov spaces. We develop functional calculus based on the notion of local operators. This allows to define…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…