115 research outputs found
Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice
This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well
Formalization and Model Checking of BPMN Collaboration Diagrams with DD-LOTOS
Business Process Model and Notation (BPMN) is a standard graphical notation for modeling complex business processes. Given the importance of business processes, the modeling analysis and validation stage for BPMN is essential. In recent years, BPMN notation has become a widespread practice in business process modeling because of these intuitive diagrams. BPMN diagrams are built from basic elements. The major challenge of BPMN diagrams is the lack of formal semantics, which leads to several interpretations of the concerned diagrams. Hence, this work aims to propose an approach for checking BPMN collaboration diagrams to guarantee some properties of smooth functioning of systems modeled by BPMN notation. The verification approach used in this work is based on model checking techniques. The approach proposes as a first step a formal semantics of the collaboration diagrams in terms of the formal language DD-LOTOS, i.e., a phase of the transformation of collaboration diagrams into DD-LOTOS. This transformation is guided by applying the inference rules of the formal semantics of the DD-LOTOS formal language, and we then use the UPPAAL model checker to check the absence of deadlock, safety properties, and liveness properties
Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity
Previous work on applications of Abstract Differential Geometry (ADG) to
discrete Lorentzian quantum gravity is brought to its categorical climax by
organizing the curved finitary spacetime sheaves of quantum causal sets
involved therein, on which a finitary (:locally finite), singularity-free,
background manifold independent and geometrically prequantized version of the
gravitational vacuum Einstein field equations were seen to hold, into a topos
structure. This topos is seen to be a finitary instance of both an elementary
and a Grothendieck topos, generalizing in a differential geometric setting, as
befits ADG, Sorkin's finitary substitutes of continuous spacetime topologies.
The paper closes with a thorough discussion of four future routes we could take
in order to further develop our topos-theoretic perspective on ADG-gravity
along certain categorical trends in current quantum gravity research.Comment: 49 pages, latest updated version (errata corrected, references
polished) Submitted to the International Journal of Theoretical Physic
Graphical representation of covariant-contravariant modal formulae
Covariant-contravariant simulation is a combination of standard (covariant)
simulation, its contravariant counterpart and bisimulation. We have previously
studied its logical characterization by means of the covariant-contravariant
modal logic. Moreover, we have investigated the relationships between this
model and that of modal transition systems, where two kinds of transitions (the
so-called may and must transitions) were combined in order to obtain a simple
framework to express a notion of refinement over state-transition models. In a
classic paper, Boudol and Larsen established a precise connection between the
graphical approach, by means of modal transition systems, and the logical
approach, based on Hennessy-Milner logic without negation, to system
specification. They obtained a (graphical) representation theorem proving that
a formula can be represented by a term if, and only if, it is consistent and
prime. We show in this paper that the formulae from the covariant-contravariant
modal logic that admit a "graphical" representation by means of processes,
modulo the covariant-contravariant simulation preorder, are also the consistent
and prime ones. In order to obtain the desired graphical representation result,
we first restrict ourselves to the case of covariant-contravariant systems
without bivariant actions. Bivariant actions can be incorporated later by means
of an encoding that splits each bivariant action into its covariant and its
contravariant parts.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407
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