A linear time algorithm for the orbit problem over cyclic groups

The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same orbit with respect to a given finite permutation group (represented by their generators) acting on this set of configurations by permuting indices. It is known that the problem is in general as hard as the graph isomorphism problem, whose precise complexity (whether it is solvable in polynomial-time) is a long-standing open problem. In this paper, we consider the restriction of the orbit problem when the permutation group is cyclic (i.e. generated by a single permutation), an important restriction of the problem. It is known that this subproblem is solvable in polynomial-time. Our main result is a linear-time algorithm for this subproblem.Comment: Accepted in Acta Informatica in Nov 201

A computational group theoretic symmetry reduction package for the SPIN model checker

Symmetry reduced model checking is hindered by two problems: how to identify state space symmetry when systems are not fully symmetric, and how to determine equivalence of states during search. We present TopSpin, a fully automatic symmetry reduction package for the Spin model checker. TopSpin uses the Gap computational algebra system to effectively detect state space symmetry from the associated Promela specification, and to choose an efficient symmetry reduction strategy by classifying automorphism groups as a disjoint/wreath product of subgroups. We present encouraging experimental results for a variety of Promela examples

Advancing Dynamic Fault Tree Analysis

This paper presents a new state space generation approach for dynamic fault trees (DFTs) together with a technique to synthesise failures rates in DFTs. Our state space generation technique aggressively exploits the DFT structure --- detecting symmetries, spurious non-determinism, and don't cares. Benchmarks show a gain of more than two orders of magnitude in terms of state space generation and analysis time. Our approach supports DFTs with symbolic failure rates and is complemented by parameter synthesis. This enables determining the maximal tolerable failure rate of a system component while ensuring that the mean time of failure stays below a threshold

Effective Marking Equivalence Checking in Systems with Dynamic Process Creation

The starting point of this work is a framework allowing to model systems with dynamic process creation, equipped with a procedure to detect symmetric executions (ie., which differ only by the identities of processes). This allows to reduce the state space, potentially to an exponentially smaller size, and, because process identifiers are never reused, this also allows to reduce to finite size some infinite state spaces. However, in this approach, the procedure to detect symmetries does not allow for computationally efficient algorithms, mainly because each newly computed state has to be compared with every already reached state. In this paper, we propose a new approach to detect symmetries in this framework that will solve this problem, thus enabling for efficient algorithms. We formalise a canonical representation of states and identify a sufficient condition on the analysed model that guarantees that every symmetry can be detected. For the models that do not fall into this category, our approach is still correct but does not guarantee a maximal reduction of state space.Comment: In Proceedings Infinity 2012, arXiv:1302.310

A template-based approach for the generation of abstractable and reducible models of featured networks

We investigate the relationship between symmetry reduction and inductive reasoning when applied to model checking networks of featured components. Popular reduction techniques for combatting state space explosion in model checking, like abstraction and symmetry reduction, can only be applied effectively when the natural symmetry of a system is not destroyed during specification. We introduce a property which ensures this is preserved, open symmetry. We describe a template-based approach for the construction of open symmetric Promela specifications of featured systems. For certain systems (safely featured parameterised systems) our generated specifications are suitable for conversion to abstract specifications representing any size of network. This enables feature interaction analysis to be carried out, via model checking and induction, for systems of any number of featured components. In addition, we show how, for any balanced network of components, by using a graphical representation of the features and the process communication structure, a group of permutations of the underlying state space of the generated specification can be determined easily. Due to the open symmetry of our Promela specifications, this group of permutations can be used directly for symmetry reduced model checking. The main contributions of this paper are an automatic method for developing open symmetric specifications which can be used for generic feature interaction analysis, and the novel application of symmetry detection and reduction in the context of model checking featured networks. We apply our techniques to a well known example of a featured network – an email system

A GNN Based Approach to LTL Model Checking

Model Checking is widely applied in verifying complicated and especially concurrent systems. Despite of its popularity, model checking suffers from the state space explosion problem that restricts it from being applied to certain systems, or specifications. Many works have been proposed in the past to address the state space explosion problem, and they have achieved some success, but the inherent complexity still remains an obstacle for purely symbolic approaches. In this paper, we propose a Graph Neural Network (GNN) based approach for model checking, where the model is expressed using a B{\"u}chi automaton and the property to be verified is expressed using Linear Temporal Logic (LTL). We express the model as a GNN, and propose a novel node embedding framework that encodes the LTL property and characteristics of the model. We reduce the LTL model checking problem to a graph classification problem, where there are two classes, 1 (if the model satisfies the specification) and 0 (if the model does not satisfy the specification). The experimental results show that our framework is up to 17 times faster than state-of-the-art tools. Our approach is particularly useful when dealing with very large LTL formulae and small to moderate sized models