#### Research group within the Department of Computer Engineering (Technische Informatik) at the University of the Federal Armed Forces Munich.

Group members are:

#### Head: Prof. Dr.-Ing. Markus Siegle

Current members: Dipl.-Math. Alexander Gouberman and Bharath Siva Kumar Tati, M.Sc.

Former members: Dr.-Ing. Martin Riedl, Dr. Johann Schuster, Dr.-Ing. Kai Lampka, Dr.-Ing. Matthias Kuntz, Dr.-Ing. Joachim Meyer-Kayser.

#### Overview

The group develops techniques and tools to support the design and analysis of computer and communication systems. The focus is on model-based performance and dependability evaluation of such systems, working with stochastic models which are specified with the help of stochastic process algebra or related formalisms. We are working on the specification and automatic verification of complex performability requirements.

#### Projects / Cooperations

We conducted the DFG-sponsored project "Efficient Analysis Algorithms for Performability-Evaluation of Distributed Systems", where we developed novel data structures and algorithms for the analysis of Markovian models. This included a symbolic elimination algorithms for vanishing states, an efficient k-shortest path algorithm and a new parallel multilevel method for numerical analysis. Another DFG-sponsored project was PerformVER, where we developed highly expressive logics for formally specifying complex performability properties of concurrent systems. We devised efficient algorithms for symbolic model checking, and implementedd them in prototype software tools. Prior to this, we had conducted two more DFG-sponsered projects: BDDana, which investigated efficient performance analysis on the basis of BDDs, and AutoVer, where we investigated the automatic verification of quality of service requirements of distributed systems. In the past, we have cooperated, among others

- with the Universities of Aachen, Dresden, Münster, Nijmegen, Saarbrücken and Twente, supported by the DFG-NWO-sponsored project ROCKS (completed)
- with the Technical University of Munich, supported by the DFG-sponsored project "Model-based Dependability Analysis of Complex Fault-Tolerant Systems" (completed)
- with the Universities of Aachen, Bonn, Nijmegen, Saarbrücken and Twente, supported by the DFG-NWO-sponsored project VOSS (completed)
- with the Universities of Birmingham and Edinburgh, a collaboration originally supported by the DAAD project StochVer (completed)
- with the the University of Illinois at Urbana-Champaign and the University of Cape Town.

#### LARES: Specification Language and Toolset for Reconfigurable Dependable Systems

For bridging the gap between high-level formalisms and formal modelling languages, the LAnguage for REconfigurable dependable Systems (LARES) has been defined [ WGRSS09, RS12, GRS13, GGRSS09, GRS17]. LARES provides means for hierarchical modelling, i.e. it separates between the definition of structure and behaviour and introduces scopes to restrict visibility of definitions. The formal semantics of LARES is defined either by means of flat labelled Markov chains or by stochastic process algebra (CASPA, see below). The LARES website is a resource for the LARES specification, tutorials on modelling and analysis using the LARES IDE, links to example models and news on current developments.

#### Semantics of probabilistic / stochastic models

We studied weak bisimulation of Markov automata, therein introducing the notion of non-naively vanishing states [ SS14]. In [ SS13], we showed that the class of compact bisimilar probabilistic automata forms lattices. We also developed necessary and sufficient criteria that guarantee scale-freeness of stochastic process algebra models with weigthed immediate actions [ SS12].

#### Model checking and model repair of stochastic systems

Recently, we have studied the problem of model repair, i.e. the question of how an existing system should be modified in case it violates a given requirement. We consider labelled CTMC models and requirements formulated with the help of the logic CSL. Our repair method does not alter the structure of the model, but works by reducing certain well-defined sets of transition rates by a common factor [ TS15]. We consider untimed and time-bounded requirements [ TS16, GST17]. Building on our model repair algorithms, we also work on controller synthesis, where a controller is constructed, to be composed in parallel with a given plant, such that the resulting system will satisfy requirements formulated in the logic asCSL.

Earlier we developed the action-based logic aCSL [HKMS00] for model checking action-labelled Markov chains stemming from stochastic process algebra specifications. Then we were working on logics which extend the combined expressivity of CSL and aCSL by specifying arbitrarily complex execution paths which are characterised by regular expressions of actions and so-called tests. Two logics resulting from this work are sPDL [KS03, KS06] and asCSL [BCHKS04].

We were among the first to develop a model checker for probabilistic / stochastic systems: The tool ETMCC enables its users to check labelled CTMCs, where Continuous Stochastic Logic (CSL) and action-based CSL (aCSL) are used as the basic requirements specification languages [HKMS03]. ETMCC realises CTL-type model checking algorithms built on top of sophisticated numerical analysis techniques, based on sparse data structures.

#### Representation and analysis of large Markov chains

In many areas of system design and analysis, there is the need to generate, manipulate and analyse very large state spaces. State space explosion is a serious problem when modelling parallel and distributed systems, because of the memory limitations of the available computing equipment.

We have made contributions to the symbolic representation of large labelled CTMCs, based on binary decision diagrams (BDD) and extensions thereof. We use multi-terminal BDDs (MTBDD) and partially shared zero-suppressed MTBDDs (pZDD) [S02, LS06a]. In the presence of structured models which are composed of interacting submodels, the symbolic approach leads to provably compact representations of huge state spaces [HKNPS03]. For arbitrary models without any particular structure, the so-called activity-local scheme [LS03, LS06a] generates the state graph and processes reward-related information in a manner that is highly runtime- and memory-efficient [ LS14]. Numerical analysis methods have successfully been adapted to the ZDDdata structure [ LS06b].

We have developed several prototypical tools for BDD-based model generation, manipulation and analysis. Originally we used TIPPtool as a front end, but now our tool CASPA [KSW04] is a powerful stand-alone stochastic process algebra tool based entirely on symbolic data structures. One of our activities concerned the integration of symbolic techniques into the multi-formalism modelling tool Möbius which led, among other results, to the implementation of an AFI for state-level objects represented by ZDDs.