Certifying Confluence of Almost Orthogonal CTRSs via Exact Tree Automata Completion

Suzuki et al. showed that properly oriented, right-stable, orthogonal, and oriented conditional term rewrite systems with extra variables in right-hand sides are confluent. We present our Isabelle/HOL formalization of this result, including two generalizations. On the one hand, we relax proper orientedness and orthogonality to extended proper orientedness and almost orthogonality modulo infeasibility, as suggested by Suzuki et al. On the other hand, we further loosen the requirements of the latter, enabling more powerful methods for proving infeasibility of conditional critical pairs. Furthermore, we formalized a construction by Jacquemard that employs exact tree automata completion for non-reachability analysis and apply it to certify infeasibility of conditional critical pairs. Combining these two results and extending the conditional confluence checker ConCon accordingly, we are able to automatically prove and certify confluence of an important class of conditional term rewrite systems

SOTER: A Runtime Assurance Framework for Programming Safe Robotics Systems

The recent drive towards achieving greater autonomy and intelligence in robotics has led to high levels of complexity. Autonomous robots increasingly depend on third party off-the-shelf components and complex machine-learning techniques. This trend makes it challenging to provide strong design-time certification of correct operation. To address these challenges, we present SOTER, a robotics programming framework with two key components: (1) a programming language for implementing and testing high-level reactive robotics software and (2) an integrated runtime assurance (RTA) system that helps enable the use of uncertified components, while still providing safety guarantees. SOTER provides language primitives to declaratively construct a RTA module consisting of an advanced, high-performance controller (uncertified), a safe, lower-performance controller (certified), and the desired safety specification. The framework provides a formal guarantee that a well-formed RTA module always satisfies the safety specification, without completely sacrificing performance by using higher performance uncertified components whenever safe. SOTER allows the complex robotics software stack to be constructed as a composition of RTA modules, where each uncertified component is protected using a RTA module. To demonstrate the efficacy of our framework, we consider a real-world case-study of building a safe drone surveillance system. Our experiments both in simulation and on actual drones show that the SOTER-enabled RTA ensures the safety of the system, including when untrusted third-party components have bugs or deviate from the desired behavior

Formal Verification of Neural Network Controlled Autonomous Systems

In this paper, we consider the problem of formally verifying the safety of an autonomous robot equipped with a Neural Network (NN) controller that processes LiDAR images to produce control actions. Given a workspace that is characterized by a set of polytopic obstacles, our objective is to compute the set of safe initial conditions such that a robot trajectory starting from these initial conditions is guaranteed to avoid the obstacles. Our approach is to construct a finite state abstraction of the system and use standard reachability analysis over the finite state abstraction to compute the set of the safe initial states. The first technical problem in computing the finite state abstraction is to mathematically model the imaging function that maps the robot position to the LiDAR image. To that end, we introduce the notion of imaging-adapted sets as partitions of the workspace in which the imaging function is guaranteed to be affine. We develop a polynomial-time algorithm to partition the workspace into imaging-adapted sets along with computing the corresponding affine imaging functions. Given this workspace partitioning, a discrete-time linear dynamics of the robot, and a pre-trained NN controller with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge is to analyze the behavior of the neural network. To that end, we utilize a Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible segments of different ReLUs. SMC solvers then use a Boolean satisfiability solver and a convex programming solver and decompose the problem into smaller subproblems. To accelerate this process, we develop a pre-processing algorithm that could rapidly prune the space feasible ReLU segments. Finally, we demonstrate the efficiency of the proposed algorithms using numerical simulations with increasing complexity of the neural network controller

