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NASA NTRS1992

Formal methods technology transfer: Some lessons learned

IBM has a long history in the application of formal methods to software development and verification. There have been many successes in the development of methods, tools and training to support formal methods. And formal methods have been very successful on several projects. However, the use of formal methods has not been as widespread as hoped. This presentation summarizes several approaches that have been taken to encourage more widespread use of formal methods, and discusses the results so far. The basic problem is one of technology transfer, which is a very difficult problem. It is even more difficult for formal methods. General problems of technology transfer, especially the transfer of formal methods technology, are also discussed. Finally, some prospects for the future are mentioned.

Hamilton, David↗

NASA NTRS2018

A Formally Verified Floating-Point Implementation of the Compact Position Reporting Algorithm

The Automatic Dependent Surveillance-Broadcast (ADS-B) system allows aircraft to communicate their current state, including position and velocity information, to other aircraft in their vicinity and to ground stations. The Compact Position Reporting (CPR) algorithm is the ADS-B module responsible for the encoding and decoding of aircraft positions. CPR is highly sensitive to computer arithmetic since it heavily relies on functions that are intrinsically unstable such as floor and modulo. In this paper, a formally-verified double-precision floating-point implementation of the CPR algorithm is presented. The verification proceeds in three steps. First, an alternative version of CPR, which reduces the floating-point rounding error is proposed. Then, the Prototype Verification System (PVS) is used to formally prove that the ideal real-number counterpart of the improved algorithm is mathematically equivalent to the standard CPR definition. Finally, the static analyzer Frama-C is used to verify that the double-precision implementation of the improved algorithm is correct with respect to its operational requirement. The alternative algorithm is currently being considered for inclusion in the revised version of the ADS-B standards document as the reference implementation of the CPR algorithm.

Laura Titolo↗

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 NTRS2012

Quantified Event Automata: Towards Expressive and Efficient Runtime Monitors

Runtime verification is the process of checking a property on a trace of events produced by the execution of a computational system. Runtime verification techniques have recently focused on parametric specifications where events take data values as parameters. These techniques exist on a spectrum inhabited by both efficient and expressive techniques. These characteristics are usually shown to be conflicting - in state-of-the-art solutions, efficiency is obtained at the cost of loss of expressiveness and vice-versa. To seek a solution to this conflict we explore a new point on the spectrum by defining an alternative runtime verification approach.We introduce a new formalism for concisely capturing expressive specifications with parameters. Our technique is more expressive than the currently most efficient techniques while at the same time allowing for optimizations.

state machines↗

NASA NTRSDate not supplied

Interpretation and Formalization of the Right-of-Way Rules

This paper presents an interpretation and mathematical definition of the right-of-way rules as stated in USA, Title 14 of the Code of Federal Regulations, Part 91, Section 91.113 (14 CFR 91.113). In an encounter between two aircraft, the right-of-way rules defines which aircraft, if any, has the right-of-way and which AQ2 aircraft must maneuver to stay well clear of the other aircraft. The objective of the work presented in this paper is to give an unambiguous interpretation of the rules. From the interpretation, a precise mathematical formulation is created that can be used for analysis and proof of properties. The mathematical formulation has been defined in the Prototype Verification System (PVS) and properties of well formedness and core properties of the formalization have been mechanically proved. This mathematical formulation can be implemented digitally, so that right-of-way rules can be used in simulation or in future autonomous operations.

Right-of-Way↗

NASA NTRSDate not supplied

Automatic Generation of Guard-Stable Floating-Point Code

In floating-point programs, test instability occurs when the control flow of a conditional statement diverges from its ideal execution under real arithmetic. This phenomenon is caused by the presence of round-off errors in floating-point computations. Writing programs that correctly handle test instability often require expertise on finite precision computations and rounding errors. This paper presents a fully automatic tool chain that generates and formally verifies a test-stable floating-point C program from its functional specification in real arithmetic. The generated program is instrumented to soundly detect when unstable tests may occur and, in these cases, to issue a warning. The proposed approach combines the PRECiSA floating-point static analyzer, the Frama-C software verification suite, and the PVS theorem prover.

Floating-Point Arithmetic↗

NASA NTRS2002

Theorem Proving In Higher Order Logics

The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.

