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Taylor T. Johnson

Taylor T. Johnson appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine LearningSystems and Controleess.SYDistributed, Parallel, and Cluster ComputingLogic in Computer ScienceArtificial IntelligenceComputer VisionFormal Languages and Automata Theorymath.OCMultiagent SystemsRoboticsSymbolic Computation

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Published work

10 published item(s)

preprint2026arXiv

k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics

While conventional (k=1) discrete-time barrier certificate conditions impose strict safety constraints by requiring the function to be non-increasing at every step, k-inductive barrier certificates relax this by allowing a temporary increase -- up to k-1 times, each within a threshold $ε$ -- while maintaining overall safety, and improving flexibility. This paper leverages neural networks and constructs k-inductive neural barrier certificates (k-NBCs) for (partially) unknown nonlinear systems. While neural networks offer scalability in the design process, they lack formal guarantees, requiring additional approaches such as counterexample-guided inductive synthesis (CEGIS) with satisfiability modulo theories (SMT) for verification. However, the CEGIS-SMT framework requires knowledge of system dynamics, which is unavailable in practical settings. To address this, we leverage the generalization of the Willems et al.'s fundamental lemma, using a single state trajectory, to construct a data-driven representation of (partially) unknown models for SMT verification without sacrificing accuracy. Additionally, CEGIS-SMT further removes the constraint of restricting barrier certificates to specific function classes, such as sum-of-squares, enabling greater flexibility in their design. We validate our approach on three nonlinear case studies with (partially) unknown dynamics.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Reward Shaping and Action Masking for Compositional Tasks using Behavior Trees and LLMs

Decomposing complex tasks into a sequence of simpler subtasks can improve learning efficiency for an autonomous agent. Reinforcement learning (RL) can be used to optimize agent policies to complete subtasks, but requires well-defined subtask rewards and benefits from action masking. Recent work uses large language models (LLMs) to automate reward shaping and action masking, however none of them fully address reactivity to subtask failure and modularity to varying objects for compositional tasks. To overcome these challenges, we develop masking reward behavior tree (MRBT), a symbolic structure used as a reactive and modular reward and action mask function. We design an MRBT template and derive logical specifications to construct and verify MRBTs for a sequence of object-interaction subtasks. Further, we develop an automated pipeline that uses an LLM to generate MRBTs robust to varying task objects, an SMT-solver to verify correctness of specifications, and a neurosymbolic RL loop to train agents on compositional tasks. Experiments demonstrate successful generation and refinement of five MRBTs, consistently improving training efficiency and task success rates over baselines and MRBTs without action masking. We further highlight three advantages of MRBTs: transferability, modularity, and verifiability.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Model Checking for Rectangular Hybrid Systems: A Quantified Encoding Approach

Satisfiability Modulo Theories (SMT) solvers have been successfully applied to solve many problems in formal verification such as bounded model checking (BMC) for many classes of systems from integrated circuits to cyber-physical systems. Typically, BMC is performed by checking satisfiability of a possibly long, but quantifier-free formula. However, BMC problems can naturally be encoded as quantified formulas over the number of BMC steps. In this approach, we then use decision procedures supporting quantifiers to check satisfiability of these quantified formulas. This approach has previously been applied to perform BMC using a Quantified Boolean Formula (QBF) encoding for purely discrete systems, and then discharges the QBF checks using QBF solvers. In this paper, we present a new quantified encoding of BMC for rectangular hybrid automata (RHA), which requires using more general logics due to the real (dense) time and real-valued state variables modeling continuous states. We have implemented a preliminary experimental prototype of the method using the HyST model transformation tool to generate the quantified BMC (QBMC) queries for the Z3 SMT solver. We describe experimental results on several timed and hybrid automata benchmarks, such as the Fischer and Lynch-Shavit mutual exclusion algorithms. We compare our approach to quantifier-free BMC approaches, such as those in the dReach tool that uses the dReal SMT solver, and the HyComp tool built on top of nuXmv that uses the MathSAT SMT solver. Based on our promising experimental results, QBMC may in the future be an effective and scalable analysis approach for RHA and other classes of hybrid automata as further improvements are made in quantifier handling in SMT solvers such as Z3.

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preprint2022arXiv

Reachability Analysis of a General Class of Neural Ordinary Differential Equations

Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis techniques for these systems. In this paper, we consider a general class of neural ODEs with varying architectures and layers, and introduce a novel reachability framework that allows for the formal analysis of their behavior. The methods developed for the reachability analysis of neural ODEs are implemented in a new tool called NNVODE. Specifically, our work extends an existing neural network verification tool to support neural ODEs. We demonstrate the capabilities and efficacy of our methods through the analysis of a set of benchmarks that include neural ODEs used for classification, and in control and dynamical systems, including an evaluation of the efficacy and capabilities of our approach with respect to existing software tools within the continuous-time systems reachability literature, when it is possible to do so.

