Probalistic Timed Graph Transformation Systems
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Probalistic Timed Graph Transformation Systems
Author: Maximove, Maria
language: en
Publisher: Universitätsverlag Potsdam
Release Date: 2017-11-30
Today, software has become an intrinsic part of complex distributed embedded real-time systems. The next generation of embedded real-time systems will interconnect the today unconnected systems via complex software parts and the service-oriented paradigm. Therefore besides timed behavior and probabilistic behaviour also structure dynamics, where the architecture can be subject to changes at run-time, e.g. when dynamic binding of service end-points is employed or complex collaborations are established dynamically, is required. However, a modeling and analysis approach that combines all these necessary aspects does not exist so far. To fill the identified gap, we propose Probabilistic Timed Graph Transformation Systems (PTGTSs) as a high-level description language that supports all the necessary aspects of structure dynamics, timed behavior, and probabilistic behavior. We introduce the formal model of PTGTSs in this paper and present a mapping of models with finite state spaces to probabilistic timed automata (PTA) that allows to use the PRISM model checker to analyze PTGTS models with respect to PTCTL properties.
Interval Probabilistic Timed Graph Transformation Systems
Author: Maria Maximova
language: en
Publisher: Universitätsverlag Potsdam
Release Date: 2022-05-19
The formal modeling and analysis is of crucial importance for software development processes following the model based approach. We present the formalism of Interval Probabilistic Timed Graph Transformation Systems (IPTGTSs) as a high-level modeling language. This language supports structure dynamics (based on graph transformation), timed behavior (based on clocks, guards, resets, and invariants as in Timed Automata (TA)), and interval probabilistic behavior (based on Discrete Interval Probability Distributions). That is, for the probabilistic behavior, the modeler using IPTGTSs does not need to provide precise probabilities, which are often impossible to obtain, but rather provides a probability range instead from which a precise probability is chosen nondeterministically. In fact, this feature on capturing probabilistic behavior distinguishes IPTGTSs from Probabilistic Timed Graph Transformation Systems (PTGTSs) presented earlier. Following earlier work on Interval Probabilistic Timed Automata (IPTA) and PTGTSs, we also provide an analysis tool chain for IPTGTSs based on inter-formalism transformations. In particular, we provide in our tool AutoGraph a translation of IPTGTSs to IPTA and rely on a mapping of IPTA to Probabilistic Timed Automata (PTA) to allow for the usage of the Prism model checker. The tool Prism can then be used to analyze the resulting PTA w.r.t. probabilistic real-time queries asking for worst-case and best-case probabilities to reach a certain set of target states in a given amount of time.
Compositional Analysis of Probabilistic Timed Graph Transformation Systems
Author: Maria Maximova
language: en
Publisher: Universitätsverlag Potsdam
Release Date: 2022-05-19
The analysis of behavioral models is of high importance for cyber-physical systems, as the systems often encompass complex behavior based on e.g. concurrent components with mutual exclusion or probabilistic failures on demand. The rule-based formalism of probabilistic timed graph transformation systems is a suitable choice when the models representing states of the system can be understood as graphs and timed and probabilistic behavior is important. However, model checking PTGTSs is limited to systems with rather small state spaces. We present an approach for the analysis of large scale systems modeled as probabilistic timed graph transformation systems by systematically decomposing their state spaces into manageable fragments. To obtain qualitative and quantitative analysis results for a large scale system, we verify that results obtained for its fragments serve as overapproximations for the corresponding results of the large scale system. Hence, our approach allows for the detection of violations of qualitative and quantitative safety properties for the large scale system under analysis. We consider a running example in which we model shuttles driving on tracks of a large scale topology and for which we verify that shuttles never collide and are unlikely to execute emergency brakes. In our evaluation, we apply an implementation of our approach to the running example.