486 research outputs found
Conditional Transition Systems with Upgrades
We introduce a variant of transition systems, where activation of transitions
depends on conditions of the environment and upgrades during runtime
potentially create additional transitions. Using a cornerstone result in
lattice theory, we show that such transition systems can be modelled in two
ways: as conditional transition systems (CTS) with a partial order on
conditions, or as lattice transition systems (LaTS), where transitions are
labelled with the elements from a distributive lattice. We define equivalent
notions of bisimilarity for both variants and characterise them via a
bisimulation game.
We explain how conditional transition systems are related to featured
transition systems for the modelling of software product lines. Furthermore, we
show how to compute bisimilarity symbolically via BDDs by defining an operation
on BDDs that approximates an element of a Boolean algebra into a lattice. We
have implemented our procedure and provide runtime results
Approximate reasoning for real-time probabilistic processes
We develop a pseudo-metric analogue of bisimulation for generalized
semi-Markov processes. The kernel of this pseudo-metric corresponds to
bisimulation; thus we have extended bisimulation for continuous-time
probabilistic processes to a much broader class of distributions than
exponential distributions. This pseudo-metric gives a useful handle on
approximate reasoning in the presence of numerical information -- such as
probabilities and time -- in the model. We give a fixed point characterization
of the pseudo-metric. This makes available coinductive reasoning principles for
reasoning about distances. We demonstrate that our approach is insensitive to
potentially ad hoc articulations of distance by showing that it is intrinsic to
an underlying uniformity. We provide a logical characterization of this
uniformity using a real-valued modal logic. We show that several quantitative
properties of interest are continuous with respect to the pseudo-metric. Thus,
if two processes are metrically close, then observable quantitative properties
of interest are indeed close.Comment: Preliminary version appeared in QEST 0
Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems
Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of
behavioural pseudometrics for probabilistic transition systems. These
pseudometrics are a quantitative analogue of probabilistic bisimilarity.
Distance zero captures probabilistic bisimilarity. Each pseudometric has a
discount factor, a real number in the interval (0, 1]. The smaller the discount
factor, the more the future is discounted. If the discount factor is one, then
the future is not discounted at all. Desharnais et al. showed that the
behavioural distances can be calculated up to any desired degree of accuracy if
the discount factor is smaller than one. In this paper, we show that the
distances can also be approximated if the future is not discounted. A key
ingredient of our algorithm is Tarski's decision procedure for the first order
theory over real closed fields. By exploiting the Kantorovich-Rubinstein
duality theorem we can restrict to the existential fragment for which more
efficient decision procedures exist
Labelled transition systems as a Stone space
A fully abstract and universal domain model for modal transition systems and
refinement is shown to be a maximal-points space model for the bisimulation
quotient of labelled transition systems over a finite set of events. In this
domain model we prove that this quotient is a Stone space whose compact,
zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree
of bisimilarity such that image-finite labelled transition systems are dense.
Using this compactness we show that the set of labelled transition systems that
refine a modal transition system, its ''set of implementations'', is compact
and derive a compactness theorem for Hennessy-Milner logic on such
implementation sets. These results extend to systems that also have partially
specified state propositions, unify existing denotational, operational, and
metric semantics on partial processes, render robust consistency measures for
modal transition systems, and yield an abstract interpretation of compact sets
of labelled transition systems as Scott-closed sets of modal transition
systems.Comment: Changes since v2: Metadata updat
Expressive Logics for Coinductive Predicates
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata
Abstractions of stochastic hybrid systems
Many control systems have large, infinite state space that can not be easily abstracted. One method to analyse and verify these systems is reachability analysis. It is frequently used for air traffic control and power plants. Because of lack of complete information about the environment or unpredicted changes, the stochastic approach is a viable alternative. In this paper, different ways of introducing rechability under uncertainty are presented. A new concept of stochastic bisimulation is introduced and its connection with the reachability analysis is established. The work is mainly motivated by safety critical situations in air traffic control (like collision detection and avoidance) and formal tools are based on stochastic analysis
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