12 research outputs found
Distances for Weighted Transition Systems: Games and Properties
We develop a general framework for reasoning about distances between
transition systems with quantitative information. Taking as starting point an
arbitrary distance on system traces, we show how this leads to natural
definitions of a linear and a branching distance on states of such a transition
system. We show that our framework generalizes and unifies a large variety of
previously considered system distances, and we develop some general properties
of our distances. We also show that if the trace distance admits a recursive
characterization, then the corresponding branching distance can be obtained as
a least fixed point to a similar recursive characterization. The central tool
in our work is a theory of infinite path-building games with quantitative
objectives.Comment: In Proceedings QAPL 2011, arXiv:1107.074
Weighted Branching Simulation Distance for Parametric Weighted Kripke Structures
This paper concerns branching simulation for weighted Kripke structures with
parametric weights. Concretely, we consider a weighted extension of branching
simulation where a single transitions can be matched by a sequence of
transitions while preserving the branching behavior. We relax this notion to
allow for a small degree of deviation in the matching of weights, inducing a
directed distance on states. The distance between two states can be used
directly to relate properties of the states within a sub-fragment of weighted
CTL. The problem of relating systems thus changes to minimizing the distance
which, in the general parametric case, corresponds to finding suitable
parameter valuations such that one system can approximately simulate another.
Although the distance considers a potentially infinite set of transition
sequences we demonstrate that there exists an upper bound on the length of
relevant sequences, thereby establishing the computability of the distance.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
A Quantitative Characterization of Weighted Kripke Structures in Temporal Logic
We extend the usual notion of Kripke structures with a weighted transition relation and generalize the classical Boolean interpretation of CTL to a map which assigns to states and temporal formulae a real-valued distance describing the degree of satisfaction. We describe a general approach to obtaining quantitative interpretations for a generic extension of the CTL syntax and show that, for one such interpretation, the logic is both adequate and expressive with respect to quantitative bisimulation
Computing Branching Distances Using Quantitative Games
We lay out a general method for computing branching distances between labeled
transition systems. We translate the quantitative games used for defining these
distances to other, path-building games which are amenable to methods from the
theory of quantitative games. We then show for all common types of branching
distances how the resulting path-building games can be solved. In the end, we
achieve a method which can be used to compute all branching distances in the
linear-time--branching-time spectrum
The quantitative linear-time–branching-time spectrum
International audienceWe present a distance-agnostic approach to quantitative verification. Taking as input an unspecified distance on system traces, or executions, we develop a game-based framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance. Thus we extend the classic linear-time–branching-time spectrum to a quantitative setting, parametrized by trace distance. We also provide fixed-point characterizations of all system distances, and we prove a general transfer principle which allows us to transfer counterexamples from the qualitative to the quantitative setting, showing that all system distances are mutually topologically inequivalent
The quantitative linear-time–branching-time spectrum
International audienceWe present a distance-agnostic approach to quantitative verification. Taking as input an unspecified distance on system traces, or executions, we develop a game-based framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance. Thus we extend the classic linear-time–branching-time spectrum to a quantitative setting, parametrized by trace distance. We also prove a general transfer principle which allows us to transfer counterexamples from the qualitative to the quantitative setting, showing that all system distances are mutually topologically inequivalent