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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
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↗
NASA NTRS2006

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.

Metzger, Philip T.↗
NASA NTRS1991

Arbitrary nonlinearity is sufficient to represent all functions by neural networks - A theorem

It is proved that if we have neurons implementing arbitrary linear functions and a neuron implementing one (arbitrary but smooth) nonlinear function g(x), then for every continuous function f(x sub 1,..., x sub m) of arbitrarily many variables, and for arbitrary e above 0, we can construct a network that consists of g-neurons and linear neurons, and computes f with precision e.

Kreinovich, Vladik YA.↗
DOE OSTI2024

New nonrenormalization theorem from UV/IR mixing

In this paper, we prove a new nonrenormalization theorem which arises from UV/IR mixing. This theorem and its corollaries are relevant for all four-dimensional perturbative tachyon-free closed string theories which can be realized from higher-dimensional theories via geometric compactifications. As such, our theorem therefore holds regardless of the presence or absence of spacetime supersymmetry and regardless of the gauge symmetries or matter content involved. This theorem resolves a hidden clash between modular invariance and the process of decompactification, and enables us to uncover a number of surprising phenomenological properties of these theories. Chief among these is the fact that certain physical quantities within such theories cannot exhibit logarithmic or power-law running and instead enter an effective fixed-point regime above the compactification scale. This cessation of running occurs as the result of the UV/IR mixing inherent in the theory. These effects apply not only for gauge couplings but also for the Higgs mass and other quantities of phenomenological interest, thereby eliminating the logarithmic and/or power-law running that might have otherwise appeared for such quantities. These results illustrate the power of UV/IR mixing to tame divergences—even without supersymmetry—and reinforce the notion that UV/IR mixing may play a vital role in resolving hierarchy problems without supersymmetry. Published by the American Physical Society 2024

Abel, Steven (ORCID:000000031213907X)↗
NASA NTRS1991

Verification of the FtCayuga fault-tolerant microprocessor system. Volume 2: Formal specification and correctness theorems

Presented here is a formal specification and verification of a property of a quadruplicately redundant fault tolerant microprocessor system design. A complete listing of the formal specification of the system and the correctness theorems that are proved are given. The system performs the task of obtaining interactive consistency among the processors using a special instruction on the processors. The design is based on an algorithm proposed by Pease, Shostak, and Lamport. The property verified insures that an execution of the special instruction by the processors correctly accomplishes interactive consistency, providing certain preconditions hold, using a computer aided design verification tool, Spectool, and the theorem prover, Clio. A major contribution of the work is the demonstration of a significant fault tolerant hardware design that is mechanically verified by a theorem prover.

Bickford, Mark↗
NASA NTRS2000

A Geometrical Approach to Bell's Theorem

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

Rubincam, David Parry↗
NASA NTRS1977

Applications of Algebraic Geometry to Systems Theory

Basic theorems of algebraic geometry are applied to prove some pole-placement theorems, including an improved version of pole placement with output feedback. Examples are given which show the limitations of the algebro-geometric theorems and their potential value for systems theory. This paper and those to follow might contribute towards making the powerful theorems of modern algebraic geometry accessible and applicable to problems of engineering.

Hermann, Robert↗
DOE OSTI2024

Characterizing non-Markovian and coherent errors in quantum simulation

Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1978

Forced oscillations in quadratically damped systems

Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.

Bayliss, A.↗
NASA NTRS1984

On some properties of force-free magnetic fields in infinite regions of space

Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.

Aly, J. J.↗
NASA NTRS1985

Hopf bifurcation in the presence of symmetry

Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.

Golubitsky, M.↗
NASA NTRS1994

Exploiting structure: Introduction and motivation

This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix.

Xu, Zhong Ling↗
NASA NTRS1994

Progress in navigation filter estimate fusion and its application to spacecraft rendezvous

A new derivation of an algorithm which fuses the outputs of two Kalman filters is presented within the context of previous research in this field. Unlike other works, this derivation clearly shows the combination of estimates to be optimal, minimizing the trace of the fused covariance matrix. The algorithm assumes that the filters use identical models, and are stable and operating optimally with respect to their own local measurements. Evidence is presented which indicates that the error ellipsoid derived from the covariance of the optimally fused estimate is contained within the intersections of the error ellipsoids of the two filters being fused. Modifications which reduce the algorithm's data transmission requirements are also presented, including a scalar gain approximation, a cross-covariance update formula which employs only the two contributing filters' autocovariances, and a form of the algorithm which can be used to reinitialize the two Kalman filters. A sufficient condition for using the optimally fused estimates to periodically reinitialize the Kalman filters in this fashion is presented and proved as a theorem. When these results are applied to an optimal spacecraft rendezvous problem, simulated performance results indicate that the use of optimally fused data leads to significantly improved robustness to initial target vehicle state errors. The following applications of estimate fusion methods to spacecraft rendezvous are also described: state vector differencing, and redundancy management.

Carpenter, J. Russell↗
NASA NTRS1995

The AAMP5/AAMP-FV project

This presentation describes a project, formal verification of the microcode in the AAMP5 microprocessor, conducted to explore how formal techniques for specification and verification could be introduced into an industrial process. Sponsored by the Systems Validation Branch of NASA Langley and by Collins Commercial Avionics, a division of Rockwell International, it was conducted by Collins and the SRI International Computer Science Laboratory. The project consisted of specifying in the PVS language developed by SRI a portion of a Rockwell proprietary microprocessor, the AAMP5, at both the instruction set and register-transfer levels and using the PVS theorem prover to prove the microcode correct for a representative subset of instructions. While this presentation includes a brief technical overview, its emphasis is on the lessons learned in using PVS for an example of this size and the implications for using formal methods in an industrial setting. The central result of this project was to demonstrate the feasibility of formally specifying a commercial microprocessor and the use of mechanical proofs of correctness to verify microcode. This is particularly significant since the AAMP5 was not designed for formal verification, but to provide a more than three fold performance improvement, by pipelining instruction execution, while remaining object code compatible with the earlier AAMP2. As a consequence, the AAMP5 is one of the most complex microprocessors to which formal methods have been applied. Another key result was the discovery of both actual and seeded errors. Two actual microcode errors were discovered and corrected during development of the formal specification, illustrating the value of simply creating a precise specification. Two seeded errors were systematically uncovered while doing correctness proofs. One of these was an actual error that had been discovered after first fabrication but left in the microcode provided to SRI. The other error was designed to be unlikely to be detected by walkthroughs, testing, or simulation. Several other results emerged during the project, including the ease with which practicing engineers became comfortable with PVS, the need for libraries of general purpose theories, the usefulness of formal specification in revealing errors, the natural fit between formal specification and inspections, the difficulty of selecting the best style of specification for a new problem domain, the high level of assurance provided by proofs of correctness, and the need to engineer proof strategies for reuse.

Miller, Steven P.↗