866 research outputs found
Integrating multiple sources to answer questions in Algebraic Topology
We present in this paper an evolution of a tool from a user interface for a
concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to
a front-end allowing the interoperability among different sources for
computation and deduction. The architecture allows the system not only to
interface several systems, but also to make them cooperate in shared
calculations.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
A Purely Functional Computer Algebra System Embedded in Haskell
We demonstrate how methods in Functional Programming can be used to implement
a computer algebra system. As a proof-of-concept, we present the
computational-algebra package. It is a computer algebra system implemented as
an embedded domain-specific language in Haskell, a purely functional
programming language. Utilising methods in functional programming and prominent
features of Haskell, this library achieves safety, composability, and
correctness at the same time. To demonstrate the advantages of our approach, we
have implemented advanced Gr\"{o}bner basis algorithms, such as Faug\`{e}re's
and , in a composable way.Comment: 16 pages, Accepted to CASC 201
Probabilistic Model Checking for Energy Analysis in Software Product Lines
In a software product line (SPL), a collection of software products is
defined by their commonalities in terms of features rather than explicitly
specifying all products one-by-one. Several verification techniques were
adapted to establish temporal properties of SPLs. Symbolic and family-based
model checking have been proven to be successful for tackling the combinatorial
blow-up arising when reasoning about several feature combinations. However,
most formal verification approaches for SPLs presented in the literature focus
on the static SPLs, where the features of a product are fixed and cannot be
changed during runtime. This is in contrast to dynamic SPLs, allowing to adapt
feature combinations of a product dynamically after deployment. The main
contribution of the paper is a compositional modeling framework for dynamic
SPLs, which supports probabilistic and nondeterministic choices and allows for
quantitative analysis. We specify the feature changes during runtime within an
automata-based coordination component, enabling to reason over strategies how
to trigger dynamic feature changes for optimizing various quantitative
objectives, e.g., energy or monetary costs and reliability. For our framework
there is a natural and conceptually simple translation into the input language
of the prominent probabilistic model checker PRISM. This facilitates the
application of PRISM's powerful symbolic engine to the operational behavior of
dynamic SPLs and their family-based analysis against various quantitative
queries. We demonstrate feasibility of our approach by a case study issuing an
energy-aware bonding network device.Comment: 14 pages, 11 figure
Automated Cryptographic Analysis of the Pedersen Commitment Scheme
Aiming for strong security assurance, recently there has been an increasing
interest in formal verification of cryptographic constructions. This paper
presents a mechanised formal verification of the popular Pedersen commitment
protocol, proving its security properties of correctness, perfect hiding, and
computational binding. To formally verify the protocol, we extended the theory
of EasyCrypt, a framework which allows for reasoning in the computational
model, to support the discrete logarithm and an abstraction of commitment
protocols. Commitments are building blocks of many cryptographic constructions,
for example, verifiable secret sharing, zero-knowledge proofs, and e-voting.
Our work paves the way for the verification of those more complex
constructions.Comment: 12 pages, conference MMM-ACNS 201
Testing Component-Based Real Time Systems
International audienceThis paper focuses on studying efficient solutions for modeling and deriving compositional tests for component-based real-time systems. In this work, we propose a coherent framework that does not require the computation of the synchronous product (composition) of components, and therefore avoids a major bottleneck in this class of test. For this framework, we introduce an approach and associated algorithm. In our approach, the overall behavior of the system is obtained by restricting free runs of components to those involving interactions between them. This restriction is achieved through the use of a particular component called assembly controller. For the generation algorithm, compositional test cases are derived from the assembly controller model using symbolic analysis. This reduces the state space size (a practical size) and enables the generation of sequences which cover all critical interaction scenarios
Towards OpenMath Content Dictionaries as Linked Data
"The term 'Linked Data' refers to a set of best practices for publishing and
connecting structured data on the web". Linked Data make the Semantic Web work
practically, which means that information can be retrieved without complicated
lookup mechanisms, that a lightweight semantics enables scalable reasoning, and
that the decentral nature of the Web is respected. OpenMath Content
Dictionaries (CDs) have the same characteristics - in principle, but not yet in
practice. The Linking Open Data movement has made a considerable practical
impact: Governments, broadcasting stations, scientific publishers, and many
more actors are already contributing to the "Web of Data". Queries can be
answered in a distributed way, and services aggregating data from different
sources are replacing hard-coded mashups. However, these services are currently
entirely lacking mathematical functionality. I will discuss real-world
scenarios, where today's RDF-based Linked Data do not quite get their job done,
but where an integration of OpenMath would help - were it not for certain
conceptual and practical restrictions. I will point out conceptual shortcomings
in the OpenMath 2 specification and common bad practices in publishing CDs and
then propose concrete steps to overcome them and to contribute OpenMath CDs to
the Web of Data.Comment: Presented at the OpenMath Workshop 2010, http://cicm2010.cnam.fr/om
Rewriting the check of 8-rewritability for
The group is called -rewritable for , if for each sequence of
elements there exists a non-identity permutation
such that . Using computers, Blyth and Robinson (1990) verified that
the alternating group is 8-rewritable. We report on an independent
verification of this statement using the computational algebra system GAP, and
compare the performance of our sequential and parallel code with the original
one.Comment: 5 page
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