Lattice structures for bisimilar Probabilistic Automata

The paper shows that there is a deep structure on certain sets of bisimilar Probabilistic Automata (PA). The key prerequisite for these structures is a notion of compactness of PA. It is shown that compact bisimilar PA form lattices. These results are then used in order to establish normal forms not only for finite automata, but also for infinite automata, as long as they are compact.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Model Checking Markov Chains with Actions and State Labels

In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure

Parameter and Controller Synthesis for Markov Chains with Actions and State Labels

This paper introduces a novel approach for synthesizing parameters and controllers for Markov Chains with Actions and State Labels (ASMC). Requirements which are to be met by the controlled system are specified as formulas of asCSL, which is a powerful temporal logic for characterizing both state properties and action sequences of a labeled Markov chain. The paper proposes two separate - but related - algorithms for untimed until type and untimed general asCSL formulas. In the former case, a set of transition rates and a common rate reduction factor are determined. In the latter case, a controller which is to be composed in parallel with the given ASMC is synthesized. Both algorithms are based on some rather simple heuristics

Partially-shared zero-suppressed multi-terminal BDDs: concept, algorithms and applications

Multi-Terminal Binary Decision Diagrams (MTBDDs) are a well accepted technique for the state graph (SG) based quantitative analysis of large and complex systems specified by means of high-level model description techniques. However, this type of Decision Diagram (DD) is not always the best choice, since finite functions with small satisfaction sets, and where the fulfilling assignments possess many 0-assigned positions, may yield relatively large MTBDD based representations. Therefore, this article introduces zero-suppressed MTBDDs and proves that they are canonical representations of multi-valued functions on finite input sets. For manipulating DDs of this new type, possibly defined over different sets of function variables, the concept of partially-shared zero-suppressed MTBDDs and respective algorithms are developed. The efficiency of this new approach is demonstrated by comparing it to the well-known standard type of MTBDDs, where both types of DDs have been implemented by us within the C++-based DD-package JINC. The benchmarking takes place in the context of Markovian analysis and probabilistic model checking of systems. In total, the presented work extends existing approaches, since it not only allows one to directly employ (multi-terminal) zero-suppressed DDs in the field of quantitative verification, but also clearly demonstrates their efficienc

On the use of MTBDDs for performability analysis and verification of stochastic systems

AbstractThis paper describes how to employ multi-terminal binary decision diagrams (MTBDDs) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and non-deterministic behaviour. It is shown how the notorious problem of state space explosion can be circumvented by compositionally constructing symbolic (i.e. MTBDD-based) representations of complex systems from small-scale components. We emphasise, however, that compactness of the representation can only be achieved if heuristics are applied with insight into the structure of the system under investigation. We report on our experiences concerning compact representation, performance analysis and verification of performability properties

Neurodata Without Borders: Creating a Common Data Format for Neurophysiology

The Neurodata Without Borders (NWB) initiative promotes data standardization in neuroscience to increase research reproducibility and opportunities. In the first NWB pilot project, neurophysiologists and software developers produced a common data format for recordings and metadata of cellular electrophysiology and optical imaging experiments. The format specification, application programming interfaces, and sample datasets have been released

Advances in Model Representations

We review high-level specification formalisms for Markovian performability models, thereby emphasising the role of structuring concepts as realised par excellence by stochastic process algebras. Symbolic representations based on decision diagrams are presented, and it is shown that they quite ideally support compositional model construction and analysis