467 research outputs found
Compositional Performance Modelling with the TIPPtool
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations
Test Derivation from Timed Automata
A real-time system is a discrete system whose state changes occur in real-numbered time [AH97]. For testing real-time systems, specification languages must be extended with constructs for expressing real-time constraints, the implementation relation must be generalized to consider the temporal dimension, and the data structures and algorithms used to generate tests must be revised to operate on a potentially infinite set of states
Algebra, coalgebra, and minimization in polynomial differential equations
We consider reasoning and minimization in systems of polynomial ordinary
differential equations (ode's). The ring of multivariate polynomials is
employed as a syntax for denoting system behaviours. We endow this set with a
transition system structure based on the concept of Lie-derivative, thus
inducing a notion of L-bisimulation. We prove that two states (variables) are
L-bisimilar if and only if they correspond to the same solution in the ode's
system. We then characterize L-bisimilarity algebraically, in terms of certain
ideals in the polynomial ring that are invariant under Lie-derivation. This
characterization allows us to develop a complete algorithm, based on building
an ascending chain of ideals, for computing the largest L-bisimulation
containing all valid identities that are instances of a user-specified
template. A specific largest L-bisimulation can be used to build a reduced
system of ode's, equivalent to the original one, but minimal among all those
obtainable by linear aggregation of the original equations. A computationally
less demanding approximate reduction and linearization technique is also
proposed.Comment: 27 pages, extended and revised version of FOSSACS 2017 pape
Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs
Verification of PCTL properties of MDPs with convex uncertainties has been
investigated recently by Puggelli et al. However, model checking algorithms
typically suffer from state space explosion. In this paper, we address
probabilistic bisimulation to reduce the size of such an MDPs while preserving
PCTL properties it satisfies. We discuss different interpretations of
uncertainty in the models which are studied in the literature and that result
in two different definitions of bisimulations. We give algorithms to compute
the quotients of these bisimulations in time polynomial in the size of the
model and exponential in the uncertain branching. Finally, we show by a case
study that large models in practice can have small branching and that a
substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Syntactic Markovian Bisimulation for Chemical Reaction Networks
In chemical reaction networks (CRNs) with stochastic semantics based on
continuous-time Markov chains (CTMCs), the typically large populations of
species cause combinatorially large state spaces. This makes the analysis very
difficult in practice and represents the major bottleneck for the applicability
of minimization techniques based, for instance, on lumpability. In this paper
we present syntactic Markovian bisimulation (SMB), a notion of bisimulation
developed in the Larsen-Skou style of probabilistic bisimulation, defined over
the structure of a CRN rather than over its underlying CTMC. SMB identifies a
lumpable partition of the CTMC state space a priori, in the sense that it is an
equivalence relation over species implying that two CTMC states are lumpable
when they are invariant with respect to the total population of species within
the same equivalence class. We develop an efficient partition-refinement
algorithm which computes the largest SMB of a CRN in polynomial time in the
number of species and reactions. We also provide an algorithm for obtaining a
quotient network from an SMB that induces the lumped CTMC directly, thus
avoiding the generation of the state space of the original CRN altogether. In
practice, we show that SMB allows significant reductions in a number of models
from the literature. Finally, we study SMB with respect to the deterministic
semantics of CRNs based on ordinary differential equations (ODEs), where each
equation gives the time-course evolution of the concentration of a species. SMB
implies forward CRN bisimulation, a recently developed behavioral notion of
equivalence for the ODE semantics, in an analogous sense: it yields a smaller
ODE system that keeps track of the sums of the solutions for equivalent
species.Comment: Extended version (with proofs), of the corresponding paper published
at KimFest 2017 (http://kimfest.cs.aau.dk/
Symbolic Models for Stochastic Switched Systems: A Discretization and a Discretization-Free Approach
Stochastic switched systems are a relevant class of stochastic hybrid systems
with probabilistic evolution over a continuous domain and control-dependent
discrete dynamics over a finite set of modes. In the past few years several
different techniques have been developed to assist in the stability analysis of
stochastic switched systems. However, more complex and challenging objectives
related to the verification of and the controller synthesis for logic
specifications have not been formally investigated for this class of systems as
of yet. With logic specifications we mean properties expressed as formulae in
linear temporal logic or as automata on infinite strings. This paper addresses
these complex objectives by constructively deriving approximately equivalent
(bisimilar) symbolic models of stochastic switched systems. More precisely,
this paper provides two different symbolic abstraction techniques: one requires
state space discretization, but the other one does not require any space
discretization which can be potentially more efficient than the first one when
dealing with higher dimensional stochastic switched systems. Both techniques
provide finite symbolic models that are approximately bisimilar to stochastic
switched systems under some stability assumptions on the concrete model. This
allows formally synthesizing controllers (switching signals) that are valid for
the concrete system over the finite symbolic model, by means of mature
automata-theoretic techniques in the literature. The effectiveness of the
results are illustrated by synthesizing switching signals enforcing logic
specifications for two case studies including temperature control of a six-room
building.Comment: 25 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1302.386
Design and Optimisation of the FlyFast Front-end for Attribute-based Coordination
Collective Adaptive Systems (CAS) consist of a large number of interacting
objects. The design of such systems requires scalable analysis tools and
methods, which have necessarily to rely on some form of approximation of the
system's actual behaviour. Promising techniques are those based on mean-field
approximation. The FlyFast model-checker uses an on-the-fly algorithm for
bounded PCTL model-checking of selected individual(s) in the context of very
large populations whose global behaviour is approximated using deterministic
limit mean-field techniques. Recently, a front-end for FlyFast has been
proposed which provides a modelling language, PiFF in the sequel, for the
Predicate-based Interaction for FlyFast. In this paper we present details of
PiFF design and an approach to state-space reduction based on probabilistic
bisimulation for inhomogeneous DTMCs.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
- âŠ