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Results for “Theorem Proving”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

The use of a formal simulator to verify a simple real time control program

The authors present an initial and elementary investigation of the formal specification and mechanical verification of programs that interact with environments. They describe a mechanical proof that a simple, real time control program keeps a vehicle on a straightline course in a variable crosswind. To formalize the specification they define a mathematical function which models the interaction of the program and its environment. They then state and proved two theorems about this function: the simulated vehicle never gets farther than three units away from the intended course, and it comes to the course if the wind ever remains steady for at least four sampling units.

Boyer, R. S.↗
NASA NTRS1985

A note on finite-dimensional estimators for infinite-dimensional systems

In this note two theorems are proved regarding finite-dimensional estimators for infinite-dimensional systems. The first concerns the finite dimensionality of the model and the second concerns the finite dimensionality of the observation space. The analysis applies to very general systems, but appears to be most useful for the estimation of static systems from point sensing.

Milman, M. H.↗
NASA NTRS1988

Nonlinear Analysis Of Rotor Dynamics

Study explores analytical consequences of nonlinear Jeffcott equations of rotor dynamics. Section 1: Summary of previous studies. Section 2: Jeffcott Equations. Section 3: Proves two theorems that provide inequalities on coefficients of differential equations and magnitude of forcing function in absence of side force. Section 4: Numerical investigation of multiple-forcing-function problem by introducing both side force and mass imbalance. Section 5: Examples of numberical solutions of complex generalized Jeffcott equation with two forcing functions of different frequencies f1 and f2. Section 6: Boundedness and stability of solutions.Section 7: Concludes report reviewing analytical results and significance.

Day, William B.↗
NASA NTRS1988

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗
NASA NTRS1988

Hardware proofs using EHDM and the RSRE verification methodology

Examined is a methodology for hardware verification developed by Royal Signals and Radar Establishment (RSRE) in the context of the SRI International's Enhanced Hierarchical Design Methodology (EHDM) specification/verification system. The methodology utilizes a four-level specification hierarchy with the following levels: functional level, finite automata model, block model, and circuit level. The properties of a level are proved as theorems in the level below it. This methodology is applied to a 6-bit counter problem and is critically examined. The specifications are written in EHDM's specification language, Extended Special, and the proofs are improving both the RSRE methodology and the EHDM system.

Butler, Ricky W.↗
NASA NTRS1990

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗
NASA NTRS1990

The perturbation of ground tracks of periodic orbits

Some geometric characteristics of the ground tracks of periodic orbits are examined. In particular, two theorems are proved concerning points on the ground tracks that are invariant with respect to two periodic orbits. An application of the results to the Topex/Poseidon mission is presented.

Lo, Martin W.↗
NASA NTRS1994

Causality problems for Fermi's two-atom system

Let A and B be two atoms or, more generally, a 'source' and a 'detector' separated by some distance R. At t = 0 A is in an excited state, B in its ground state, and no photons are present. A theorem is proved that in contrast to Einstein causality and finite signal velocity the excitation probability of B is nonzero immediately after t = 0. Implications are discussed.

Hegerfeldt, Gerhard C.↗
NASA NTRS1994

Further evidence for the EPNT assumption

We recently proved a theorem extending the Greenberger-Horne-Zeilinger (GHZ) Theorem from multi-particle systems to two-particle systems. This proof depended upon an auxiliary assumption, the EPNT assumption (Emptiness of Paths Not Taken). According to this assumption, if there exists an Einstein-Rosen-Podolsky (EPR) element of reality that determines that a path is empty, then there can be no entity associated with the wave that travels this path (pilot-waves, empty waves, etc.) and reports information to the amplitude, when the paths recombine. We produce some further evidence in support of this assumption, which is certainly true in quantum theory. The alternative is that such a pilot-wave theory would have to violate EPR locality.

Greenberger, Daniel M.↗
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 NTRSDate not supplied

Formal Verification of Termination Criteria for​ First-Order Recursive Functions

This talk presents a formalization of several termination criteria for first-order recursive functions. The formalization, which is developed in the Prototype Verification System (PVS), includes the specification and proof of equivalence of semantic termination, Turing termination, size change principle, calling context graphs, and matrix-weighted graphs. These termination criteria are defined on a computational model that consists of a basic functional language called PVS0, which is an embedding of recursive first-order functions. Through this embedding, the native mechanism for checking termination of recursive functions in PVS could be soundly extended with semi-automatic termination criteria such as calling contexts graphs.

Termination↗
NASA NTRSDate not supplied

Proof Mate: An Interactive Proof Helper for PVS (Tool Paper)

This paper presents Proof Mate, an interactive proof helper for the PVS verification system. The helper is integrated in VSCode-PVS, the Visual Studio Code extension for PVS. It extends the capabilities of VSCode-PVS by introducing new functionalities for suggesting proof commands, sketching proof attempts, and repairing broken proofs during interactive proof sessions. This work further aligns VSCode-PVS to the functionalities provided by modern development tools, with the ultimate aim to facilitate the adoption of formal methods in engineering practices and education.

Interactive Theorem Proving↗
NASA NTRSDate not supplied

Proof Mate: An Interactive Proof Helper for PVS

This paper presents Proof Mate, an interactive proof helper for the PVS verification system. The helper is integrated in VSCode-PVS, the Visual Studio Code extension for PVS. It extends the capabilities of VSCode-PVS by introducing new functionalities for suggesting proof commands, sketching proof attempts, and repairing broken proofs during interactive proof sessions. This work further aligns VSCode-PVS to the functionalities provided by modern development tools, with the ultimate aim to facilitate the adoption of formal methods in engineering practices and education.

Formal Methods↗
NASA NTRSDate not supplied

A Formal Verification Framework for Runtime Assurance

The simplex architecture is an instance of Runtime Assurance (RTA) where a trusted component takes control of a safety-critical system when an untrusted component violates a safety property. This paper presents a formalization of the simplex RTA framework in the language of hybrid programs. A feature of this formal verification framework is that, for a given system, a specific instantiation can be created and its safety properties are guaranteed by construction. Instantiations may be kept at varying levels of generality, allowing for black box components, such as ML/AI-based controllers, to be modeled. The framework is written in the Prototype Verification System (PVS) using Plaidypvs, an embedding of differential dynamic logic in PVS. As a proof of concept, the framework is illustrated on an automatic vehicle braking system.

Runtime assurance↗
NASA NTRSDate not supplied

A Formal Verification Framework for Runtime Assurance

The simplex architecture is an instance of Runtime Assurance (RTA) where a trusted component takes control of a safety-critical system when an untrusted component violates a safety property. This paper presents a formalization of the simplex RTA framework in the language of hybrid programs. A feature of this formal verification framework is that, for a given system, a specific instantiation can be created and its safety properties are guaranteed by construction. Instantiations may be kept at varying levels of generality, allowing for black box components, such as ML/AI-based controllers, to be modeled. The framework is written in the Prototype Verification System (PVS) using Plaidypvs, an embedding of differential dynamic logic in PVS. As a proof of concept, the framework is illustrated on an automatic vehicle braking system.

Runtime assurance↗