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NASA NTRS2022

Formal Methods for Trusted Space Autonomy, Boon or Bane?

Trusted Space Autonomy is challenging in that space systems are complex artifacts deployed in a high stakes environment with complicated operational settings. Thus far these challenges have been met using the full arsenal of tools: formal methods, informal methods, testing, runtime techniques, and operations processes. Using examples from previous deployments of autonomy to the Remote Agent on DS-1, Autonomous Sciencecraft on EO-1, WATCH on MER, IPEX, AEGIS on MER, MSL, and M2020, and the M2020 Onboard planner, we discuss how each of these approaches have been used to enable successful deployment of autonomy. We next focus on relatively limited use of formal methods (both prior to deployment and runtime methods). From the needs perspective, formal methods represent the best chance for reliable autonomy as testing, informal methods, and operations accommodations do not scale well with increasing complexity of the autonomous system. However from the practice perspective, formal methods have been limited in their application due to difficulty in eliciting formal specifications and challenges in representing complex constraints such as metric time and resources. We discuss some of these challenges as well as the opportunity to extend formal and informal methods into runtime validation systems.

Chien, Steve↗

NASA NTRSDate not supplied

Applying Formal Methods to Safety-Critical Systems

How do you know a proof is correct? Traditionally, mathematical proofs are socially verified – at least one human, following a set of implicit rules of natural language and logic, determines if the proof is believable. If the proof becomes overly tedious and/or is essential to some safety- or mission-critical application, it becomes necessary to determine the soundness to a higher standard. 'Formal methods' refer to mathematically rigorous techniques and tools that enable specification, design, and verification of hardware and software systems. The specification used in formal methods are statements in a mathematical logic while the formal verifications are deductions in that logic. Formal methods can be difficult or time/resource intensive, but offer a higher level of assurance than standard verification through testing or handwritten proofs. This talk will introduce formal methods, motivated by applications of interest to NASA, including uncrewed aircraft operations in the national airspace, urban air environments, and wildfire areas. The audience will be given a crash course in mechanically verified proofs in the Prototype Verification System (PVS), an interactive theorem prover.

Formal Methods↗

DOE OSTI2022

Designing Secure and Resilient Cyber-Physical Systems Using Formal Models

This work-in-progress paper proposes a design methodology that addresses the complexity and heterogeneity of cyber-physical systems (CPS) while simultaneously proving resilient control logic and security properties. The design methodology involves a formal methods-based approach by translating the complex control logic and security properties of a water flow CPS into timed automata. Timed automata are a formal model that describes system behaviors and properties using mathematics-based logic languages with precision. Due to the semantics that are used in developing the formal models, verification techniques, such as theorem proving and model checking, are used to mathematically prove the specifications and security properties of the CPS. This work-in-progress paper aims to highlight the need for formalizing plant models by creating a timed automata of the physical portions of the water flow CPS. Extending the time automata with control logic, network security, and privacy control processes is investigated. The final model will be formally verified to prove the design specifications of the water flow CPS to ensure efficacy and security.

42 ENGINEERING↗

NASA NTRS1974

The generation of gravitational waves. 1. Weak-field sources: A plug-in-and-grind formalism

A plug-in-and-grind formalism is derived for calculating the gravitational waves emitted by any system with weak internal gravitational fields. If the internal fields have negligible influence on the system's motions, then the formalism reduces to standard linearized theory. Whether or not gravity affects the motions, if the motions are slow and internal stresses are weak, then the new formalism reduces to the standard quadrupole-moment formalism. In the general case the new formalism expresses the radiation in terms of a retarded Green's function for slightly curved spacetime, and then breaks the Green's-function integral into five easily understood pieces: direct radiation, produced directly by the motions of the sources; whump radiation, produced by the the gravitational stresses of the source; transition radiation, produced by a time-changing time delay (Shapiro effect) in the propagation of the nonradiative, 1/r field of the source; focussing radiation produced when one portion of the source focusses, in a time-dependent way, the nonradiative field of another portion of the source, and tail radiation, produced by backscatter of the nonradiative field in regions of focussing.

