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

Isomorphism Checking for Symmetry Reduction

In this paper, we show how isomorphism checking can be used as an effective technique for symmetry reduction. Reduced state spaces are equivalent to the original ones under a strong notion of bisimilarity which preserves the multiplicity of outgoing transitions, and therefore also preserves stochastic temporal logics. We have implemented this in a setting where states are arbitrary graphs. Since no efficiently computable canonical representation is known for arbitrary graphs modulo isomorphism, we define an isomorphism-predicting hash function on the basis of an existing partition refinement algorithm. As an example, we report a factorial state space reduction on a model of an ad-hoc network connectivity protocol

Symmetry Reduction Enables Model Checking of More Complex Emergent Behaviours of Swarm Navigation Algorithms

The emergent global behaviours of robotic swarms are important to achieve their navigation task goals. These emergent behaviours can be verified to assess their correctness, through techniques like model checking. Model checking exhaustively explores all possible behaviours, based on a discrete model of the system, such as a swarm in a grid. A common problem in model checking is the state-space explosion that arises when the states of the model are numerous. We propose a novel implementation of symmetry reduction, in the form of encoding navigation algorithms relatively with respect to a reference, based on the symmetrical properties of swarms in grids. We applied the relative encoding to a swarm navigation algorithm, Alpha, modelled for the NuSMV model checker. A comparison of the state-space and verification results with an absolute (or global) and a relative encoding of the Alpha algorithm highlights the advantages of our approach, allowing model checking larger grid sizes and number of robots, and consequently, verifying more complex emergent behaviours. For example, a property was verified for a grid with 3 robots and a maximum allowed size of 8x8 cells in a global encoding, whereas this size was increased to 16x16 using a relative encoding. Also, the time to verify a property for a swarm of 3 robots in a 6x6 grid was reduced from almost 10 hours to only 7 minutes. Our approach is transferable to other swarm navigation algorithms.Comment: Accepted for presentation in Towards Autonomous Robotic Systems (TAROS) 2015, Liverpool, U

Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking

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

State space c-reductions for concurrent systems in rewriting logic

We present c-reductions, a state space reduction technique. The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer function, which maps each state into a (non necessarily unique) canonical representative of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: exibility and simplicity in the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization of the reduction infrastructure via Maude's meta-programming features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools

Symmetry reduction and heuristic search for error detection in model checking

The state explosion problem is the main limitation of model checking. Symmetries in the system being verified can be exploited in order to avoid this problem by defining an equivalence (symmetry) relation on the states of the system, which induces a semantically equivalent quotient system of smaller size. On the other hand, heuristic search algorithms can be applied to improve the bug finding capabilities of model checking. Such algorithms use heuristic functions to guide the exploration. Bestfirst is used for accelerating the search, while A* guarantees optimal error trails if combined with admissible estimates. We analyze some aspects of combining both approaches, concentrating on the problem of finding the optimal path to the equivalence class of a given error state. Experimental results evaluate our approach

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization