24 research outputs found
The Spectrum of Strong Behavioral Equivalences for Nondeterministic and Probabilistic Processes
We present a spectrum of trace-based, testing, and bisimulation equivalences
for nondeterministic and probabilistic processes whose activities are all
observable. For every equivalence under study, we examine the discriminating
power of three variants stemming from three approaches that differ for the way
probabilities of events are compared when nondeterministic choices are resolved
via deterministic schedulers. We show that the first approach - which compares
two resolutions relatively to the probability distributions of all considered
events - results in a fragment of the spectrum compatible with the spectrum of
behavioral equivalences for fully probabilistic processes. In contrast, the
second approach - which compares the probabilities of the events of a
resolution with the probabilities of the same events in possibly different
resolutions - gives rise to another fragment composed of coarser equivalences
that exhibits several analogies with the spectrum of behavioral equivalences
for fully nondeterministic processes. Finally, the third approach - which only
compares the extremal probabilities of each event stemming from the different
resolutions - yields even coarser equivalences that, however, give rise to a
hierarchy similar to that stemming from the second approach.Comment: In Proceedings QAPL 2013, arXiv:1306.241
Process Algebraic Modeling and Analysis of Power-Aware Real-Time Systems
The paper describes a unified formal framework for designing and reasoning about power-constrained, real-time systems. The framework is based on process algebra, a formalism which has been developed to describe and analyze communicating, concurrent systems. The proposed extension allows the modeling of probabilistic resource failures, priorities of resource usages, and power consumption by resources within the same formalism. Thus, it is possible to evaluate alternative power-consumption behaviors and tradeoffs under different real-time schedulers, resource limitations, resource failure probabilities, etc. This paper describes the modeling and analysis techniques, and illustrates them with examples, including a dynamic voltage-scaling algorithm
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata
We study the bisimilarity problem for probabilistic pushdown automata (pPDA)
and subclasses thereof. Our definition of pPDA allows both probabilistic and
non-deterministic branching, generalising the classical notion of pushdown
automata (without epsilon-transitions). We first show a general
characterization of probabilistic bisimilarity in terms of two-player games,
which naturally reduces checking bisimilarity of probabilistic labelled
transition systems to checking bisimilarity of standard (non-deterministic)
labelled transition systems. This reduction can be easily implemented in the
framework of pPDA, allowing to use known results for standard
(non-probabilistic) PDA and their subclasses. A direct use of the reduction
incurs an exponential increase of complexity, which does not matter in deriving
decidability of bisimilarity for pPDA due to the non-elementary complexity of
the problem. In the cases of probabilistic one-counter automata (pOCA), of
probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic
process algebras (i.e., single-state pPDA) we show that an implicit use of the
reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and
2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic
versions. The bisimilarity problems for OCA and vPDA are known to have matching
lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively);
we show that these lower bounds also hold for fully probabilistic versions that
do not use non-determinism
Probabilistic Mobility Models for Mobile and Wireless Networks
International audienceIn this paper we present a probabilistic broadcast calculus for mobile and wireless networks whose connections are unreliable. In our calculus, broadcasted messages can be lost with a certain probability, and due to mobility the connection probabilities may change. If a network broadcasts a message from a location, it will evolve to a network distribution depending on whether nodes at other locations receive the message or not. Mobility of nodes is not arbitrary but guarded by a probabilistic mobility function (PMF), and we also define the notion of a weak bisimulation given a PMF. It is possible to have weak bisimular networks which have different probabilistic connectivity information. We furthermore examine the relation between our weak bisimulation and a minor variant of PCTL* [1]. Finally, we apply our calculus on a small example called the Zeroconf protocol [2]
Verification of random behaviours
We introduce abstraction in a probabilistic process algebra. The process algebra can be employed for specifying processes that exhibit both probabilistic and non-deterministic choices in their behaviours. Several rules and axioms are identified, allowing us to rewrite processes to less complex processes by removing redundant internal activity. Using these rules, we have successfully
conducted a verification of the Concurrent Alternating Bit Protocol. The verification shows that after abstraction of internal activity, the protocol behaves as a buffer
On the Efficiency of Deciding Probabilistic Automata Weak Bisimulation
Weak probabilistic bisimulation on probabilistic automata can be decided by an algorithm that needs to check a polynomial number of linear programming problems encoding weak transitions. It is hence polynomial, but not guaranteed to be strongly polynomial. In this paper we show that for polynomial rational proba- bilistic automata strong polynomial complexity can be ensured. We further discuss complexity bounds for generic probabilistic automata. Then we consider several practical algorithms and LP transformations that enable an efficient solution for the concrete weak transition problem. This sets the ground for effective compositional minimisation approaches for probabilistic automata and Markov decision processes