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NASA NTRSDate not supplied

Formalization of the Bellman-Ford Algorithm for Airspace Applications

This paper describes the formal verification of one of the most well-known algorithms for finding the shortest path between all vertices in a directed graph, namely the Bellman-Ford algorithm. This formal verification, performed in the Prototype Verification System (PVS), is motivated by two applications in the aerospace domain which use the algorithm for path planning. The first is a pre-flight calculation that uses an adapted version of Bellman-Ford to find a route intended to maximize GNSS availability throughout the flight. The second is a more traditional application intended to find the shortest path between an autonomous aircraft's current position and a goal waypoint, while avoiding regions of space specified by geofences. A novel aspect of this formal verification effort is the inclusion of two distinct models of computation for the algorithm, one being a traditional serial computation, and the other being an explicitly parallel computation. The ability to use parallel computation in the Bellman-Ford algorithm is in fact why it was chosen over other traditionally more performant algorithms, especially for the GNSS application, where the size of the graph makes a purely serial computation infeasible.

formal verification↗
NASA NTRS1979

Formal methods for achieving reliable software

Requirements for reliable avionic systems are discussed in terms of the effectiveness of programming methodology. The need for methods to cope with the complexity of critical real-time systems is emphasized. Some general concepts about formal methods are presented and an example is given of the SRI hierarchical development methodology taken from the executive system of the SIFT fault tolerant computer. Formal methods with alternatives are compared and the prospects for introducing formal methods into practice are considered.

Goldberg, J.↗
NASA NTRS1982

Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms

Various aspects of the convergence, uniqueness, and existence properties associated with solutions generated via the elliptically constrained incremental Newton-Raphson (ECINR) algorithm are analyzed. Several theorems are developed, and the formal behavior of the elliptically constrained scheme developed by Padovan (1981) is discussed in detail. Consideration is given to global and local rates of convergence, to the determination of the occurrence of safety zones wherein the algorithm yields inherently convergent results, to formal limitations on the class of functions which the scheme can be applied to solve, and to single and multidimensional formalisms on existence uniqueness and convergence. Special attention is given to functions whose Jacobian matrix exhibit positive, negative, semi and indefinite properties. Several significant advantages of ECINR over the classical INR are mentioned.

Padovan, J.↗
NASA NTRS1989

Formal verification of a fault tolerant clock synchronization algorithm

A formal specification and mechanically assisted verification of the interactive convergence clock synchronization algorithm of Lamport and Melliar-Smith is described. Several technical flaws in the analysis given by Lamport and Melliar-Smith were discovered, even though their presentation is unusally precise and detailed. It seems that these flaws were not detected by informal peer scrutiny. The flaws are discussed and a revised presentation of the analysis is given that not only corrects the flaws but is also more precise and easier to follow. Some of the corrections to the flaws require slight modifications to the original assumptions underlying the algorithm and to the constraints on its parameters, and thus change the external specifications of the algorithm. The formal analysis of the interactive convergence clock synchronization algorithm was performed using the Enhanced Hierarchical Development Methodology (EHDM) formal specification and verification environment. This application of EHDM provides a demonstration of some of the capabilities of the system.

Rushby, John↗
NASA NTRS1989

Formal verification of AI software

The application of formal verification techniques to Artificial Intelligence (AI) software, particularly expert systems, is investigated. Constraint satisfaction and model inversion are identified as two formal specification paradigms for different classes of expert systems. A formal definition of consistency is developed, and the notion of approximate semantics is introduced. Examples are given of how these ideas can be applied in both declarative and imperative forms.

Rushby, John↗
NASA NTRS1991

Beyond formalism

The ongoing debate over the role of formalism and formal specifications in software features many speakers with diverse positions. Yet, in the end, they share the conviction that the requirements of a software system can be unambiguously specified, that acceptable software is a product demonstrably meeting the specifications, and that the design process can be carried out with little interaction between designers and users once the specification has been agreed to. This conviction is part of a larger paradigm prevalent in American management thinking, which holds that organizations are systems that can be precisely specified and optimized. This paradigm, which traces historically to the works of Frederick Taylor in the early 1900s, is no longer sufficient for organizations and software systems today. In the domain of software, a new paradigm, called user-centered design, overcomes the limitations of pure formalism. Pioneered in Scandinavia, user-centered design is spreading through Europe and is beginning to make its way into the U.S.

