101 research outputs found
A Graph Model for Imperative Computation
Scott's graph model is a lambda-algebra based on the observation that
continuous endofunctions on the lattice of sets of natural numbers can be
represented via their graphs. A graph is a relation mapping finite sets of
input values to output values.
We consider a similar model based on relations whose input values are finite
sequences rather than sets. This alteration means that we are taking into
account the order in which observations are made. This new notion of graph
gives rise to a model of affine lambda-calculus that admits an interpretation
of imperative constructs including variable assignment, dereferencing and
allocation.
Extending this untyped model, we construct a category that provides a model
of typed higher-order imperative computation with an affine type system. An
appropriate language of this kind is Reynolds's Syntactic Control of
Interference. Our model turns out to be fully abstract for this language. At a
concrete level, it is the same as Reddy's object spaces model, which was the
first "state-free" model of a higher-order imperative programming language and
an important precursor of games models. The graph model can therefore be seen
as a universal domain for Reddy's model
A unifying theorem for algebraic semantics and dynamic logics
AbstractA unified single proof is given which implies theorems in such diverse fields as continuous algebras of algebraic semantics, dynamic algebras of logics of programs, and program verification methods for total correctness. The proof concerns ultraproducts and diagonalization
Improved Complexity Bounds for Counting Points on Hyperelliptic Curves
We present a probabilistic Las Vegas algorithm for computing the local zeta
function of a hyperelliptic curve of genus defined over . It
is based on the approaches by Schoof and Pila combined with a modeling of the
-torsion by structured polynomial systems. Our main result improves on
previously known complexity bounds by showing that there exists a constant
such that, for any fixed , this algorithm has expected time and space
complexity as grows and the characteristic is large
enough.Comment: To appear in Foundations of Computational Mathematic
An inexact linearized proximal algorithm for a class of DC composite optimization problems and applications
This paper is concerned with a class of DC composite optimization problems
which, as an extension of the convex composite optimization problem and the DC
program with nonsmooth components, often arises from robust factorization
models of low-rank matrix recovery. For this class of nonconvex and nonsmooth
problems, we propose an inexact linearized proximal algorithm (iLPA) which in
each step computes an inexact minimizer of a strongly convex majorization
constructed by the partial linearization of their objective functions. The
generated iterate sequence is shown to be convergent under the
Kurdyka-{\L}ojasiewicz (KL) property of a potential function, and the
convergence admits a local R-linear rate if the potential function has the KL
property of exponent at the limit point. For the latter assumption, we
provide a verifiable condition by leveraging the composite structure, and
clarify its relation with the regularity used for the convex composite
optimization. Finally, the proposed iLPA is applied to a robust factorization
model for matrix completions with outliers, DC programs with nonsmooth
components, and -norm exact penalty of DC constrained programs, and
numerical comparison with the existing algorithms confirms the superiority of
our iLPA in computing time and quality of solutions
- …