7 research outputs found
On-the-fly Probabilistic Model Checking
Model checking approaches can be divided into two broad categories: global
approaches that determine the set of all states in a model M that satisfy a
temporal logic formula f, and local approaches in which, given a state s in M,
the procedure determines whether s satisfies f. When s is a term of a process
language, the model checking procedure can be executed "on-the-fly", driven by
the syntactical structure of s. For certain classes of systems, e.g. those
composed of many parallel components, the local approach is preferable because,
depending on the specific property, it may be sufficient to generate and
inspect only a relatively small part of the state space. We propose an
efficient, on-the-fly, PCTL model checking procedure that is parametric with
respect to the semantic interpretation of the language. The procedure comprises
both bounded and unbounded until modalities. The correctness of the procedure
is shown and its efficiency is compared with a global PCTL model checker on
representative applications.Comment: In Proceedings ICE 2014, arXiv:1410.701
On-the-fly Fast Mean-Field Model-Checking: Extended Version
A novel, scalable, on-the-fly model-checking procedure is presented to verify
bounded PCTL properties of selected individuals in the context of very large
systems of independent interacting objects. The proposed procedure combines
on-the-fly model checking techniques with deterministic mean-field
approximation in discrete time. The asymptotic correctness of the procedure is
shown and some results of the application of a prototype implementation of the
FlyFast model-checker are presented
On Formal Methods for Collective Adaptive System Engineering. {Scalable Approximated, Spatial} Analysis Techniques. Extended Abstract
In this extended abstract a view on the role of Formal Methods in System
Engineering is briefly presented. Then two examples of useful analysis
techniques based on solid mathematical theories are discussed as well as the
software tools which have been built for supporting such techniques. The first
technique is Scalable Approximated Population DTMC Model-checking. The second
one is Spatial Model-checking for Closure Spaces. Both techniques have been
developed in the context of the EU funded project QUANTICOL.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200
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
Collective Adaptive Systems: Qualitative and Quantitative Modelling and Analysis (Dagstuhl Seminar 14512)
This report documents the program and the outcomes of Dagstuhl Seminar 14512 "Collective Adaptive Systems: Qualitative and Quantitative Modelling and Analysis". Besides presentations on current work in the area, the seminar focused on the following topics:
(i) Modelling techniques and languages for collective adaptive systems based on the above formalisms. (ii) Verification of collective adaptive systems. (iii) Humans-in-the-loop in collective adaptive systems
Algorithms for reachability problems on stochastic Markov reward models
Probabilistic model-checking is a field which seeks to automate the formal analysis of probabilistic models such as Markov chains. In this thesis, we study and develop the stochastic Markov reward model (sMRM) which extends the Markov chain with rewards as random variables. The model recently being introduced, does not have much in the way of techniques and algorithms for their analysis. The purpose of this study is to derive such algorithms that are both scalable and accurate.
Additionally, we derive the necessary theory for probabilistic model-checking of sMRMs against existing temporal logics such as PRCTL. We present the equations for computing \textit{first-passage reward densities}, \textit{expected value problems}, and other \textit{reachability problems}. Our focus however is on finding strictly numerical solutions for \textit{first-passage reward densities}. We solve for these by firstly adapting known direct linear algebra algorithms such as Gaussian elimination, and iterative methods such as the power method, Jacobi and Gauss-Seidel. We provide solutions for both discrete-reward sMRMs, where all rewards discrete (lattice) random variables. And also for continuous-reward sMRMs, where all rewards are strictly continuous random variables, but not necessarily having continuous probability density functions (pdfs). Our solutions involve the use of fast Fourier transform (FFT) for faster computation, and we adapted existing quadrature rules for convolution to gain more accurate solutions, rules such as the trapezoid rule, Simpson's rule or Romberg's method.
In the discrete-reward setting, existing solutions are either derived by hands, or a combination of graph-reduction algorithms and symbolically solving them via computer algebra systems. The symbolic approach is not scalable, and for this we present strictly numerical but relatively more scalable algorithms. We found each - direct and iterative - capable of solving problems with larger state spaces. The best performer was the power method, owed partially to its simplicity, leading to easier vectorization of its implementation. Whilst, the Gauss-Seidel method was shown to converge with fewer iterations, it was slower due to costs of deconvolution. The Gaussian Elimination algorithm performed poorly relative to these.
In the continuous-reward setting, existing solutions are adaptable from literature on semi-Markov processes. However, it appears that other algorithms should still be researched for the cases where rewards have discontinuous pdfs. The algorithm we have developed has the ability to resolve such a case, albeit the solution does not appear as scalable as the discrete-reward setting