Thorne, K. S.↗

NASA NTRS1993

Formalizing structured file services for the data storage and retrieval subsystem of the data management system for Spacestation Freedom

A brief example of the use of formal methods techniques in the specification of a software system is presented. The report is part of a larger effort targeted at defining a formal methods pilot project for NASA. One possible application domain that may be used to demonstrate the effective use of formal methods techniques within the NASA environment is presented. It is not intended to provide a tutorial on either formal methods techniques or the application being addressed. It should, however, provide an indication that the application being considered is suitable for a formal methods by showing how such a task may be started. The particular system being addressed is the Structured File Services (SFS), which is a part of the Data Storage and Retrieval Subsystem (DSAR), which in turn is part of the Data Management System (DMS) onboard Spacestation Freedom. This is a software system that is currently under development for NASA. An informal mathematical development is presented. Section 3 contains the same development using Penelope (23), an Ada specification and verification system. The complete text of the English version Software Requirements Specification (SRS) is reproduced in Appendix A.

Jamsek, Damir A.↗

NASA NTRS1993

Applying formal methods and object-oriented analysis to existing flight software

Correctness is paramount for safety-critical software control systems. Critical software failures in medical radiation treatment, communications, and defense are familiar to the public. The significant quantity of software malfunctions regularly reported to the software engineering community, the laws concerning liability, and a recent NRC Aeronautics and Space Engineering Board report additionally motivate the use of error-reducing and defect detection software development techniques. The benefits of formal methods in requirements driven software development ('forward engineering') is well documented. One advantage of rigorously engineering software is that formal notations are precise, verifiable, and facilitate automated processing. This paper describes the application of formal methods to reverse engineering, where formal specifications are developed for a portion of the shuttle on-orbit digital autopilot (DAP). Three objectives of the project were to: demonstrate the use of formal methods on a shuttle application, facilitate the incorporation and validation of new requirements for the system, and verify the safety-critical properties to be exhibited by the software.

Cheng, Betty H. C.↗

NASA NTRS1994

A spectral formalism for computing three-dimensional deformations due to surface loads. 1: Theory

We outline a complete spectral formalism for computing high spatial resolution three-dimensional deformations arising from the surface mass loading of a spherically symmetric planet. The main advantages of the formalism are that all surface mass loads are always described using a consistent mathematical representation and that calculations of deformation fields for various spatial resolutions can be performed by simpley altering the spherical harmonic degree truncation level of the procedure. The latter may be important when incorporating improved observational constraints on a particular surface mass load, when considering potential errors in the computed field associated with mass loading having a spatial scale unresolved by the observational constraints, or when treating a number of global surface mass loads constrained with different spatial resolutions. The advantages do not extend to traditional 'Green's function' approaches which involve surface element discretizations of the global mass loads. Another advantage of the spectral formalism, over the Green's function approach, is that a posteriori analyses of the computed deformation fields are easily performed. In developing the spectral formalism, we consider specific cases where the Earth's mantle is assumed to respond as an elastic, slightly anelastic, or linear viscoelastic medium. In the case of an elastic or slightly anelastic mantle rheology the spectral response equations incorporate frequency dependent Love numbers. The formalism can therefore be used, for example, to compute the potentially resonant deformational response associated with the free core nutation and Chandler wobble eigenfunctions. For completeness, the spectral response equations include both body forces, as arise from the gravitational attraction of the Sun and the Moon, and surface mass loads. In either case, and for both elastic and anelastic mantle rheologies, we outline a pseudo-spectral technique for computing the ocean adjustment associated with the total gravitational perturbation induced by the external forcing. Three-dimensional deformations computed using the usual Love number approach are generally referenced to an origin at the center of mass of the undeformed planet. We derive a spectral technique for transforming the results to an origin located at the center of mass of the deformed planet.

