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NASA NTRS1991

Probabilistic composite analysis

Formal procedures are described which are used to computationally simulate the probabilistic behavior of composite structures. The computational simulation starts with the uncertainties associated with all aspects of a composite structure (constituents, fabrication, assembling, etc.) and encompasses all aspects of composite behavior (micromechanics, macromechanics, combined stress failure, laminate theory, structural response, and tailoring) optimization. Typical cases are included to illustrate the formal procedure for computational simulation. The collective results of the sample cases demonstrate that uncertainties in composite behavior and structural response can be probabilistically quantified.

Chamis, C. C.↗

NASA NTRS1990

An analysis of scatter decomposition

A formal analysis of a powerful mapping technique known as scatter decomposition is presented. Scatter decomposition divides an irregular computational domain into a large number of equal sized pieces, and distributes them modularly among processors. A probabilistic model of workload in one dimension is used to formally explain why, and when scatter decomposition works. The first result is that if correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance. The second result shows that if the workload process is stationary Gaussian and the correlation function decreases linearly in distance until becoming zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally it is shown that if the correlation function decreases linearly across the entire domain, then among all mappings that assign an equal number of domain pieces to each processor, scatter decomposition minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with situations where a coarser granularity actually achieves better load balance.

Nicol, David M.↗

NASA NTRS1971

Analysis of parallel systems.

A formal analysis procedure for hardware and software computer systems is described. A system is described by a flow table model. The concept of an output hazard is introduced to account for effects of unbounded line delays. Necessary and sufficient conditions for the absence of output hazards are given. A system that contains no output hazards is said to operate correctly if the system state graph that describes all system states and state transitions is free from forbidden states and forbidden state sequences. A flow table solution for the two-component mutual exclusion problem is analyzed and shown to be correct.

Bredt, T. H.↗

NASA NTRS1990

An analysis of scatter decomposition

A formal analysis of a mapping method known as scatter decomposition (SD) is presented. SD divides an irregular domain into many equal-size pieces and distributes them modularly among processors. It is shown that, if a correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance; if the workload process is stationary Gaussian and the correlation function decreases linearly in distance to zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally, if the correlation function decreases linearly across the entire domain, then (among all mappings that assign an equal number of domain pieces to each processor) SD minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with cases where a coarser granularity actually achieves better load balance.

Nicol, David M.↗

DOE OSTI2024

Formal threat analysis of machine learning-based control systems: A study on smart healthcare systems

Not Available

Haque, Nur Imtiazul (ORCID:000000032865632X)↗

NASA NTRS2016

Deductive Evaluation: Formal Code Analysis With Low User Burden

We describe a framework for symbolically evaluating iterative C code using a deductive approach that automatically discovers and proves program properties. Although verification is not performed, the method can infer detailed program behavior. Software engineering work flows could be enhanced by this type of analysis. Floyd-Hoare verification principles are applied to synthesize loop invariants, using a library of iteration-specific deductive knowledge. When needed, theorem proving is interleaved with evaluation and performed on the fly. Evaluation results take the form of inferred expressions and type constraints for values of program variables. An implementation using PVS (Prototype Verification System) is presented along with results for sample C functions.

Di Vito, Ben. L↗

NASA NTRS2006

ADGS-2100 Adaptive Display and Guidance System Window Manager Analysis

Recent advances in modeling languages have made it feasible to formally specify and analyze the behavior of large system components. Synchronous data flow languages, such as Lustre, SCR, and RSML-e are particularly well suited to this task, and commercial versions of these tools such as SCADE and Simulink are growing in popularity among designers of safety critical systems, largely due to their ability to automatically generate code from the models. At the same time, advances in formal analysis tools have made it practical to formally verify important properties of these models to ensure that design defects are identified and corrected early in the lifecycle. This report describes how these tools have been applied to the ADGS-2100 Adaptive Display and Guidance Window Manager being developed by Rockwell Collins Inc. This work demonstrates how formal methods can be easily and cost-efficiently used to remove defects early in the design cycle.

Whalen, Mike W.↗

NASA NTRS2013

Modeling and Analysis of Asynchronous Systems Using SAL and Hybrid SAL

We present formal models and results of formal analysis of two different asynchronous systems. We first examine a mid-value select module that merges the signals coming from three different sensors that are each asynchronously sampling the same input signal. We then consider the phase locking protocol proposed by Daly, Hopkins, and McKenna. This protocol is designed to keep a set of non-faulty (asynchronous) clocks phase locked even in the presence of Byzantine-faulty clocks on the network. All models and verifications have been developed using the SAL model checking tools and the Hybrid SAL abstractor.

Tiwari, Ashish↗

NASA NTRS2009

Rewriting Logic Semantics of a Plan Execution Language

The Plan Execution Interchange Language (PLEXIL) is a synchronous language developed by NASA to support autonomous spacecraft operations. In this paper, we propose a rewriting logic semantics of PLEXIL in Maude, a high-performance logical engine. The rewriting logic semantics is by itself a formal interpreter of the language and can be used as a semantic benchmark for the implementation of PLEXIL executives. The implementation in Maude has the additional benefit of making available to PLEXIL designers and developers all the formal analysis and verification tools provided by Maude. The formalization of the PLEXIL semantics in rewriting logic poses an interesting challenge due to the synchronous nature of the language and the prioritized rules defining its semantics. To overcome this difficulty, we propose a general procedure for simulating synchronous set relations in rewriting logic that is sound and, for deterministic relations, complete. We also report on the finding of two issues at the design level of the original PLEXIL semantics that were identified with the help of the executable specification in Maude.