Carreno, Victor A.↗

NASA NTRS2015

Survey of Verification and Validation Techniques for Small Satellite Software Development

The purpose of this paper is to provide an overview of the current trends and practices in small-satellite software verification and validation. This document is not intended to promote a specific software assurance method. Rather, it seeks to present an unbiased survey of software assurance methods used to verify and validate small satellite software and to make mention of the benefits and value of each approach. These methods include simulation and testing, verification and validation with model-based design, formal methods, and fault-tolerant software design with run-time monitoring. Although the literature reveals that simulation and testing has by far the longest legacy, model-based design methods are proving to be useful for software verification and validation. Some work in formal methods, though not widely used for any satellites, may offer new ways to improve small satellite software verification and validation. These methods need to be further advanced to deal with the state explosion problem and to make them more usable by small-satellite software engineers to be regularly applied to software verification. Last, it is explained how run-time monitoring, combined with fault-tolerant software design methods, provides an important means to detect and correct software errors that escape the verification process or those errors that are produced after launch through the effects of ionizing radiation.

Small Satellite Technology↗

DOE OSTI2026

Towards a Verifiable Domain-Specific Language for Hardware-Accelerated Stencils

Defining a domain-specific language (DSL) that supports vector-calculus abstractions eases the porting of partial differential equation (PDE) solvers to specialized architectures. Sufficiently high-level abstractions empower users to express universal laws with sufficient generality that the laws must always hold true within their domain of validity. A broad class of PDE solvers employs stencil-based algorithms, the target domain of Berkeley Lab's stencil accelerator chip co-design project. First released as open-source in January 2026, the Formal software framework lays a foundation for defining an embedded DSL based on composable operators that implement mimetic numerical methods -- stencil algorithms that guarantee satisfaction of discrete versions of important vector calculus theorems. The Formal DSL will be the frontend to a new class of stencil-PDE accelerators developed jointly by LBNL, UHCL, and UC Berkeley through the DOE Competitive Portfolios for Computer Science Project. This offers the potential of an order of magnitude acceleration for this important category of computational methods to serve the DOE mission. Future work on the Formal DSL will facilitate software verification via type-safe templates that enable problem-specific correctness proofs relying upon generic function theory and carefully crafted unit tests.

Rouson, Damian↗

NASA NTRS1984

Software control and system configuration management: A systems-wide approach

A comprehensive software control and system configuration management process for flight-crucial digital control systems of advanced aircraft has been developed and refined to insure efficient flight system development and safe flight operations. Because of the highly complex interactions among the hardware, software, and system elements of state-of-the-art digital flight control system designs, a systems-wide approach to configuration control and management has been used. Specific procedures are implemented to govern discrepancy reporting and reconciliation, software and hardware change control, systems verification and validation testing, and formal documentation requirements. An active and knowledgeable configuration control board reviews and approves all flight system configuration modifications and revalidation tests. This flexible process has proved effective during the development and flight testing of several research aircraft and remotely piloted research vehicles with digital flight control systems that ranged from relatively simple to highly complex, integrated mechanizations.

Petersen, K. L.↗

NASA NTRS1983

Software control and system configuration management - A process that works

Petersen, K. L.↗

NASA NTRS1997

Experiences Using Lightweight Formal Methods for Requirements Modeling

This paper describes three case studies in the lightweight application of formal methods to requirements modeling for spacecraft fault protection systems. The case studies differ from previously reported applications of formal methods in that formal methods were applied very early in the requirements engineering process, to validate the evolving requirements. The results were fed back into the projects, to improve the informal specifications. For each case study, we describe what methods were applied, how they were applied, how much effort was involved, and what the findings were. In all three cases, formal methods enhanced the existing verification and validation processes, by testing key properties of the evolving requirements, and helping to identify weaknesses. We conclude that the benefits gained from early modeling of unstable requirements more than outweigh the effort needed to maintain multiple representations.

Easterbrook, Steve↗

NASA NTRS2004

Separating essentials from incidentals: an execution architecture for real-time control systems

This paper describes an execution architecture that makes such systems far more analyzable and verifiable by aggressive separation of concerns. The architecture separates two key software concerns: transformations of global state, as defined in pure functions; and sequencing/timing of transformations, as performed by an engine that enforces four prime invariants. The important advantage of this architecture, besides facilitating verification, is that it encourages formal specification of systems in a vocabulary that brings systems engineering closer to software engineering.

execution architecture↗

DOE OSTI2024

Replication Package for "Union-Find and Usability: A Case Study and Analysis of Rust Formal Verifier

This replication package is a case study on automated deductive verification for Rust for practical programs. It is a companion artifact to a corresponding usability study on verification titled "Union-Find and Usability: A Case Study and Analysis of Rust Formal Verifiers". It seeks to answer the question "Can Rust developers today use Rust verifiers to verify their code?". To answer this question, the study contrasts the verification experience of two mature Rust verifiers, Creusot and Prusti, by using the tools to develop a verified implementation of union-find in Rust. The union-find implementation is based on real-world code as used in the popular egg E-graph library. The artifact consists of two different verified libraries, one using Creusot and one using Prusti. The libraries have similar Rust interfaces and high-level proofs but differ in their details: Creusot and Prusti have different annotation languages and support different proof styles. Each implementation can be verified with its respective tool and compiles as a traditional Rust development.

