Results 1  10
of
15
The Measurable Space of Stochastic Processes
, 2013
"... We introduce a stochastic extension of CCS endowed with structural operational semantics expressed in terms of measure theory. The set of processes is organised as a measurable space by the sigmaalgebra generated by structural congruence. The structural operational semantics associates to each pro ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
We introduce a stochastic extension of CCS endowed with structural operational semantics expressed in terms of measure theory. The set of processes is organised as a measurable space by the sigmaalgebra generated by structural congruence. The structural operational semantics associates to each process a set of measures over the space of processes. The measures encode the rates of the transitions from a process (state of a system) to a measurable set of processes. We prove that stochastic bisimulation is a congruence that extends structural congruence. In addition to an elegant operational semantics, our calculus provides a canonic way to define metrics on processes that measure that measure how similar two processes are in terms of behaviour.
Concurrency and Composition in a Stochastic World
, 2012
"... Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give a detailled account of the concept of relations on distributions, and discuss how this can generalise known notions of weak simulation and bisimulation, such as to fuse sequences of internal transitions. 1
Ratebased Transition Systems for Stochastic Process Calculi
 AUTOMATA, LANGUAGES AND PROGRAMMING  C. LNCS
, 2009
"... A variant of Rate Transition Systems (RTS), proposed by Klin and Sassone, is introduced and used as the basic model for defining stochastic behaviour of processes. The transition relation used in our variant associates to each process, for each action, the set of possible futures paired with a mea ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
A variant of Rate Transition Systems (RTS), proposed by Klin and Sassone, is introduced and used as the basic model for defining stochastic behaviour of processes. The transition relation used in our variant associates to each process, for each action, the set of possible futures paired with a measure indicating their rates. We show how RTS can be used for providing the operational semantics of stochastic extensions of three classical formalisms, namely CSP, CCS and picalculus. It is also shown that, in contrast with the original definition by Priami, our semantics for stochastic picalculus guarantees associativity of parallel composition.
M.: Structural operational semantics for continuous state probabilistic processes
 In: Proc. CMCS’12. Lecture Notes in Computer Science
, 2012
"... Abstract. We consider the problem of modeling syntax and semantics of probabilistic processes with continuous states (e.g. with continuous data). Syntax and semantics of these systems can be defined as algebras and coalgebras of suitable endofunctors over Meas, the category of measurable spaces. In ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We consider the problem of modeling syntax and semantics of probabilistic processes with continuous states (e.g. with continuous data). Syntax and semantics of these systems can be defined as algebras and coalgebras of suitable endofunctors over Meas, the category of measurable spaces. In order to give a more concrete representation for these coalgebras, we present an SOSlike rule format which induces an universal semantics, for which behavioural equivalence is a congruence. To this end, we solve several problems. In particular, the format has to specify how to compose the semantics of processes (which basically are continuous state Markov processes). This is achieved by defining a language of measure terms, i.e., expressions specifically designed for describing probabilistic measures. Thus, the transition relation associates processes with measure terms. As an example application, we model a CCSlike calculus of processes placed in an Euclidean space. The approach we follow in this case can be readily adapted to other quantitative aspects, e.g. Quality of Service, physical and chemical parameters in biological systems, etc. 1
On a Uniform Framework for the Definition of Stochastic Process Languages ⋆
"... Abstract. In this paper we show how Rate Transition Systems (RT Ss) can be used as a unifying framework for the definition of the semantics of stochastic process algebras. RT Ss facilitate the compositional definition of such semantics exploiting operators on the next state functions which are the f ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we show how Rate Transition Systems (RT Ss) can be used as a unifying framework for the definition of the semantics of stochastic process algebras. RT Ss facilitate the compositional definition of such semantics exploiting operators on the next state functions which are the functional counterpart of classical process algebra operators. We apply this framework to representative fragments of major stochastic process calculi namely TIPP, PEPA and IML and show how they solve the issue of transition multiplicity in a simple and elegant way. We, moreover, show how RT Ss help describing different languages, their differences and their similarities. For each calculus, we also show the formal correspondence between the RT Ss semantics and the standard SOS one. 1
Stochastic PiCalculus Revisited
