13 research outputs found
Characterising Probabilistic Processes Logically
In this paper we work on (bi)simulation semantics of processes that exhibit
both nondeterministic and probabilistic behaviour. We propose a probabilistic
extension of the modal mu-calculus and show how to derive characteristic
formulae for various simulation-like preorders over finite-state processes
without divergence. In addition, we show that even without the fixpoint
operators this probabilistic mu-calculus can be used to characterise these
behavioural relations in the sense that two states are equivalent if and only
if they satisfy the same set of formulae.Comment: 18 page
Characterising Testing Preorders for Finite Probabilistic Processes
In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and
Hennessy to processes featuring probabilistic as well as nondeterministic
choice. They concluded with two problems that have remained open throughout the
years, namely to find complete axiomatisations and alternative
characterisations for these preorders. This paper solves both problems for
finite processes with silent moves. It characterises the may preorder in terms
of simulation, and the must preorder in terms of failure simulation. It also
gives a characterisation of both preorders using a modal logic. Finally it
axiomatises both preorders over a probabilistic version of CSP.Comment: 33 page
Monads and Quantitative Equational Theories for Nondeterminism and Probability
The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. In this work we lift this monad from the category of sets to the category of extended metric spaces, by means of the Hausdorff and Kantorovich metric liftings. Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare, Panangaden and Plotkin
Open Bisimulation for Quantum Processes
Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between quantum processes. We also give a modal characterisation of open bisimulation, by extending the Hennessy-Milner logic to a quantum setting
Analyzing Divergence for Nondeterministic Probabilistic Models
Branching and weak probabilistic bisimilarities are two well-known notions
capturing behavioral equivalence between nondeterministic probabilistic
systems. For probabilistic systems, divergence is of major concern. Recently
several divergence-sensitive refinements of branching and weak probabilistic
bisimilarities have been proposed in the literature. Both the definitions of
these equivalences and the techniques to investigate them differ significantly.
This paper presents a comprehensive comparative study on divergence-sensitive
behavioral equivalence relations that refine the branching and weak
probabilistic bisimilarities. Additionally, these equivalence relations are
shown to have efficient checking algorithms. The techniques of this paper might
be of independent interest in a more general setting
A Probabilistic Kleene Theorem
International audienceWe provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. We prove that probabilistic expressions and probabilistic automata are expressively equivalent. Our result actually extends to two-way probabilistic automata with pebbles and corresponding expressions
A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences
Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully
probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing
single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing
equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models
Measures on probabilistic automata
In questa tesi consideriamo i processi probabilistici non-deterministici modellati attraverso automi. Il nostro obiettivo \`e l'analisi dei problemi di bisimulazioni approssimate. Queste relazioni sono usate, generalmente, per semplificare i modelli di alcuni sistemi e per modellare agenti e attaccanti nei protocolli di sicurezza. In questo ultimo campo ci sono diversi proposte di utilizzo di metriche, le quali sono l'analogo quantitativo della bisimulazione probabilistica e permettono una miglior precisione. Una metrica \`e grossomodo un grado di similarit\`a tra stati. Iniziando dalla formalizzazione di (bi)simulazione approssimata data nel lavoro di Turrini, definiamo due metriche su stati e su distribuzioni. Queste metriche sono basate sul concetto di errore ammesso durante la simulazione di uno stato rispetto un altro stato. Investigheremo la relazione tra queste metriche con una metrica largamente utilizzata, la metrica di Kantorovich, e scopriremo che esse sono equivalenti. Poi riadatteremo per gli automi probabilistici il trasformatore di misure proposto da De Alfaro e al., ottenendo un nuovo funzionale F che \`e una estensione conservativa dei trasformatori proposti in letteratura. Mostreremo che il minimo punto fisso di F coincide con la sua sovra-approssimazione dalle misure derivate dal lavoro di Turrini, attraverso la dimostrazione dell'esistenza di una stretta relazione tra le bisimulazioni approssimate di Turrini con le metriche in letteratura.In this thesis we consider nondeterministic probabilistic processes modeled by automata. Our purpose is the analysis of the problem of approximated bisimulations. These relations are used, generally, to simplify the models of some systems and to model agents and attackers in security protocols. For the latter field there are several proposals to use metrics, which are the quantitative analogue of probabilistic bisimilarity and allow a greater precision. A metric is about a degree of similarity between states. Starting from the formalisation of approximate (bi)simulation given in Turrini's work, we define two metrics on states and on distributions. These metrics are based on the concept of error allowed during the simulation of a state with respect to another one. We investigate the relation between these metrics with a largely used one, the Kantorovich metric, and discover that they are equivalent. Then we recast for probabilistic automata the transformer of measures proposed by De Alfaro et al., obtaining a new functional F that is a conservative extension of the transformers proposed in the literature. We show that the minimum fix point of F coincides with its over-aproximated by the measures derived from Turrini's work thus showing the existence of a strict relation between the Turrini\u2019s approximate bisimulations with the literature on metrics