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

A Review of Formal Methods applied to Machine Learning

We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability of mature tools, their use is well established in the industry, and in particular to check safety-critical applications as they undergo a stringent certification process. As machine learning is becoming more popular, machine-learned components are now considered for inclusion in critical systems. This raises the question of their safety and their verification. Yet, established formal methods are limited to classic, i.e. non machine-learned software. Applying formal methods to verify systems that include machine learning has only been considered recently and poses novel challenges in soundness, precision, and scalability. We first recall established formal methods and their current use in an exemplar safety-critical field, avionic software, with a focus on abstract interpretation based techniques as they provide a high level of scalability. This provides a golden standard and sets high expectations for machine learning verification. We then provide a comprehensive and detailed review of the formal methods developed so far for machine learning, highlighting their strengths and limitations. The large majority of them verify trained neural networks and employ either SMT, optimization, or abstract interpretation techniques. We also discuss methods for support vector machines and decision tree ensembles, as well as methods targeting training and data preparation, which are critical but often neglected aspects of machine learning. Finally, we offer perspectives for future research directions towards the formal verification of machine learning systems

Modular and Safe Event-Driven Programming

Asynchronous event-driven systems are ubiquitous across domains such as device drivers, distributed systems, and robotics. These systems are notoriously hard to get right as the programmer needs to reason about numerous control paths resulting from the complex interleaving of events (or messages) and failures. Unsurprisingly, it is easy to introduce subtle errors while attempting to fill in gaps between high-level system specifications and their concrete implementations.This dissertation proposes new methods for programming safe event-driven asynchronous systems.In the first part of the thesis, we present ModP, a modular programming framework for compositional programming and testing of event-driven asynchronous systems.The ModP module system supports a novel theory of compositional refinement for assume-guarantee reasoning of dynamic event-driven asynchronous systems. We build a complex distributed systems software stack using ModP.Our results demonstrate that compositional reasoning can help scale model-checking (both explicit and symbolic) to large distributed systems.ModP is transforming the way asynchronous software is built at Microsoft and Amazon Web Services (AWS). Microsoft uses ModP for implementing safe device drivers and other software in the Windows kernel.AWS uses ModP for compositional model checking of complex distributed systems. While ModP simplifies analysis of such systems, the state space of industrial-scale systems remains extremely large.In the second part of this thesis, we present scalable verification and systematic testing approaches to further mitigate this state-space explosion problem.First, we introduce the concept of a delaying explorer to perform prioritized exploration of the behaviors of an asynchronous reactive program. A delaying explorer stratifies the search space using a custom strategy (tailored towards finding bugs faster), and a delay operation that allows deviation from that strategy. We show that prioritized search with a delaying explorer performs significantly better than existing approaches for finding bugs in asynchronous programs.Next, we consider the challenge of verifying time-synchronized systems; these are almost-synchronous systems as they are neither completely asynchronous nor synchronous.We introduce approximate synchrony, a sound and tunable abstraction for verification of almost-synchronous systems. We show how approximate synchrony can be used for verification of both time-synchronization protocols and applications running on top of them.Moreover, we show how approximate synchrony also provides a useful strategy to guide state-space exploration during model-checking.Using approximate synchrony and implementing it as a delaying explorer, we were able to verify the correctness of the IEEE 1588 distributed time-synchronization protocol and, in the process, uncovered a bug in the protocol that was well appreciated by the standards committee.In the final part of this thesis, we consider the challenge of programming a special class of event-driven asynchronous systems -- safe autonomous robotics systems.Our approach towards achieving assured autonomy for robotics systems consists of two parts: (1) a high-level programming language for implementing and validating the reactive robotics software stack; and (2) an integrated runtime assurance system to ensure that the assumptions used during design-time validation of the high-level software hold at runtime.Combining high-level programming language and model-checking with runtime assurance helps us bridge the gap between design-time software validation that makes assumptions about the untrusted components (e.g., low-level controllers), and the physical world, and the actual execution of the software on a real robotic platform in the physical world. We implemented our approach as DRONA, a programming framework for building safe robotics systems.We used DRONA for building a distributed mobile robotics system and deployed it on real drone platforms. Our results demonstrate that DRONA (with the runtime-assurance capabilities) enables programmers to build an autonomous robotics software stack with formal safety guarantees.To summarize, this thesis contributes new theory and tools to the areas of programming languages, verification, systematic testing, and runtime assurance for programming safe asynchronous event-driven across the domains of fault-tolerant distributed systems and safe autonomous robotics systems