2,639 research outputs found
Abstract Acceleration in Linear relation analysis (extended version)
Linear relation analysis is a classical abstract interpretation based on an over-approximation of reachable numerical states of a program by convex polyhedra. Since it works with a lattice of infinite height, it makes use of a widening operator to enforce the convergence of fixed point computations. Abstract acceleration is a method that computes the precise abstract effect of loops wherever possible and uses widening in the general case. Thus, it improves both the precision and the efficiency of the analysis. This research report gives a comprehensive tutorial on abstract acceleration: its origins in Presburger-based acceleration including new insights w.r.t. the linear accelerability of linear transformations, methods for simple and nested loops, recent extensions, tools and applications, and a detailed discussion of related methods and future perspectives. This is the long version of a paper under submission
Generalization Strategies for the Verification of Infinite State Systems
We present a method for the automated verification of temporal properties of
infinite state systems. Our verification method is based on the specialization
of constraint logic programs (CLP) and works in two phases: (1) in the first
phase, a CLP specification of an infinite state system is specialized with
respect to the initial state of the system and the temporal property to be
verified, and (2) in the second phase, the specialized program is evaluated by
using a bottom-up strategy. The effectiveness of the method strongly depends on
the generalization strategy which is applied during the program specialization
phase. We consider several generalization strategies obtained by combining
techniques already known in the field of program analysis and program
transformation, and we also introduce some new strategies. Then, through many
verification experiments, we evaluate the effectiveness of the generalization
strategies we have considered. Finally, we compare the implementation of our
specialization-based verification method to other constraint-based model
checking tools. The experimental results show that our method is competitive
with the methods used by those other tools. To appear in Theory and Practice of
Logic Programming (TPLP).Comment: 24 pages, 2 figures, 5 table
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Stochastic hybrid system : modelling and verification
Hybrid systems now form a classical computational paradigm unifying discrete and continuous system aspects. The modelling, analysis and verification of these systems are very difficult.
One way to reduce the complexity of hybrid system models is to consider randomization. The need for stochastic models has actually multiple motivations. Usually, when building models complete information is not available and we have to consider stochastic versions. Moreover, non-determinism and uncertainty are inherent to complex systems. The stochastic approach can be thought of as a way of quantifying non-determinism (by assigning a probability to each
possible execution branch) and managing uncertainty. This is built upon to the - now classical - approach in algorithmics that provides polynomial complexity algorithms via randomization.
In this thesis we investigate the stochastic hybrid systems, focused on modelling and analysis.
We propose a powerful unifying paradigm that combines analytical and formal methods. Its
applications vary from air traffic control to communication networks and healthcare systems.
The stochastic hybrid system paradigm has an explosive development. This is because of its
very powerful expressivity and the great variety of possible applications. Each hybrid system model can be randomized in different ways, giving rise to many classes of stochastic hybrid systems.
Moreover, randomization can change profoundly the mathematical properties of discrete and continuous aspects and also can influence their interaction. Beyond the profound foundational and semantics issues, there is the possibility to combine and cross-fertilize techniques from analytic mathematics (like optimization, control, adaptivity, stability, existence and uniqueness of trajectories, sensitivity analysis) and formal methods (like bisimulation, specification, reachability
analysis, model checking). These constitute the major motivations of our research. We
investigate new models of stochastic hybrid systems and their associated problems. The main difference from the existing approaches is that we do not follow one way (based only on continuous or discrete mathematics), but their cross-fertilization. For stochastic hybrid systems we introduce concepts that have been defined only for discrete transition systems. Then, techniques
that have been used in discrete automata now come in a new analytical fashion. This is partly explained by the fact that popular verification methods (like theorem proving) can hardly work even on probabilistic extensions of discrete systems. When the continuous dimension is added, the idea to use continuous mathematics methods for verification purposes comes in a natural
way.
The concrete contribution of this thesis has four major milestones:
1. A new and a very general model for stochastic hybrid systems;
2. Stochastic reachability for stochastic hybrid systems is introduced together with an approximating method to compute reach set probabilities;
3. Bisimulation for stochastic hybrid systems is introduced and relationship with reachability analysis is investigated.
4. Considering the communication issue, we extend the modelling paradigm
CHARDA: Causal Hybrid Automata Recovery via Dynamic Analysis
We propose and evaluate a new technique for learning hybrid automata
automatically by observing the runtime behavior of a dynamical system. Working
from a sequence of continuous state values and predicates about the
environment, CHARDA recovers the distinct dynamic modes, learns a model for
each mode from a given set of templates, and postulates causal guard conditions
which trigger transitions between modes. Our main contribution is the use of
information-theoretic measures (1)~as a cost function for data segmentation and
model selection to penalize over-fitting and (2)~to determine the likely causes
of each transition. CHARDA is easily extended with different classes of model
templates, fitting methods, or predicates. In our experiments on a complex
videogame character, CHARDA successfully discovers a reasonable
over-approximation of the character's true behaviors. Our results also compare
favorably against recent work in automatically learning probabilistic timed
automata in an aircraft domain: CHARDA exactly learns the modes of these
simpler automata.Comment: 7 pages, 2 figures. Accepted for IJCAI 201
Synthesising Strategy Improvement and Recursive Algorithms for Solving 2.5 Player Parity Games
2.5 player parity games combine the challenges posed by 2.5 player
reachability games and the qualitative analysis of parity games. These two
types of problems are best approached with different types of algorithms:
strategy improvement algorithms for 2.5 player reachability games and recursive
algorithms for the qualitative analysis of parity games. We present a method
that - in contrast to existing techniques - tackles both aspects with the best
suited approach and works exclusively on the 2.5 player game itself. The
resulting technique is powerful enough to handle games with several million
states
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