Denning, Peter J.↗
NASA NTRS1992

Moving formal methods into practice. Verifying the FTPP Scoreboard: Results, phase 1

This report documents the Phase 1 results of an effort aimed at formally verifying a key hardware component, called Scoreboard, of a Fault-Tolerant Parallel Processor (FTPP) being built at Charles Stark Draper Laboratory (CSDL). The Scoreboard is part of the FTPP virtual bus that guarantees reliable communication between processors in the presence of Byzantine faults in the system. The Scoreboard implements a piece of control logic that approves and validates a message before it can be transmitted. The goal of Phase 1 was to lay the foundation of the Scoreboard verification. A formal specification of the functional requirements and a high-level hardware design for the Scoreboard were developed. The hardware design was based on a preliminary Scoreboard design developed at CSDL. A main correctness theorem, from which the functional requirements can be established as corollaries, was proved for the Scoreboard design. The goal of Phase 2 is to verify the final detailed design of Scoreboard. This task is being conducted as part of a NASA-sponsored effort to explore integration of formal methods in the development cycle of current fault-tolerant architectures being built in the aerospace industry.

Srivas, Mandayam↗
NASA NTRS1992

Formal mechanization of device interactions with a process algebra

The principle emphasis is to develop a methodology to formally verify correct synchronization communication of devices in a composed hardware system. Previous system integration efforts have focused on vertical integration of one layer on top of another. This task examines 'horizontal' integration of peer devices. To formally reason about communication, we mechanize a process algebra in the Higher Order Logic (HOL) theorem proving system. Using this formalization we show how four types of device interactions can be represented and verified to behave as specified. The report also describes the specification of a system consisting of an AVM-1 microprocessor and a memory management unit which were verified in previous work. A proof of correct communication is presented, and the extensions to the system specification to add a direct memory device are discussed.

Schubert, E. Thomas↗
NASA NTRS1993

A formally verified algorithm for interactive consistency under a hybrid fault model

Consistent distribution of single-source data to replicated computing channels is a fundamental problem in fault-tolerant system design. The 'Oral Messages' (OM) algorithm solves this problem of Interactive Consistency (Byzantine Agreement) assuming that all faults are worst-cass. Thambidurai and Park introduced a 'hybrid' fault model that distinguished three fault modes: asymmetric (Byzantine), symmetric, and benign; they also exhibited, along with an informal 'proof of correctness', a modified version of OM. Unfortunately, their algorithm is flawed. The discipline of mechanically checked formal verification eventually enabled us to develop a correct algorithm for Interactive Consistency under the hybrid fault model. This algorithm withstands $a$ asymmetric, $s$ symmetric, and $b$ benign faults simultaneously, using $m+1$ rounds, provided $n is greater than 2a + 2s + b + m$, and $m\geg a$. We present this algorithm, discuss its subtle points, and describe its formal specification and verification in PVS. We argue that formal verification systems such as PVS are now sufficiently effective that their application to fault-tolerance algorithms should be considered routine.

Lincoln, Patrick↗
NASA NTRS1993

Formal methods for dependable real-time systems

The motivation for using formal methods to specify and reason about real time properties is outlined and approaches that were proposed and used are sketched. The formal verifications of clock synchronization algorithms are concluded as showing that mechanically supported reasoning about complex real time behavior is feasible. However, there was significant increase in the effectiveness of verification systems since those verifications were performed, at it is to be expected that verifications of comparable difficulty will become fairly routine. The current challenge lies in developing perspicuous and economical approaches to the formalization and specification of real time properties.

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 NTRS1999

Formal Verification of the AAMP-FV Microcode

This report describes the experiences of Collins Avionics & Communications and SRI International in formally specifying and verifying the microcode in a Rockwell proprietary microprocessor, the AAMP-FV, using the PVS verification system. This project built extensively on earlier experiences using PVS to verify the microcode in the AAMP5, a complex, pipelined microprocessor designed for use in avionics displays and global positioning systems. While the AAMP5 experiment demonstrated the technical feasibility of formal verification of microcode, the steep learning curve encountered left unanswered the question of whether it could be performed at reasonable cost. The AAMP-FV project was conducted to determine whether the experience gained on the AAMP5 project could be used to make formal verification of microcode cost effective for safety-critical and high volume devices.

Miller, Steven P.↗
NASA NTRS1999

The Formal Semantics of PVS

A specification language is a medium for expressing what is computed rather than how it is computed. Specification languages share some features with programming languages but are also different in several important ways. For our purpose, a specification language is a logic within which the behavior of computational systems can be formalized. Although a specification can be used to simulate the behavior of such systems, we mainly use specifications to state and prove system properties with mechanical assistance. We present the formal semantics of the specification language of SRI's Prototype Verification System (PVS). This specification language is based on the simply typed lambda calculus. The novelty in PVS is that it contains very expressive language features whose static analysis (e.g., typechecking) requires the assistance of a theorem prover. The formal semantics illuminates several of the design considerations underlying PVS, the interaction between theorem proving and typechecking.

