1,345 research outputs found
Concrete Semantics with Coq and CoqHammer
The "Concrete Semantics" book gives an introduction to imperative programming
languages accompanied by an Isabelle/HOL formalization. In this paper we
discuss a re-formalization of the book using the Coq proof assistant. In order
to achieve a similar brevity of the formal text we extensively use CoqHammer,
as well as Coq Ltac-level automation. We compare the formalization efficiency,
compactness, and the readability of the proof scripts originating from a Coq
re-formalization of two chapters from the book
A Formal Approach based on Fuzzy Logic for the Specification of Component-Based Interactive Systems
Formal methods are widely recognized as a powerful engineering method for the
specification, simulation, development, and verification of distributed
interactive systems. However, most formal methods rely on a two-valued logic,
and are therefore limited to the axioms of that logic: a specification is valid
or invalid, component behavior is realizable or not, safety properties hold or
are violated, systems are available or unavailable. Especially when the problem
domain entails uncertainty, impreciseness, and vagueness, the appliance of such
methods becomes a challenging task. In order to overcome the limitations
resulting from the strict modus operandi of formal methods, the main objective
of this work is to relax the boolean notion of formal specifications by using
fuzzy logic. The present approach is based on Focus theory, a model-based and
strictly formal method for componentbased interactive systems. The contribution
of this work is twofold: i) we introduce a specification technique based on
fuzzy logic which can be used on top of Focus to develop formal specifications
in a qualitative fashion; ii) we partially extend Focus theory to a fuzzy one
which allows the specification of fuzzy components and fuzzy interactions.
While the former provides a methodology for approximating I/O behaviors under
imprecision, the latter enables to capture a more quantitative view of
specification properties such as realizability.Comment: In Proceedings FESCA 2015, arXiv:1503.0437
Towards the Formal Reliability Analysis of Oil and Gas Pipelines
It is customary to assess the reliability of underground oil and gas
pipelines in the presence of excessive loading and corrosion effects to ensure
a leak-free transport of hazardous materials. The main idea behind this
reliability analysis is to model the given pipeline system as a Reliability
Block Diagram (RBD) of segments such that the reliability of an individual
pipeline segment can be represented by a random variable. Traditionally,
computer simulation is used to perform this reliability analysis but it
provides approximate results and requires an enormous amount of CPU time for
attaining reasonable estimates. Due to its approximate nature, simulation is
not very suitable for analyzing safety-critical systems like oil and gas
pipelines, where even minor analysis flaws may result in catastrophic
consequences. As an accurate alternative, we propose to use a
higher-order-logic theorem prover (HOL) for the reliability analysis of
pipelines. As a first step towards this idea, this paper provides a
higher-order-logic formalization of reliability and the series RBD using the
HOL theorem prover. For illustration, we present the formal analysis of a
simple pipeline that can be modeled as a series RBD of segments with
exponentially distributed failure times.Comment: 15 page
A Formal Proof of the Expressiveness of Deep Learning
International audienceDeep learning has had a profound impact on computer science in recent years, with applications to image recognition, language processing, bioinformatics, and more. Recently , Cohen et al. provided theoretical evidence for the superiority of deep learning over shallow learning. We formalized their mathematical proof using Isabelle/HOL. The Isabelle development simplifies and generalizes the original proof, while working around the limitations of the HOL type system. To support the formalization, we developed reusable libraries of formalized mathematics, including results about the matrix rank, the Borel measure, and multivariate polynomials as well as a library for tensor analysis
A Formalization of Martingales in Isabelle/HOL
This thesis presents a formalization of martingales in arbitrary Banach
spaces using Isabelle/HOL. We begin by examining formalizations in prominent
proof repositories and extend the definition of the conditional expectation
operator from the real numbers to general Banach spaces. The current
formalization of conditional expectation in the Isabelle library is limited to
real-valued functions. To overcome this limitation, we use measure theoretic
arguments to construct the conditional expectation in Banach spaces using
suitable limits of simple functions. Subsequently, we define stochastic
processes and introduce the concepts of adapted, progressively measurable and
predictable processes using suitable locale definitions. We show the relation
Furthermore, we show that progressive measurability and adaptedness are
equivalent when the indexing set is discrete. We pay special attention to
predictable processes in discrete-time, showing that
is predictable if and only if is adapted.
We rigorously define martingales, submartingales, and supermartingales,
presenting their first consequences and corollaries. Discrete-time martingales
are given special attention in the formalization. In every step of our
formalization, we make extensive use of the powerful locale system of Isabelle.
The formalization further contributes by generalizing concepts in Bochner
integration by extending their application from the real numbers to arbitrary
Banach spaces equipped with a second-countable topology. Induction schemes for
integrable simple functions on Banach spaces are introduced. Additionally, we
formalize a powerful result called the "Averaging Theorem" which allows us to
show that densities are unique in Banach spaces.Comment: 61 pages, Bachelor's Thesis in Informatics and Mathematics at the
Technical University of Munic
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