1,296 research outputs found
A General Framework for Well-Structured Graph Transformation Systems
Graph transformation systems (GTSs) can be seen as wellstructured transition
systems (WSTSs), thus obtaining decidability results for certain classes of
GTSs. In earlier work it was shown that wellstructuredness can be obtained
using the minor ordering as a well-quasiorder. In this paper we extend this
idea to obtain a general framework in which several types of GTSs can be seen
as (restricted) WSTSs. We instantiate this framework with the subgraph ordering
and the induced subgraph ordering and apply it to analyse a simple access
rights management system.Comment: Extended version (including proofs) of a paper accepted at CONCUR
201
Specifying Graph Languages with Type Graphs
We investigate three formalisms to specify graph languages, i.e. sets of
graphs, based on type graphs. First, we are interested in (pure) type graphs,
where the corresponding language consists of all graphs that can be mapped
homomorphically to a given type graph. In this context, we also study languages
specified by restriction graphs and their relation to type graphs. Second, we
extend this basic approach to a type graph logic and, third, to type graphs
with annotations. We present decidability results and closure properties for
each of the formalisms.Comment: (v2): -Fixed some typos -Added more reference
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
Coalgebraic Behavioral Metrics
We study different behavioral metrics, such as those arising from both
branching and linear-time semantics, in a coalgebraic setting. Given a
coalgebra for a functor , we define a framework for deriving pseudometrics on which
measure the behavioral distance of states.
A crucial step is the lifting of the functor on to a
functor on the category of pseudometric spaces.
We present two different approaches which can be viewed as generalizations of
the Kantorovich and Wasserstein pseudometrics for probability measures. We show
that the pseudometrics provided by the two approaches coincide on several
natural examples, but in general they differ.
If has a final coalgebra, every lifting yields in a
canonical way a behavioral distance which is usually branching-time, i.e., it
generalizes bisimilarity. In order to model linear-time metrics (generalizing
trace equivalences), we show sufficient conditions for lifting distributive
laws and monads. These results enable us to employ the generalized powerset
construction
Towards Trace Metrics via Functor Lifting
We investigate the possibility of deriving metric trace semantics in a
coalgebraic framework. First, we generalize a technique for systematically
lifting functors from the category Set of sets to the category PMet of
pseudometric spaces, showing under which conditions also natural
transformations, monads and distributive laws can be lifted. By exploiting some
recent work on an abstract determinization, these results enable the derivation
of trace metrics starting from coalgebras in Set. More precisely, for a
coalgebra on Set we determinize it, thus obtaining a coalgebra in the
Eilenberg-Moore category of a monad. When the monad can be lifted to PMet, we
can equip the final coalgebra with a behavioral distance. The trace distance
between two states of the original coalgebra is the distance between their
images in the determinized coalgebra through the unit of the monad. We show how
our framework applies to nondeterministic automata and probabilistic automata
Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems
Coalgebras in a Kleisli category yield a generic definition of trace
semantics for various types of labelled transition systems. In this paper we
apply this generic theory to generative probabilistic transition systems, short
PTS, with arbitrary (possibly uncountable) state spaces. We consider the
sub-probability monad and the probability monad (Giry monad) on the category of
measurable spaces and measurable functions. Our main contribution is that the
existence of a final coalgebra in the Kleisli category of these monads is
closely connected to the measure-theoretic extension theorem for sigma-finite
pre-measures. In fact, we obtain a practical definition of the trace measure
for both finite and infinite traces of PTS that subsumes a well-known result
for discrete probabilistic transition systems. Finally we consider two example
systems with uncountable state spaces and apply our theory to calculate their
trace measures
- …