Owre, Sam↗
NASA NTRS1998

Calculation of the Bulk Electromagnetic Properties of Thunderclouds Using a Two-Space Scattering Formalism

A two-space scatterer formalism and equivalent medium approach of Twersky are used to obtain formulae for the bulk electromagnetic parameters of a thundercloud medium that is illuminated by lightning optical emissions. A modified WKB approximation is applied to derive the two-space scattering amplitude. Optical constants of dry air, moist atmosphere, and water,.are inserted into the formulae to generate numerical values via iteration. The two-space scatterer formalism results are close to those obtained from free- or sin-le-space formalisms for the dilute case. The numerical values of the bulk parameters are required to successfully transform the scattering problem to that of an equivalent obstacle excited by an incident wave traveling in K - space but radiating in k(sub 1) -space.

Phanord, Dieudonne D.↗
NASA NTRS1998

Formal Modeling of Multi-Agent Systems using the Pi-Calculus and Epistemic Logic

Multi-agent systems have become important recently in computer science, especially in artificial intelligence (AI). We allow a broad sense of agent, but require at least that an agent has some measure of autonomy and interacts with other agents via some kind of agent communication language. We are concerned in this paper with formal modeling of multi-agent systems, with emphasis on communication. We propose for this purpose to use the pi-calculus, an extension of the process algebra CCS. Although the literature on the pi-calculus refers to agents, the term is used there in the sense of a process in general. It is our contention, however, that viewing agents in the AI sense as agents in the pi-calculus sense affords significant formal insight. One formalism that has been applied to agents in the AI sense is epistemic logic, the logic of knowledge. The success of epistemic logic in computer science in general has come in large part from its ability to handle concepts of knowledge that apply to groups. We maintain that the pi-calculus affords a natural yet rigorous means by which groups that are significant to epistemic logic may be identified, encapsulated, structured into hierarchies, and restructured in a principled way. This paper is organized as follows: Section 2 introduces the pi-calculus; Section 3 takes a scenario from the classical paper on agent-oriented programming [Sh93] and translates it into a very simple subset of the n-calculus; Section 4 then shows how more sophisticated features of the pi-calculus may bc brought into play; Section 5 discusses how the pi-calculus may be used to define groups for epistemic logic; and Section 6 is the conclusion.

Rorie, Toinette↗
NASA NTRS2000

Formal Analysis of the Remote Agent Before and After Flight

This paper describes two separate efforts that used the SPIN model checker to verify deep space autonomy flight software. The first effort occurred at the beginning of a spiral development process and found five concurrency errors early in the design cycle that the developers acknowledge would not have been found through testing. This effort required a substantial manual modeling effort involving both abstraction and translation from the prototype LISP code to the PROMELA language used by SPIN. This experience and others led to research to address the gap between formal method tools and the development cycle used by software developers. The Java PathFinder tool which directly translates from Java to PROMELA was developed as part of this research, as well as automatic abstraction tools. In 1999 the flight software flew on a space mission, and a deadlock occurred in a sibling subsystem to the one which was the focus of the first verification effort. A second quick-response "cleanroom" verification effort found the concurrency error in a short amount of time. The error was isomorphic to one of the concurrency errors found during the first verification effort. The paper demonstrates that formal methods tools can find concurrency errors that indeed lead to loss of spacecraft functions, even for the complex software required for autonomy. Second, it describes progress in automatic translation and abstraction that eventually will enable formal methods tools to be inserted directly into the aerospace software development cycle.

Havelund, Klaus↗
NASA NTRS2000

From Livingstone to SMV: Formal Verification for Autonomous Spacecrafts

To fulfill the needs of its deep space exploration program, NASA is actively supporting research and development in autonomy software. However, the reliable and cost-effective development and validation of autonomy systems poses a tough challenge. Traditional scenario-based testing methods fall short because of the combinatorial explosion of possible situations to be analyzed, and formal verification techniques typically require a tedious, manual modelling by formal method experts. This paper presents the application of formal verification techniques in the development of autonomous controllers based on Livingstone, a model-based health-monitoring system that can detect and diagnose anomalies and suggest possible recovery actions. We present a translator that converts the models used by Livingstone into specifications that can be verified with the SMV model checker. The translation frees the Livingstone developer from the tedious conversion of his design to SMV, and isolates him from the technical details of the SMV program. We describe different aspects of the translation and briefly discuss its application to several NASA domains.

Pecheur, Charles↗
NASA NTRS1996

Formalizing New Navigation Requirements for NASA's Space Shuttle

We describe a recent NASA-sponsored pilot project intended to gauge the effectiveness of using formal methods in Space Shuttle software requirements analysis. Several Change Requests (CRs) were selected as promising targets to demonstrate the utility of formal methods in this demanding application domain. A CR to add new navigation capabilities to the Shuttle, based on Global Positioning System (GPS) technology, is the focus of this industrial usage report. Portions of the GPS CR were modeled using the language of SRI's Prototype Verification System (PVS). During a limited analysis conducted on the formal specifications, numerous requirements issues were discovered. We present a summary of these encouraging results and conclusions we have drawn from the pilot project.

DiVito, Ben L.↗