124 research outputs found
On paths-based criteria for polynomial time complexity in proof-nets
Girard's Light linear logic (LLL) characterized polynomial time in the
proof-as-program paradigm with a bound on cut elimination. This logic relied on
a stratification principle and a "one-door" principle which were generalized
later respectively in the systems L^4 and L^3a. Each system was brought with
its own complex proof of Ptime soundness.
In this paper we propose a broad sufficient criterion for Ptime soundness for
linear logic subsystems, based on the study of paths inside the proof-nets,
which factorizes proofs of soundness of existing systems and may be used for
future systems. As an additional gain, our bound stands for any reduction
strategy whereas most bounds in the literature only stand for a particular
strategy.Comment: Long version of a conference pape
Typing a Core Binary Field Arithmetic in a Light Logic
We design a library for binary field arithmetic and we supply a core API
which is completely developed in DLAL, extended with a fix point formula. Since
DLAL is a restriction of linear logic where only functional programs with
polynomial evaluation cost can be typed, we obtain the core of a functional
programming setting for binary field arithmetic with built-in polynomial
complexity
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and NLogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is inspired from
proof theory and more specifically linear logic and Geometry of Interaction.
We show how unification can be used to build a model of computation by means
of specific subalgebras associated to finite permutations groups. We then prove
that whether an observation (the algebraic counterpart of a program) accepts a
word can be decided within logarithmic space. We also show that the
construction can naturally represent pointer machines, an intuitive way of
understanding logarithmic space computing
An Elementary Affine λ-Calculus with Multithreading and Side Effects
International audienceLinear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main contributions are as follows. First, we introduce a modal call-by-value λ-calculus with multithreading and side effects. Second, we provide a combinatorial proof of termination in elementary time for the language. Third, we introduce an elementary affine type system that guarantees the standard subject reduction and progress properties. Finally, we illustrate the programming of iterative functions with side effects in the presented formalism
Logic Programming and Logarithmic Space
We present an algebraic view on logic programming, related to proof theory
and more specifically linear logic and geometry of interaction. Within this
construction, a characterization of logspace (deterministic and
non-deterministic) computation is given via a synctactic restriction, using an
encoding of words that derives from proof theory.
We show that the acceptance of a word by an observation (the counterpart of a
program in the encoding) can be decided within logarithmic space, by reducing
this problem to the acyclicity of a graph. We show moreover that observations
are as expressive as two-ways multi-heads finite automata, a kind of pointer
machines that is a standard model of logarithmic space computation
A feasible algorithm for typing in Elementary Affine Logic
We give a new type inference algorithm for typing lambda-terms in Elementary
Affine Logic (EAL), which is motivated by applications to complexity and
optimal reduction. Following previous references on this topic, the variant of
EAL type system we consider (denoted EAL*) is a variant without sharing and
without polymorphism. Our algorithm improves over the ones already known in
that it offers a better complexity bound: if a simple type derivation for the
term t is given our algorithm performs EAL* type inference in polynomial time.Comment: 20 page
Resource Control for Synchronous Cooperative Threads
We develop new methods to statically bound the resources needed for the
execution of systems of concurrent, interactive threads. Our study is concerned
with a \emph{synchronous} model of interaction based on cooperative threads
whose execution proceeds in synchronous rounds called instants. Our
contribution is a system of compositional static analyses to guarantee that
each instant terminates and to bound the size of the values computed by the
system as a function of the size of its parameters at the beginning of the
instant. Our method generalises an approach designed for first-order functional
languages that relies on a combination of standard termination techniques for
term rewriting systems and an analysis of the size of the computed values based
on the notion of quasi-interpretation. We show that these two methods can be
combined to obtain an explicit polynomial bound on the resources needed for the
execution of the system during an instant. As a second contribution, we
introduce a virtual machine and a related bytecode thus producing a precise
description of the resources needed for the execution of a system. In this
context, we present a suitable control flow analysis that allows to formulte
the static analyses for resource control at byte code level
Isomorphisms of types in the presence of higher-order references (extended version)
We investigate the problem of type isomorphisms in the presence of
higher-order references. We first introduce a finitary programming language
with sum types and higher-order references, for which we build a fully abstract
games model following the work of Abramsky, Honda and McCusker. Solving an open
problem by Laurent, we show that two finitely branching arenas are isomorphic
if and only if they are geometrically the same, up to renaming of moves
(Laurent's forest isomorphism). We deduce from this an equational theory
characterizing isomorphisms of types in our language. We show however that
Laurent's conjecture does not hold on infinitely branching arenas, yielding new
non-trivial type isomorphisms in a variant of our language with natural
numbers
Effects of a home-based intervention on diet and physical activity behaviours for rural adults with or at risk of metabolic syndrome: a randomised controlled trial
BACKGROUND: This study aimed to determine whether a home-based 6-month lifestyle intervention program complemented by motivational interviewing could improve diet and physical activity behaviours in 50-69Â year olds with or at risk of metabolic syndrome, residing in a disadvantaged rural Western Australian community. METHODS: Participants from the City of Albany and surrounding towns (n?=?401) were recruited into a 6Â month randomised controlled trial. They were screened for metabolic syndrome and randomly allocated to intervention (n?=?201) or control group (n?=?200). Baseline and post-test data collection for both groups included a self-report questionnaire which incorporated the Fat and Fibre Barometer and the International Physical Activity Questionnaire Short Form. The intervention group received the program materials at baseline and the control group was waitlisted. Generalised estimating equation models assessed repeated outcome measures over time. RESULTS: A total of 151 (75.1Â %) intervention and 159 (79.5Â %) control group participants completed post-test and were included in the analysis. After controlling for confounders, the intervention group achieved a marginally significant increase in their metabolic equivalent (MET) minutes of moderate intensity physical activity per week (p?=?0.049), and significantly improved fibre intake (p?<?0.001), fat intake (p?=?0.003), and vegetable serves per day (p?=?0.002) from baseline to post-test relative to the control group. CONCLUSION: A home-based, low-cost intervention with motivational support can effectively improve the physical activity and dietary behaviours of adults aged 50-69Â years with or at risk of metabolic syndrome residing in a disadvantaged rural area. TRIAL REGISTRATION: Anzctr.org.au Identifier: ACTRN12614000512628
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