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preprint2020arXiv

NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems

This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection of reachability algorithms that make use of a variety of set representations, such as polyhedra, star sets, zonotopes, and abstract-domain representations. NNV supports both exact (sound and complete) and over-approximate (sound) reachability algorithms for verifying safety and robustness properties of feed-forward neural networks (FFNNs) with various activation functions. For learning-enabled CPS, such as closed-loop control systems incorporating neural networks, NNV provides exact and over-approximate reachability analysis schemes for linear plant models and FFNN controllers with piecewise-linear activation functions, such as ReLUs. For similar neural network control systems (NNCS) that instead have nonlinear plant models, NNV supports over-approximate analysis by combining the star set analysis used for FFNN controllers with zonotope-based analysis for nonlinear plant dynamics building on CORA. We evaluate NNV using two real-world case studies: the first is safety verification of ACAS Xu networks and the second deals with the safety verification of a deep learning-based adaptive cruise control system.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach

The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped with neural network components at various stages of sensing and control. This paper addresses the reachable set estimation and safety verification problems for dynamical systems embedded with neural network components serving as feedback controllers. The closed-loop system can be abstracted in the form of a continuous-time sampled-data system under the control of a neural network controller. First, a novel reachable set computation method in adaptation to simulations generated out of neural networks is developed. The reachability analysis of a class of feedforward neural networks called multilayer perceptrons (MLP) with general activation functions is performed in the framework of interval arithmetic. Then, in combination with reachability methods developed for various dynamical system classes modeled by ordinary differential equations, a recursive algorithm is developed for over-approximating the reachable set of the closed-loop system. The safety verification for neural network control systems can be performed by examining the emptiness of the intersection between the over-approximation of reachable sets and unsafe sets. The effectiveness of the proposed approach has been validated with evaluations on a robotic arm model and an adaptive cruise control system.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Verification of Deep Convolutional Neural Networks Using ImageStars

Convolutional Neural Networks (CNN) have redefined the state-of-the-art in many real-world applications, such as facial recognition, image classification, human pose estimation, and semantic segmentation. Despite their success, CNNs are vulnerable to adversarial attacks, where slight changes to their inputs may lead to sharp changes in their output in even well-trained networks. Set-based analysis methods can detect or prove the absence of bounded adversarial attacks, which can then be used to evaluate the effectiveness of neural network training methodology. Unfortunately, existing verification approaches have limited scalability in terms of the size of networks that can be analyzed. In this paper, we describe a set-based framework that successfully deals with real-world CNNs, such as VGG16 and VGG19, that have high accuracy on ImageNet. Our approach is based on a new set representation called the ImageStar, which enables efficient exact and over-approximative analysis of CNNs. ImageStars perform efficient set-based analysis by combining operations on concrete images with linear programming (LP). Our approach is implemented in a tool called NNV, and can verify the robustness of VGG networks with respect to a small set of input states, derived from adversarial attacks, such as the DeepFool attack. The experimental results show that our approach is less conservative and faster than existing zonotope methods, such as those used in DeepZ, and the polytope method used in DeepPoly.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Order-Reduction Abstractions for Safety Verification of High-Dimensional Linear Systems

Order-reduction is a standard automated approximation technique for computer-aided design, analysis, and simulation of many classes of systems, from circuits to buildings. For a given system, these methods produce a reduced-order system where the dimension of the state-space is smaller, while attempting to preserve behaviors similar to those of the full-order original system. To be used as a sound abstraction for formal verification, a measure of the similarity of behavior must be formalized and computed, which we develop in a computational way for a class of linear systems and periodically-switched systems as the main contributions of this paper. We have implemented the order-reduction as a sound abstraction process through a source-to-source model transformation in the HyST tool and use SpaceEx to compute sets of reachable states to verify properties of the full-order system through analysis of the reduced-order system. Our experimental results suggest systems with on the order of a thousand state variables can be reduced to systems with tens of state variables such that the order-reduction overapproximation error is small enough to prove or disprove safety properties of interest using current reachability analysis tools. Our results illustrate this approach is effective to alleviate the state-space explosion problem for verification of high-dimensional linear systems.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Virtual Prototyping and Distributed Control for Solar Array with Distributed Multilevel Inverter

In this paper, we present the virtual prototyping of a solar array with a grid-tie implemented as a distributed inverter and controlled using distributed algorithms. Due to the distributed control and inherent redundancy in the array composed of many panels and inverter modules, the virtual prototype exhibits fault-tolerance capabilities. The distributed identifier algorithm allows the system to keep track of the number of operating panels to appropriately regulate the DC voltage output of the panels using buck-boost converters, and determine appropriate switching times for H-bridges in the grid-tie. We evaluate the distributed inverter, its control strategy, and fault-tolerance through simulation in Simulink/Stateflow. Our virtual prototyping framework allows for generating arrays and grid-ties consisting of many panels, and we evaluate arrays of five to dozens of panels. Our analysis suggests the achievable total harmonic distortion (THD) of the system may allow for operating the array in spite of failures of the power electronics, control software, and other subcomponents.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Safe and Stabilizing Distributed Multi-Path Cellular Flows

We study the problem of distributed traffic control in the partitioned plane, where the movement of all entities (robots, vehicles, etc.) within each partition (cell) is coupled. Establishing liveness in such systems is challenging, but such analysis will be necessary to apply such distributed traffic control algorithms in applications like coordinating robot swarms and the intelligent highway system. We present a formal model of a distributed traffic control protocol that guarantees minimum separation between entities, even as some cells fail. Once new failures cease occurring, in the case of a single target, the protocol is guaranteed to self-stabilize and the entities with feasible paths to the target cell make progress towards it. For multiple targets, failures may cause deadlocks in the system, so we identify a class of non-deadlocking failures where all entities are able to make progress to their respective targets. The algorithm relies on two general principles: temporary blocking for maintenance of safety and local geographical routing for guaranteeing progress. Our assertional proofs may serve as a template for the analysis of other distributed traffic control protocols. We present simulation results that provide estimates of throughput as a function of entity velocity, safety separation, single-target path complexity, failure-recovery rates, and multi-target path complexity.

0 citations0 reviewsNo code linkedOpen access