Mitrovica, J. X.↗

NASA NTRS1995

Formal methods demonstration project for space applications

The Space Shuttle program is cooperating in a pilot project to apply formal methods to live requirements analysis activities. As one of the larger ongoing shuttle Change Requests (CR's), the Global Positioning System (GPS) CR involves a significant upgrade to the Shuttle's navigation capability. Shuttles are to be outfitted with GPS receivers and the primary avionics software will be enhanced to accept GPS-provided positions and integrate them into navigation calculations. Prior to implementing the CR, requirements analysts at Loral Space Information Systems, the Shuttle software contractor, must scrutinize the CR to identify and resolve any requirements issues. We describe an ongoing task of the Formal Methods Demonstration Project for Space Applications whose goal is to find an effective way to use formal methods in the GPS CR requirements analysis phase. This phase is currently under way and a small team from NASA Langley, ViGYAN Inc. and Loral is now engaged in this task. Background on the GPS CR is provided and an overview of the hardware/software architecture is presented. We outline the approach being taken to formalize the requirements, only a subset of which is being attempted. The approach features the use of the PVS specification language to model 'principal functions', which are major units of Shuttle software. Conventional state machine techniques form the basis of our approach. Given this background, we present interim results based on a snapshot of work in progress. Samples of requirements specifications rendered in PVS are offered to illustration. We walk through a specification sketch for the principal function known as GPS Receiver State processing. Results to date are summarized and feedback from Loral requirements analysts is highlighted. Preliminary data is shown comparing issues detected by the formal methods team versus those detected using existing requirements analysis methods. We conclude by discussing our plan to complete the remaining activities of this task.

Divito, Ben L.↗

NASA NTRS1996

Applications of Formal Methods to Specification and Safety of Avionics Software

This report treats several topics in applications of formal methods to avionics software development. Most of these topics concern decision tables, an orderly, easy-to-understand format for formally specifying complex choices among alternative courses of action. The topics relating to decision tables include: generalizations fo decision tables that are more concise and support the use of decision tables in a refinement-based formal software development process; a formalism for systems of decision tables with behaviors; an exposition of Parnas tables for users of decision tables; and test coverage criteria and decision tables. We outline features of a revised version of ORA's decision table tool, Tablewise, which will support many of the new ideas described in this report. We also survey formal safety analysis of specifications and software.

Hoover, D. N.↗

NASA NTRS1997

Formal Methods of V&V of Partial Specifications: An Experience Report

This paper describes our work exploring the suitability of formal specification methods for independent verification and validation (IV&V) of software specifications for large, safety critical systems. An IV&V contractor often has to perform rapid analysis on incomplete specifications, with no control over how those specifications are represented. Lightweight formal methods show significant promise in this context, as they offer a way of uncovering major errors, without the burden of full proofs of correctness. We describe an experiment in the application of the method SCR. to testing for consistency properties of a partial model of requirements for Fault Detection Isolation and Recovery on the space station. We conclude that the insights gained from formalizing a specification is valuable, and it is the process of formalization, rather than the end product that is important. It was only necessary to build enough of the formal model to test the properties in which we were interested. Maintenance of fidelity between multiple representations of the same requirements (as they evolve) is still a problem, and deserves further study.

Easterbrook, Steve↗

NASA NTRS2004

Properties of a Formal Method for Prediction of Emergent Behaviors in Swarm-based Systems

Autonomous intelligent swarms of satellites are being proposed for NASA missions that have complex behaviors and interactions. The emergent properties of swarms make these missions powerful, but at the same time more difficult to design and assure that proper behaviors will emerge. This paper gives the results of research into formal methods techniques for verification and validation of NASA swarm-based missions. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft. The NASA ANTS mission was used as an example of swarm intelligence for which to apply the formal methods. This paper will give the evaluation of these formal methods and give partial specifications of the ANTS mission using four selected methods. We then give an evaluation of the methods and the needed properties of a formal method for effective specification and prediction of emergent behavior in swarm-based systems.

Rouff, Christopher↗

NASA NTRS2006

A High-Level Formalization of Floating-Point Number in PVS

We develop a formalization of floating-point numbers in PVS based on a well-known formalization in Coq. We first describe the definitions of all the needed notions, e.g., floating-point number, format, rounding modes, etc.; then, we present an application to polynomial evaluation for elementary function evaluation. The application already existed in Coq, but our formalization shows a clear improvement in the quality of the result due to the automation provided by PVS. We finally integrate our formalization into a PVS hardware-level formalization of the IEEE-854 standard previously developed at NASA.

