A compositional algorithm for parallel model checking of polygonal hybrid systems

The reachability problem as well as the computation of the phase portrait for the class of planar hybrid systems defined by constant differential inclusions (SPDI), has been shown to be decidable. The existing reachability algorithm is based on the exploitation of topological properties of the plane which are used to accelerate certain kind of cycles. The complexity of the algorithm makes the analysis of large systems generally unfeasible. In this paper we present a compositional parallel algorithm for reachability analysis of SPDIs. The parallelization is based on the qualitative information obtained from the phase portrait of an SPDI, in particular the controllability kernel.The United Nations Univ., Int. Inst. for Softw. Technol., Macau,Tunisian Ministry of Higher Education,University of New South Wales, UKpeer-reviewe

Improving polygonal hybrid systems reachability analysis through the use of the phase portrait

Polygonal hybrid systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant dierential inclusions. The computation of certain objects of the phase portrait of an SPDI, namely the viability, controllability, invariance kernels and semi-separatrix curves have been shown to be eciently decidable. On the other hand, although the reachability problem for SPDIs is known to be decidable, its complexity makes it unfeasible on large systems. We summarise our recent results on the use of the SPDI phase portraits for improving reachability analysis by (i) state-space reduction and (ii) decomposition techniques of the state space, enabling compositional parallelisation of the analysis. Both techniques contribute to increasing the feasability of reachability analysis on large SPDI systems.peer-reviewe

ParaPlan: A Tool for Parallel Reachability Analysis of Planar Polygonal Differential Inclusion Systems

Andrei Sandler, and Olga Tveretina, ‘ParaPlan: A Tool for Parallel Reachability Analysis of Planar Polygonal Differential Inclusion Systems’, in Patricia Bouyer, Andrea Orlandini and Pierluigi San Pietro, eds. Proceedings Eight International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2017), Rome, Italy, 20-22 September 2017, Electronic Proceedings in Theoretical Computer Science, Vol. 256: 283-296, September 2017. © 2017 The Author(s). This work is licensed under the Creative Commons Attribution License CC BY 4.0 https://creativecommons.org/licenses/by/4.0/We present the ParaPlan tool which provides the reachability analysis of planar hybrid systems defined by differential inclusions (SPDI). It uses the parallelized and optimized version of the algorithm underlying the SPeeDI tool. The performance comparison demonstrates the speed-up of up to 83 times with respect to the sequential implementation on various benchmarks. Some of the benchmarks we used are randomly generated with the novel approach based on the partitioning of the plane with Voronoi diagrams

Reachability analysis of linear hybrid systems via block decomposition

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.Comment: Accepted at EMSOFT 202

Algorithmic Verification of Continuous and Hybrid Systems

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Model checking learning agent systems using Promela with embedded C code and abstraction

As autonomous systems become more prevalent, methods for their verification will become more widely used. Model checking is a formal verification technique that can help ensure the safety of autonomous systems, but in most cases it cannot be applied by novices, or in its straight \off-the-shelf" form. In order to be more widely applicable it is crucial that more sophisticated techniques are used, and are presented in a way that is reproducible by engineers and verifiers alike. In this paper we demonstrate in detail two techniques that are used to increase the power of model checking using the model checker SPIN. The first of these is the use of embedded C code within Promela specifications, in order to accurately re ect robot movement. The second is to use abstraction together with a simulation relation to allow us to verify multiple environments simultaneously. We apply these techniques to a fairly simple system in which a robot moves about a fixed circular environment and learns to avoid obstacles. The learning algorithm is inspired by the way that insects learn to avoid obstacles in response to pain signals received from their antennae. Crucially, we prove that our abstraction is sound for our example system { a step that is often omitted but is vital if formal verification is to be widely accepted as a useful and meaningful approach

Sampling-Based Approximation Algorithms for Reachability Analysis with Provable Guarantees

The successful deployment of many autonomous systems in part hinges on providing rigorous guarantees on their performance and safety through a formal verification method, such as reachability analysis. In this work, we present a simple-to-implement, sampling-based algorithm for reachability analysis that is provably optimal up to any desired approximation accuracy. Our method achieves computational efficiency by judiciously sampling a finite subset of the state space and generating an approximate reachable set by conducting reachability analysis on this finite set of states. We prove that the reachable set generated by our algorithm approximates the ground-truth reachable set for any user-specified approximation accuracy. As a corollary to our main method, we introduce an asymptoticallyoptimal, anytime algorithm for reachability analysis. We present simulation results that reaffirm the theoretical properties of our algorithm and demonstrate its effectiveness in real-world inspired scenariosNational Science Foundation (U.S.

Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges

In recent years, formal methods have been extensively used in the design of autonomous systems. By employing mathematically rigorous techniques, formal methods can provide fully automated reasoning processes with provable safety guarantees for complex dynamic systems with intricate interactions between continuous dynamics and discrete logics. This paper provides a comprehensive review of formal controller synthesis techniques for safety-critical autonomous systems. Specifically, we categorize the formal control synthesis problem based on diverse system models, encompassing deterministic, non-deterministic, and stochastic, and various formal safety-critical specifications involving logic, real-time, and real-valued domains. The review covers fundamental formal control synthesis techniques, including abstraction-based approaches and abstraction-free methods. We explore the integration of data-driven synthesis approaches in formal control synthesis. Furthermore, we review formal techniques tailored for multi-agent systems (MAS), with a specific focus on various approaches to address the scalability challenges in large-scale systems. Finally, we discuss some recent trends and highlight research challenges in this area