Sarracino, John↗

NASA NTRS1993

Formal methods and digital systems validation for airborne systems

This report has been prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook. Its purpose is as follows: to outline the technical basis for formal methods in computer science; to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used on board aircraft; and to suggest factors for consideration when formal methods are offered in support of certification. These latter factors assume the context for software development and assurance described in RTCA document DO-178B, 'Software Considerations in Airborne Systems and Equipment Certification,' Dec. 1992.

Rushby, John↗

NASA NTRS1995

Formal methods and their role in digital systems validation for airborne systems

This report is based on one prepared as a chapter for the FAA Digital Systems Validation Handbook (a guide to assist FAA certification specialists with advanced technology issues). Its purpose is to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used in critical applications; and to suggest factors for consideration when formal methods are offered in support of certification. The presentation concentrates on the rationale for formal methods and on their contribution to assurance for critical applications within a context such as that provided by DO-178B (the guidelines for software used on board civil aircraft); it is intended as an introduction for those to whom these topics are new.

Rushby, John↗

NASA NTRS2008

NASA Langley's Formal Methods Research in Support of the Next Generation Air Transportation System

This talk will provide a brief introduction to the formal methods developed at NASA Langley and the National Institute for Aerospace (NIA) for air traffic management applications. NASA Langley's formal methods research supports the Interagency Joint Planning and Development Office (JPDO) effort to define and develop the 2025 Next Generation Air Transportation System (NGATS). The JPDO was created by the passage of the Vision 100 Century of Aviation Reauthorization Act in Dec 2003. The NGATS vision calls for a major transformation of the nation s air transportation system that will enable growth to 3 times the traffic of the current system. The transformation will require an unprecedented level of safety-critical automation used in complex procedural operations based on 4-dimensional (4D) trajectories that enable dynamic reconfiguration of airspace scalable to geographic and temporal demand. The goal of our formal methods research is to provide verification methods that can be used to insure the safety of the NGATS system. Our work has focused on the safety assessment of concepts of operation and fundamental algorithms for conflict detection and resolution (CD&R) and self- spacing in the terminal area. Formal analysis of a concept of operations is a novel area of application of formal methods. Here one must establish that a system concept involving aircraft, pilots, and ground resources is safe. The formal analysis of algorithms is a more traditional endeavor. However, the formal analysis of ATM algorithms involves reasoning about the interaction of algorithmic logic and aircraft trajectories defined over an airspace. These trajectories are described using 2D and 3D vectors and are often constrained by trigonometric relations. Thus, in many cases it has been necessary to unload the full power of an advanced theorem prover. The verification challenge is to establish that the safety-critical algorithms produce valid solutions that are guaranteed to maintain separation under all possible scenarios. Current research has assumed perfect knowledge of the location of other aircraft in the vicinity so absolute guarantees are possible, but increasingly we are relaxing the assumptions to allow incomplete, inaccurate, and/or faulty information from communication sources.

Butler, Ricky W.↗

NASA NTRS2002

A Conceptual Design for a Reliable Optical Bus (ROBUS)

The Scalable Processor-Independent Design for Electromagnetic Resilience (SPIDER) is a new family of fault-tolerant architectures under development at NASA Langley Research Center (LaRC). The SPIDER is a general-purpose computational platform suitable for use in ultra-reliable embedded control applications. The design scales from a small configuration supporting a single aircraft function to a large distributed configuration capable of supporting several functions simultaneously. SPIDER consists of a collection of simplex processing elements communicating via a Reliable Optical Bus (ROBUS). The ROBUS is an ultra-reliable, time-division multiple access broadcast bus with strictly enforced write access (no babbling idiots) providing basic fault-tolerant services using formally verified fault-tolerance protocols including Interactive Consistency (Byzantine Agreement), Internal Clock Synchronization, and Distributed Diagnosis. The conceptual design of the ROBUS is presented in this paper including requirements, topology, protocols, and the block-level design. Verification activities, including the use of formal methods, are also discussed.

Miner, Paul S.↗