Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

Multi-core Symbolic Bisimulation Minimisation

Bisimulation minimisation alleviates the exponential growth of transition systems in model checking by computing the smallest system that has the same behavior as the original system according to some notion of equivalence. One popular strategy to compute a bisimulation minimisation is signature-based partition refinement. This can be performed symbolically using binary decision diagrams to allow models with larger state spaces to be minimised. This paper studies strong and branching symbolic bisimulation for labeled transition systems, continuous-time markov chains, and interactive markov chains. We introduce the notion of partition refinement with partial signatures. We extend the parallel BDD library Sylvan to parallelize the signature refinement algorithm, and develop a new parallel BDD algorithm to refine a partition, which conserves previous block numbers and uses a parallel data structure to store block assignments. We also present a specialized BDD algorithm for the computation of inert transitions. The experimental evaluation, based on benchmarks from the literature, demonstrates a speedup of up to 95x sequentially. In addition, we find parallel speedups of up to 17x due to parallelisation with 48 cores. Finally, we present the implementation of these algorithms as a versatile tool that can be customized for bisimulation minimisation in various contexts

Analysis of Timed and Long-Run Objectives for Markov Automata

Markov automata (MAs) extend labelled transition systems with random delays and probabilistic branching. Action-labelled transitions are instantaneous and yield a distribution over states, whereas timed transitions impose a random delay governed by an exponential distribution. MAs are thus a nondeterministic variation of continuous-time Markov chains. MAs are compositional and are used to provide a semantics for engineering frameworks such as (dynamic) fault trees, (generalised) stochastic Petri nets, and the Architecture Analysis & Design Language (AADL). This paper considers the quantitative analysis of MAs. We consider three objectives: expected time, long-run average, and timed (interval) reachability. Expected time objectives focus on determining the minimal (or maximal) expected time to reach a set of states. Long-run objectives determine the fraction of time to be in a set of states when considering an infinite time horizon. Timed reachability objectives are about computing the probability to reach a set of states within a given time interval. This paper presents the foundations and details of the algorithms and their correctness proofs. We report on several case studies conducted using a prototypical tool implementation of the algorithms, driven by the MAPA modelling language for efficiently generating MAs.Comment: arXiv admin note: substantial text overlap with arXiv:1305.705

Algebra, coalgebra, and minimization in polynomial differential equations

We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow this set with a transition system structure based on the concept of Lie-derivative, thus inducing a notion of L-bisimulation. We prove that two states (variables) are L-bisimilar if and only if they correspond to the same solution in the ode's system. We then characterize L-bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest L-bisimulation containing all valid identities that are instances of a user-specified template. A specific largest L-bisimulation can be used to build a reduced system of ode's, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations. A computationally less demanding approximate reduction and linearization technique is also proposed.Comment: 27 pages, extended and revised version of FOSSACS 2017 pape

Model reduction techniques for probabilistic verification of Markov chains

Probabilistic model checking is a quantitative verification technique that aims to verify the correctness of probabilistic systems. Nevertheless, it suffers from the so-called state space explosion problem. In this thesis, we propose two new model reduction techniques to improve the efficiency and scalability of verifying probabilistic systems, focusing on discrete-time Markov chains (DTMCs). In particular, our emphasis is on verifying quantitative properties that bound the time or cost of an execution. We also focus on methods that avoid the explicit construction of the full state space. We first present a finite-horizon variant of probabilistic bisimulation for DTMCs, which preserves a bounded fragment of PCTL. We also propose another model reduction technique that reduces what we call linear inductive DTMCs, a class of models whose state space grows linearly with respect to a parameter. All the techniques presented in this thesis were developed in the PRISM model checker. We demonstrate the effectiveness of our work by applying it to a selection of existing benchmark probabilistic models, showing that both of our two new approaches can provide significant reductions in model size and in some cases outperform the existing implementations of probabilistic verification in PRISM