8 research outputs found
Classical Mathematics for a Constructive World
Interactive theorem provers based on dependent type theory have the
flexibility to support both constructive and classical reasoning. Constructive
reasoning is supported natively by dependent type theory and classical
reasoning is typically supported by adding additional non-constructive axioms.
However, there is another perspective that views constructive logic as an
extension of classical logic. This paper will illustrate how classical
reasoning can be supported in a practical manner inside dependent type theory
without additional axioms. We will see several examples of how classical
results can be applied to constructive mathematics. Finally, we will see how to
extend this perspective from logic to mathematics by representing classical
function spaces using a weak value monad.Comment: v2: Final copy for publicatio
A Mechanized Semantic Framework for Real-Time Systems
International audienceConcurrent systems consist of many components which may execute in parallel and are complex to design, to analyze, to verify, and to implement. The complexity increases if the systems have real-time constraints, which are very useful in avionic, spatial and other kind of embedded applications. In this paper we present a logical framework for defining and validating real-time formalisms as well as reasoning methods over them. For this purpose, we have implemented in the Coq proof assistant well known semantic domains for real-time systems based on labelled transitions systems and timed runs. We experiment our framework by considering the real-time CSP-based language fiacre, which has been defined as a pivot formalism for modeling languages (aadl, sdl, ...) used in the TOPCASED project. Thus, we define an extension to the formal semantic models mentioned above that facilitates the modeling of fine-grained time constraints of fiacre. Finally, we implement this extension in our framework and provide a proof method environment to deal with real-time system in order to achieve their formal certification
Dimensions of Timescales in Neuromorphic Computing Systems
This article is a public deliverable of the EU project "Memory technologies
with multi-scale time constants for neuromorphic architectures" (MeMScales,
https://memscales.eu, Call ICT-06-2019 Unconventional Nanoelectronics, project
number 871371). This arXiv version is a verbatim copy of the deliverable
report, with administrative information stripped. It collects a wide and varied
assortment of phenomena, models, research themes and algorithmic techniques
that are connected with timescale phenomena in the fields of computational
neuroscience, mathematics, machine learning and computer science, with a bias
toward aspects that are relevant for neuromorphic engineering. It turns out
that this theme is very rich indeed and spreads out in many directions which
defy a unified treatment. We collected several dozens of sub-themes, each of
which has been investigated in specialized settings (in the neurosciences,
mathematics, computer science and machine learning) and has been documented in
its own body of literature. The more we dived into this diversity, the more it
became clear that our first effort to compose a survey must remain sketchy and
partial. We conclude with a list of insights distilled from this survey which
give general guidelines for the design of future neuromorphic systems
Toward a formal theory for computing machines made out of whatever physics offers: extended version
Approaching limitations of digital computing technologies have spurred
research in neuromorphic and other unconventional approaches to computing. Here
we argue that if we want to systematically engineer computing systems that are
based on unconventional physical effects, we need guidance from a formal theory
that is different from the symbolic-algorithmic theory of today's computer
science textbooks. We propose a general strategy for developing such a theory,
and within that general view, a specific approach that we call "fluent
computing". In contrast to Turing, who modeled computing processes from a
top-down perspective as symbolic reasoning, we adopt the scientific paradigm of
physics and model physical computing systems bottom-up by formalizing what can
ultimately be measured in any physical substrate. This leads to an
understanding of computing as the structuring of processes, while classical
models of computing systems describe the processing of structures.Comment: 76 pages. This is an extended version of a perspective article with
the same title that will appear in Nature Communications soon after this
manuscript goes public on arxi
Automated Machine-Checked Hybrid System Safety Proofs
Contains fulltext :
83344.pdf ( ) (Closed access)Scientific publicatio