9,590 research outputs found
CCS Dynamic Bisimulation is Progressing
Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g.\ and are woc but and are not. This fact prevents us from characterizing CCS semantics (when is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e.\ run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two characterizations via modal logic in the style of HML, and a complete axiomatization for finite agents. Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents. Thus the title of the paper
Algebraic Models for Contextual Nets
We extend the algebraic approach of Meseguer and Montanari from ordinary place/transition Petri nets to contextual nets, covering both the collective and the individual token philosophy uniformly along the two interpretations of net behaviors
Testing Reactive Probabilistic Processes
We define a testing equivalence in the spirit of De Nicola and Hennessy for
reactive probabilistic processes, i.e. for processes where the internal
nondeterminism is due to random behaviour. We characterize the testing
equivalence in terms of ready-traces. From the characterization it follows that
the equivalence is insensitive to the exact moment in time in which an internal
probabilistic choice occurs, which is inherent from the original testing
equivalence of De Nicola and Hennessy. We also show decidability of the testing
equivalence for finite systems for which the complete model may not be known
Kleene algebra with domain
We propose Kleene algebra with domain (KAD), an extension of Kleene algebra
with two equational axioms for a domain and a codomain operation, respectively.
KAD considerably augments the expressiveness of Kleene algebra, in particular
for the specification and analysis of state transition systems. We develop the
basic calculus, discuss some related theories and present the most important
models of KAD. We demonstrate applicability by two examples: First, an
algebraic reconstruction of Noethericity and well-foundedness; second, an
algebraic reconstruction of propositional Hoare logic.Comment: 40 page
Recommended from our members
Using formal methods to support testing
Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent
years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing
Nonlinear Models of Neural and Genetic Network Dynamics:\ud \ud Natural Transformations of Łukasiewicz Logic LM-Algebras in a Łukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations \ud
A categorical and Łukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Łukasiewicz Algebraic Logic models of both neural and genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable next-state/transfer functions is extended to a Łukasiewicz Topos with an N-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.\u
Two Algebraic Process Semantics for Contextual Nets
We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs
Inductive Definition and Domain Theoretic Properties of Fully Abstract
A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF +
"parallel conditional function"), respectively, is presented. It is based on
general notions of sequential computational strategies and wittingly consistent
non-deterministic strategies introduced by the author in the seventies.
Although these notions of strategies are old, the definition of the fully
abstract models is new, in that it is given level-by-level in the finite type
hierarchy. To prove full abstraction and non-dcpo domain theoretic properties
of these models, a theory of computational strategies is developed. This is
also an alternative and, in a sense, an analogue to the later game strategy
semantics approaches of Abramsky, Jagadeesan, and Malacaria; Hyland and Ong;
and Nickau. In both cases of PCF and PCF^+ there are definable universal
(surjective) functionals from numerical functions to any given type,
respectively, which also makes each of these models unique up to isomorphism.
Although such models are non-omega-complete and therefore not continuous in the
traditional terminology, they are also proved to be sequentially complete (a
weakened form of omega-completeness), "naturally" continuous (with respect to
existing directed "pointwise", or "natural" lubs) and also "naturally"
omega-algebraic and "naturally" bounded complete -- appropriate generalisation
of the ordinary notions of domain theory to the case of non-dcpos.Comment: 50 page
- …