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Compositional reasoning for probabilistic finitestate behaviors
 In Processes, Terms and Cycles: Steps on the Road to Infinity, Essays Dedicated to Jan Willem Klop, on the Occasion of His 60th Birthday, LNCS 3838
, 2005
"... Abstract. We study a process algebra which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s simple probabilistic automata. We consider strong bisimulation and observational equivalence, and provide complete axiomatizations for a language that includes para ..."
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Abstract. We study a process algebra which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s simple probabilistic automata. We consider strong bisimulation and observational equivalence, and provide complete axiomatizations for a language that includes parallel composition and (guarded) recursion. The presence of the parallel composition introduces various technical difficulties and some restrictions are necessary in order to achieve complete axiomatizations. 1
Deriving syntax and axioms for quantitative regular behaviours
, 2009
"... We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions ar ..."
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Cited by 10 (4 self)
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We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions are assigned a value in a monoid that represents cost, duration, probability, etc. Such systems are represented as coalgebras and (1) and (2) above are derived in a modular fashion from the underlying (functor) type of these coalgebras. In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA’s) and Milner (on regular behaviours and finite LTS’s), and includes many other systems such as Mealy and Moore machines. In the present paper, we extend this framework to deal with quantitative systems. As a consequence, our results now include languages and axiomatizations, both existing and new ones, for many different kinds of probabilistic systems.
A Uniform Framework for Modeling Nondeterministic, Probabilistic, Stochastic, or Mixed Processes and their Behavioral Equivalences
, 2013
"... Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a onestep statetostate reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pai ..."
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Cited by 8 (4 self)
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Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a onestep statetostate reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pair consisting of a source state and a transition label. The state reachability distribution is a function mapping each possible target state to a value that expresses the degree of onestep 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 wellknown models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. They can be defined on ULTraS by relying on appropriate measure functions that express the degree of reachability of a set of states when performing multistep 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 except when nondeterminism and probability/stochasticity coexist; then new equivalences pop up.
A complete axiomatisation of branching bisimulation for probabilistic systems with an application in protocol verification
 In Proceedings of the 17th International Conference on Concurrency Theory, volume 4137 of Lecture Notes in Computer Science
, 2006
"... Abstract. We consider abstraction in probabilistic process algebra. The process algebra can be employed for specifying processes that exhibit both probabilistic and nondeterministic choices in their behaviour. We give a set of axioms that completely axiomatises the branching bisimulation for the st ..."
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Abstract. We consider abstraction in probabilistic process algebra. The process algebra can be employed for specifying processes that exhibit both probabilistic and nondeterministic choices in their behaviour. We give a set of axioms that completely axiomatises the branching bisimulation for the strictly alternating probabilistic graph model. In addition, several recursive verification rules are identified, allowing us to remove redundant internal activity. Using the axioms and the verification rules, we have successfully conducted a verification of the Concurrent Alternating Bit Protocol. This is a simple communication protocol, slightly more ‘sophisticated ’ than the wellknown Alternating Bit Protocol. As channels are lossy, sending continuous streams of data through the channels is a method to overcome this possible loss of data. This instigates a considerable level of parallelism (parallel activities) and as such requires more complex techniques for proving the protocol correct. Using our process algebra we show that after abstraction of internal activity, the protocol behaves as a buffer. 1
Symbolic Bisimulations for Probabilistic Systems
"... The paper introduces symbolic bisimulations for a simple probabilistic πcalculus to overcome the infinite branching problem that still exists in checking ground bisimulations between probabilistic systems. Especially the definition of weak (symbolic) bisimulation does not rely on the random capabil ..."
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The paper introduces symbolic bisimulations for a simple probabilistic πcalculus to overcome the infinite branching problem that still exists in checking ground bisimulations between probabilistic systems. Especially the definition of weak (symbolic) bisimulation does not rely on the random capability of adversaries and suggests a solution to the open problem on the axiomatization for weak bisimulation in the case of unguarded recursion. Furthermore, we present an efficient characterization of symbolic bisimulations for the calculus, which allows the ”onthefly ” instantiation of bound names and dynamic construction of equivalence relations for quantitative evaluation. This directly results in a local decision algorithm that can explore just a minimal portion of the state spaces of the probabilistic processes in question. 1
A Probabilistic Kleene Theorem
"... We 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 sta ..."
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We 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 twoway probabilistic automata with pebbles and corresponding expressions.
A COMPOSITIONAL MERGE OF PROBABILISTIC PROCESSES IN THE ALTERNATING MODEL
"... Abstract. We investigate concurrency of probabilistic systems in the alternating model. So far two different merge operators that capture two different views how concurrent probabilistic processes may interleave have been proposed. We show that neither of these operators is compositional with respec ..."
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Abstract. We investigate concurrency of probabilistic systems in the alternating model. So far two different merge operators that capture two different views how concurrent probabilistic processes may interleave have been proposed. We show that neither of these operators is compositional with respect to weak probabilistic bisimulation for the alternating model. Currently, we work on defining a variant of a merge operator that will preserve weak bisimulation. We present the basic points of our research in this presentation. 1 Models for probabilistic systems Analysis of probabilistic systems has been in the focus of researchers for more than two decades. Early research mainly addressed problems concerning modelling of probabilistic systems. Lately it has been a real challenge to investigate more complex issues concerning equivalence and preorder relations between these systems, (such as (bi)simulation relations), particularly in the presence of abstraction and internal (unobservable) activities. For the specification and verification of probabilistic systems that also incorporate
Unifying Probability with Nondeterminism
 In: FM 2009, LNCS
"... Centre of the United Nations University (UNU). It is based in Macao, and was founded in 1991. It started operations in July 1992. UNUIIST is jointly funded by the government of Macao and the governments of the People’s Republic of China and Portugal through a contribution to the UNU Endowment Fund ..."
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Centre of the United Nations University (UNU). It is based in Macao, and was founded in 1991. It started operations in July 1992. UNUIIST is jointly funded by the government of Macao and the governments of the People’s Republic of China and Portugal through a contribution to the UNU Endowment Fund. As well as providing twothirds of the endowment fund, the Macao authorities also supply UNUIIST with its office premises and furniture and subsidise fellow accommodation. The mission of UNUIIST is to assist developing countries in the application and development of software technology. UNUIIST contributes through its programmatic activities: 1. Advanced development projects, in which software techniques supported by tools are applied, 2. Research projects, in which new techniques for software development are investigated, 3. Curriculum development projects, in which courses of software technology for universities in developing countries are developed, 4. University development projects, which complement the curriculum development projects by aiming to strengthen all aspects of computer science teaching in universities in developing countries, 5. Schools and Courses, which typically teach advanced software development techniques,
Timed, Distributed, Probabilistic, Typed Processes
"... Abstract. This paper studies types and probabilistic bisimulations for a timed πcalculus as an effective tool for a compositional analysis of probabilistic distributed behaviour. The types clarify the role of timers as interface between nonterminating and terminating communication for guaranteeing ..."
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Abstract. This paper studies types and probabilistic bisimulations for a timed πcalculus as an effective tool for a compositional analysis of probabilistic distributed behaviour. The types clarify the role of timers as interface between nonterminating and terminating communication for guaranteeing distributed liveness. We add messageloss probabilities to the calculus, and introduce a notion of approximate bisimulation that discards transitions below a certain specified probability threshold. We prove this bisimulation to be a congruence, and use it for deriving quantitative bounds for practical protocols in distributed systems, including timerdriven messageloss recovery and the TwoPhase Commit protocol. 1
THEME Programs, Verification and ProofsTable of contents
"... 3.2. The probabilistic asynchronous πcalculus 2 ..."