Boldo, Sylvie↗

NASA NTRS2008

Proceedings of the Sixth NASA Langley Formal Methods (LFM) Workshop

Today's verification techniques are hard-pressed to scale with the ever-increasing complexity of safety critical systems. Within the field of aeronautics alone, we find the need for verification of algorithms for separation assurance, air traffic control, auto-pilot, Unmanned Aerial Vehicles (UAVs), adaptive avionics, automated decision authority, and much more. Recent advances in formal methods have made verifying more of these problems realistic. Thus we need to continually re-assess what we can solve now and identify the next barriers to overcome. Only through an exchange of ideas between theoreticians and practitioners from academia to industry can we extend formal methods for the verification of ever more challenging problem domains. This volume contains the extended abstracts of the talks presented at LFM 2008: The Sixth NASA Langley Formal Methods Workshop held on April 30 - May 2, 2008 in Newport News, Virginia, USA. The topics of interest that were listed in the call for abstracts were: advances in formal verification techniques; formal models of distributed computing; planning and scheduling; automated air traffic management; fault tolerance; hybrid systems/hybrid automata; embedded systems; safety critical applications; safety cases; accident/safety analysis.

Rozier, Kristin Yvonne↗

NASA NTRS2010

Formal Methods at Intel - An Overview

Since the 1990s, Intel has invested heavily in formal methods, which are now deployed in several domains: hardware, software, firmware, protocols etc. Many different formal methods tools and techniques are in active use, including symbolic trajectory evaluation, temporal logic model checking, SMT-style combined decision procedures, and interactive higher-order logic theorem proving. I will try to give a broad overview of some of the formal methods activities taking place at Intel, and describe the challenges of extending formal verification to new areas and of effectively using multiple formal techniques in combination

Harrison, John↗

NASA NTRS2010

Guidance for Using Formal Methods in a Certification Context

This paper discusses some of the challenges to using formal methods in a certification context and describes the effort by the Formal Methods Subgroup of RTCA SC-205/EUROCAE WG-71 to propose guidance to make the use of formal methods a recognized approach. This guidance, expected to take the form of a Formal Methods Technical Supplement to DO-178C/ED-12C, is described, including the activities that are needed when using formal methods, new or modified objectives with respect to the core DO-178C/ED-12C document, and evidence needed for meeting those objectives.

Brown, Duncan↗

NASA NTRS2014

Formal Methods Case Studies for DO-333

RTCA DO-333, Formal Methods Supplement to DO-178C and DO-278A provides guidance for software developers wishing to use formal methods in the certification of airborne systems and air traffic management systems. The supplement identifies the modifications and additions to DO-178C and DO-278A objectives, activities, and software life cycle data that should be addressed when formal methods are used as part of the software development process. This report presents three case studies describing the use of different classes of formal methods to satisfy certification objectives for a common avionics example - a dual-channel Flight Guidance System. The three case studies illustrate the use of theorem proving, model checking, and abstract interpretation. The material presented is not intended to represent a complete certification effort. Rather, the purpose is to illustrate how formal methods can be used in a realistic avionics software development project, with a focus on the evidence produced that could be used to satisfy the verification objectives found in Section 6 of DO-178C.

Cofer, Darren↗

NASA NTRSDate not supplied

Design, Formalization, and Verification of Decision Making for Intelligent Systems

The development of autonomous systems requires a rigorous process that can guarantee a system’s reliability in critical applications. At its core, an autonomous system bases its behavior on a well-defined decision making system. In this paper, we present a methodological basis for the design, formalization and formal verification of Decision Making systems for autonomous agents. The approach is generally applicable to operational objectives that can be functionally decomposed and subsequently represented as Hierarchical Finite State Machines. As a case study, we present the application of this method to implement a Decision Making model in Simulink. Furthermore, we present how we use NASA’s FRET tool to write requirements in structured natural language and generate formal specifications that can be automatically digested by NASA’s CoCoSim tool. Finally, we present how, by leveraging CoCoSim, we perform formal verification against the Simulink model and present analysis results.

Model-based development↗

NASA NTRSDate not supplied

Design, Formalization, and Verification of Decision Making for Intelligent Systems

Model-based development↗