Results 1 
3 of
3
Automatic verification of realtime systems with discrete probability distributions
 Theoretical Computer Science
, 1999
"... Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the ..."
Abstract

Cited by 72 (27 self)
 Add to MetaCart
Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for realtime systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”. 1
Approximate simulations for taskstructured probabilistic I/O automata
 In LICS workshop on Probabilistic Automata and Logics (PAul06
, 2006
"... A Probabilistic I/O Automaton (PIOA) is a countablestate automaton model that allows nondeterministic and probabilistic choices in state transitions. A taskPIOA adds a task structure on the locally controlled actions of a PIOA as a means for restricting the nondeterminism in the model. The taskPI ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
A Probabilistic I/O Automaton (PIOA) is a countablestate automaton model that allows nondeterministic and probabilistic choices in state transitions. A taskPIOA adds a task structure on the locally controlled actions of a PIOA as a means for restricting the nondeterminism in the model. The taskPIOA framework defines exact implementation relations based on inclusion of sets of trace distributions. In this paper we develop the theory of approximate implementations and equivalences for taskPIOAs. We propose a new kind of approximate simulation between taskPIOAs and prove that it is sound with respect to approximate implementations. Our notion of similarity of traces is based on a metric on trace distributions and therefore, we do not require the state spaces nor the space of external actions (output alphabet) of the underlying automata to be metric spaces. We discuss applications of approximate implementations to probabilistic safety verification.
Proving Approximate Implementations for Probabilistic I/O Automata?? Abstract
, 2006
"... In this paper we introduce the notion of approximate implementations for Probabilistic I/O Automata (PIOA) and develop methods for proving such relationships. We employ a task structure on the locally controlled actions and a task scheduler to resolve nondeterminism. The interaction between a schedu ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In this paper we introduce the notion of approximate implementations for Probabilistic I/O Automata (PIOA) and develop methods for proving such relationships. We employ a task structure on the locally controlled actions and a task scheduler to resolve nondeterminism. The interaction between a scheduler and an automaton gives rise to a trace distribution—a probability distribution over the set of traces. We define a PIOA to be a (discounted) approximate implementation of another PIOA if the set of trace distributions produced by the first is close to that of the latter, where closeness is measured by the (resp. discounted) uniform metric over trace distributions. We propose simulation functions for proving approximate implementations corresponding to each of the above types of approximate implementation relations. Since our notion of similarity of traces is based on a metric on trace distributions, we do not require the state spaces nor the space of external actions of the automata to be metric spaces. We discuss applications of approximate implementations to verification of probabilistic safety and termination.