47,661 research outputs found
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
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
Quantitative Graded Semantics and Spectra of Behavioural Metrics
Behavioural metrics provide a quantitative refinement of classical two-valued
behavioural equivalences on systems with quantitative data, such as metric or
probabilistic transition systems. In analogy to the classical
linear-time/branching-time spectrum of two-valued behavioural equivalences on
transition systems, behavioural metrics come in various degrees of granularity,
depending on the observer's ability to interact with the system. Graded monads
have been shown to provide a unifying framework for spectra of behavioural
equivalences. Here, we transfer this principle to spectra of behavioural
metrics, working at a coalgebraic level of generality, that is, parametrically
in the system type. In the ensuing development of quantitative graded
semantics, we discuss presentations of graded monads on the category of metric
spaces in terms of graded quantitative equational theories. Moreover, we obtain
a canonical generic notion of invariant real-valued modal logic, and provide
criteria for such logics to be expressive in the sense that logical distance
coincides with the respective behavioural distance. We thus recover recent
expressiveness results for coalgebraic branching-time metrics and for trace
distance in metric transition systems; moreover, we obtain a new expressiveness
result for trace semantics of fuzzy transition systems. We also provide a
number of salient negative results. In particular, we show that trace distance
on probabilistic metric transition systems does not admit a characteristic
real-valued modal logic at all
Hennessy-Milner Theorems via Galois Connections
We introduce a general and compositional, yet simple, framework that allows
us to derive soundness and expressiveness results for modal logics
characterizing behavioural equivalences or metrics (also known as
Hennessy-Milner theorems). It is based on Galois connections between sets of
(real-valued) predicates on the one hand and equivalence relations/metrics on
the other hand and covers a part of the linear-time-branching-time spectrum,
both for the qualitative case (behavioural equivalences) and the quantitative
case (behavioural metrics). We derive behaviour functions from a given logic
and give a condition, called compatibility, that characterizes under which
conditions a logically induced equivalence/metric is induced by a fixpoint
equation. In particular this framework allows us to derive a new fixpoint
characterization of directed trace metrics
Hennessy-Milner Theorems via Galois Connections
We introduce a general and compositional, yet simple, framework that allows to derive soundness and expressiveness results for modal logics characterizing behavioural equivalences or metrics (also known as Hennessy-Milner theorems). It is based on Galois connections between sets of (real-valued) predicates on the one hand and equivalence relations/metrics on the other hand and covers a part of the linear-time-branching-time spectrum, both for the qualitative case (behavioural equivalences) and the quantitative case (behavioural metrics). We derive behaviour functions from a given logic and give a condition, called compatibility, that characterizes under which conditions a logically induced equivalence/metric is induced by a fixpoint equation. In particular, this framework allows to derive a new fixpoint characterization of directed trace metrics
A Linear-Time Branching-Time Spectrum for Behavioral Specification Theories
We propose behavioral specification theories for most equivalences in the
linear-time--branching-time spectrum. Almost all previous work on specification
theories focuses on bisimilarity, but there is a clear interest in
specification theories for other preorders and equivalences. We show that
specification theories for preorders cannot exist and develop a general scheme
which allows us to define behavioral specification theories, based on
disjunctive modal transition systems, for most equivalences in the
linear-time--branching-time spectrum
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
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