"... Abstract. We develop a version of stochastic Picalculus with replication and fresh name quantification, endowed with a structural operational semantics expressed in terms of measure theory. The paper relies on two observations: (i) the structural congruence organizes a measurable space of processes ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We develop a version of stochastic Picalculus with replication and fresh name quantification, endowed with a structural operational semantics expressed in terms of measure theory. The paper relies on two observations: (i) the structural congruence organizes a measurable space of processes and (ii) the structural operational semantics associates to each process, in a specified rate environment, a behaviour defined by a set of measures over the space of processes. The measures, indexed with observable actions, encode the rates of the transitions from a process (state of a system) to a measurable set of processes. We extend the notion of stochastic bisimulation to include the concept of rate environment and prove that this equivalence is a congruence which includes the structural congruence. 1
On Robustness of Trust Systems
"... Abstract. Trust systems assist in dealing with users who may betray one another. Cunning users (attackers) may attempt to hide the fact that they betray others, deceiving the system. Trust systems that are difficult to deceive are considered more robust. To formally reason about robustness, we forma ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Trust systems assist in dealing with users who may betray one another. Cunning users (attackers) may attempt to hide the fact that they betray others, deceiving the system. Trust systems that are difficult to deceive are considered more robust. To formally reason about robustness, we formally model the abilities of an attacker. We prove that the attacker model is maximal, i.e. 1) the attacker can perform any feasible attack and 2) if a single attacker cannot perform an attack, then a group of attackers cannot perform that attack. Therefore, we can formulate robustness analogous to security. 1
Towards Effects in Mathematical Operational Semantics
"... In this paper, we study extensions of mathematical operational semantics with algebraic effects. Our starting point is an effectfree coalgebraic operational semantics, given by a natural transformation of syntax over behaviour. The operational semantics of the extended language arises by distributi ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
In this paper, we study extensions of mathematical operational semantics with algebraic effects. Our starting point is an effectfree coalgebraic operational semantics, given by a natural transformation of syntax over behaviour. The operational semantics of the extended language arises by distributing program syntax over effects, again inducing a coalgebraic operational semantics, but this time in the Kleisli category for the monad derived from the algebraic effects. The final coalgebra in this Kleisli category then serves as the denotational model. For it to exist, we ensure that the the Kleisli category is enriched over CPOs by considering the monad of possibly infinite terms, extended with a bottom element. Unlike the effectless setting, not all operational specifications give rise to adequate and compositional semantics. We give a proof of adequacy and compositionality provided the specifications can be described by evaluationincontext. We illustrate our techniques with a simple extension of (stateless) while programs with global store, i.e. variable lookup.
Compositionality of Probabilistic HennessyMilner Logic through Structural Operational Semantics
"... Abstract. We present a method to decompose HML formulae for reactive probabilistic processes. This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras. The satisfaction problem of a probabilistic HML formula for a process term is reduced t ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We present a method to decompose HML formulae for reactive probabilistic processes. This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras. The satisfaction problem of a probabilistic HML formula for a process term is reduced to the question of whether its subterms satisfy a derived formula obtained via the operational semantics. 1
On CSP and the Algebraic Theory of Effects
"... Abstract We consider CSP from the point of view of the algebraic theory of effects, which classifies operations as effect constructors and effect deconstructors; it also provides a link with functional programming, being a refinement of Moggi’s seminal monadic point of view. There is a natural algeb ..."
Abstract
 Add to MetaCart
Abstract We consider CSP from the point of view of the algebraic theory of effects, which classifies operations as effect constructors and effect deconstructors; it also provides a link with functional programming, being a refinement of Moggi’s seminal monadic point of view. There is a natural algebraic theory of the constructors whose free algebra functor is Moggi’s monad; we illustrate this by characterising free and initial algebras in terms of two versions of the stable failures model of CSP, one more general than the other. Deconstructors are dealt with as homomorphisms to (possibly nonfree) algebras. One can view CSP’s action and nondeterminism operators as constructors and the rest, such as concealment and concurrency, as deconstructors. Carrying this programme out results in taking deterministic external choice as constructor rather than general external choice. However, binary deconstructors, such as the CSP concurrency operator, provide unresolved difficulties. We conclude by presenting a combination of CSP with Moggi’s computational λcalculus, in which the operators, including concurrency, are polymorphic. While the paper mainly concerns CSP, it ought to be possible to carry over similar ideas to other process calculi. Rob van Glabbeek