11,471 research outputs found
Square root meadows
Let Q_0 denote the rational numbers expanded to a meadow by totalizing
inversion such that 0^{-1}=0. Q_0 can be expanded by a total sign function s
that extracts the sign of a rational number. In this paper we discuss an
extension Q_0(s ,\sqrt) of the signed rationals in which every number has a
unique square root.Comment: 9 page
A formal support to business and architectural design for service-oriented systems
Architectural Design Rewriting (ADR) is an approach for the design of software architectures developed within Sensoria by reconciling graph transformation and process calculi techniques. The key feature that makes ADR a suitable and expressive framework is the algebraic handling of structured graphs, which improves the support for specification, analysis and verification of service-oriented architectures and applications. We show how ADR is used as a formal ground for high-level modelling languages and approaches developed within Sensoria
Refinement by interpretation in {\pi}-institutions
The paper discusses the role of interpretations, understood as multifunctions
that preserve and reflect logical consequence, as refinement witnesses in the
general setting of pi-institutions. This leads to a smooth generalization of
the refinement-by-interpretation approach, recently introduced by the authors
in more specific contexts. As a second, yet related contribution a basis is
provided to build up a refinement calculus of structured specifications in and
across arbitrary pi-institutions.Comment: In Proceedings Refine 2011, arXiv:1106.348
A general conservative extension theorem in process algebras with inequalities
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc
Exploiting the Hierarchical Structure of Rule-Based Specifications for Decision Planning
Rule-based specifications have been very successful as a declarative approach in many domains, due to the handy yet solid foundations offered by rule-based machineries like term and graph rewriting. Realistic problems, however, call for suitable techniques to guarantee scalability. For instance, many domains exhibit a hierarchical structure that can be exploited conveniently. This is particularly evident for composition associations of models. We propose an explicit representation of such structured models and a methodology that exploits it for the description and analysis of model- and rule-based systems. The approach is presented in the framework of rewriting logic and its efficient implementation in the rewrite engine Maude and is illustrated with a case study.
Requirements modelling and formal analysis using graph operations
The increasing complexity of enterprise systems requires a more advanced
analysis of the representation of services expected than is currently possible.
Consequently, the specification stage, which could be facilitated by formal
verification, becomes very important to the system life-cycle. This paper presents
a formal modelling approach, which may be used in order to better represent
the reality of the system and to verify the awaited or existing system’s properties,
taking into account the environmental characteristics. For that, we firstly propose
a formalization process based upon properties specification, and secondly we
use Conceptual Graphs operations to develop reasoning mechanisms of verifying
requirements statements. The graphic visualization of these reasoning enables us
to correctly capture the system specifications by making it easier to determine if
desired properties hold. It is applied to the field of Enterprise modelling
Process algebra with strategic interleaving
In process algebras such as ACP (Algebra of Communicating Processes),
parallel processes are considered to be interleaved in an arbitrary way. In the
case of multi-threading as found in contemporary programming languages,
parallel processes are actually interleaved according to some interleaving
strategy. An interleaving strategy is what is called a process-scheduling
policy in the field of operating systems. In many systems, for instance
hardware/software systems, we have to do with both parallel processes that may
best be considered to be interleaved in an arbitrary way and parallel processes
that may best be considered to be interleaved according to some interleaving
strategy. Therefore, we extend ACP in this paper with the latter form of
interleaving. The established properties of the extension concerned include an
elimination property, a conservative extension property, and a unique expansion
property.Comment: 19 pages, this version is a revision of the published versio
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