Dowek, Gilles↗

DOE OSTI2021

Q Framework

The Q Formal Analysis Framework is a set of software tools used to formally prove that implementations of high-consequence digital systems meet mathematical specifications. The tools are designed to work together as a set. Specifications are derived directly from high-level requirements and expressed in the QSpec hierarchical state machine format. The toolkit includes QSpec, QRefact, and QReqs. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-0504 O

Hulette, GeoffreyC.↗

NASA NTRS1994

Experience report: Using formal methods for requirements analysis of critical spacecraft software

Formal specification and analysis of requirements continues to gain support as a method for producing more reliable software. However, the introduction of formal methods to a large software project is difficult, due in part to the unfamiliarity of the specification languages and the lack of graphics. This paper reports results of an investigation into the effectiveness of formal methods as an aid to the requirements analysis of critical, system-level fault-protection software on a spacecraft currently under development. Our experience indicates that formal specification and analysis can enhance the accuracy of the requirements and add assurance prior to design development in this domain. The work described here is part of a larger, NASA-funded research project whose purpose is to use formal-methods techniques to improve the quality of software in space applications. The demonstration project described here is part of the effort to evaluate experimentally the effectiveness of supplementing traditional engineering approaches to requirements specification with the more rigorous specification and analysis available with formal methods.

Lutz, Robyn R.↗

NASA NTRSDate not supplied

Authoring, Analyzing, and Monitoring Requirements for a Lift-Plus-Cruise Aircraft

Requirements specification and analysis is widely applied to ensure the correctness of industrial systems in safety critical domains. Requirements are often initially written in natural language, which is highly ambiguous, and as a second step transformed into a language with rigorous semantics for formal analysis. In this paper, we report on our experience in requirements creation and analysis, as well as run-time monitor generation using the Formal Requirement Elicitation Tool (FRET), on an industrial case study for a Lift-Plus-Cruise concept aircraft. We study the creation of requirements directly in the structured language of FRET without a prior definition of the same requirements in natural language. We focus on requirements describing state machines and discuss the challenges that we faced, in terms of creating requirements and generating monitors. We demonstrate how realizability, i.e., checking whether a requirements specification can be implemented, is crucial for understanding temporal interdependencies among requirements. Our study is the first complete attempt at using FRET to create industrial, realizable requirements and generate run-time monitors. Insight from lessons learned was materialized into new features in the FRET and JKind analysis frameworks.

Requirements engineering↗

NASA NTRSDate not supplied

Authoring, Analyzing, and Monitoring Requirements for a Lift-Plus-Cruise Aircraft

Requirements specification and analysis is widely applied to ensure the correctness of industrial systems in safety critical domains. Requirements are often initially written in natural language, which is highly ambiguous, and as a second step transformed into a language with rigorous semantics for formal analysis. [Question/problem] In this paper, we report on our experience in requirements creation and analysis, as well as run-time monitor generation using the Formal Requirement Elicitation Tool (FRET), on an industrial case study for a Lift-Plus-Cruise concept aircraft. [Principal ideas/results] We study the creation of requirements directly in the structured language of FRET without a prior definition of the same requirements in natural language. We focus on requirements describing state machines and discuss the challenges that we faced, in terms of creating requirements and generating monitors. We demonstrate how realizability, i.e., checking whether a requirements specification can be implemented, is crucial for understanding temporal interdependencies among requirements. [Contribution] Our study is the first complete attempt at using FRET to create industrial, realizable requirements and generate run-time monitors. Insight from lessons learned was materialized into new features in the FRET and JKind analysis frameworks.

Requirements engineering↗

NASA NTRS1994

Experience Report: Using Formal Methods for Requirements Analysis of Critical Spacecraft Software

Formal↗

NASA NTRS1994

Redshift data and statistical inference

Frequency histograms and the 'power spectrum analysis' (PSA) method, the latter developed by Yu & Peebles (1969), have been widely employed as techniques for establishing the existence of periodicities. We provide a formal analysis of these two classes of methods, including controlled numerical experiments, to better understand their proper use and application. In particular, we note that typical published applications of frequency histograms commonly employ far greater numbers of class intervals or bins than is advisable by statistical theory sometimes giving rise to the appearance of spurious patterns. The PSA method generates a sequence of random numbers from observational data which, it is claimed, is exponentially distributed with unit mean and variance, essentially independent of the distribution of the original data. We show that the derived random processes is nonstationary and produces a small but systematic bias in the usual estimate of the mean and variance. Although the derived variable may be reasonably described by an exponential distribution, the tail of the distribution is far removed from that of an exponential, thereby rendering statistical inference and confidence testing based on the tail of the distribution completely unreliable. Finally, we examine a number of astronomical examples wherein these methods have been used giving rise to widespread acceptance of statistically unconfirmed conclusions.

Newman, William I.↗

DOE OSTI2025

Lanczos algorithm for lattice QCD matrix elements

Recent work [M. L. Wagman, Lanczos, the transfer matrix, and the signal-to-noise problem, .] found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multistate fit results than effective masses—but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of “spurious-state filtering” involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Quantum field theory of topological spin dynamics

Here, we develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar, and general noncoplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of “intrinsic” and “topological” anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict “topological” magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. Much of the formal analysis is generalized to d spatial dimensions in order to access the $π_{d–1}(S^{d–1})$ homotopy classification of the magnetic hedgehog topological defects, and establish the possibility of novel quantum spin liquids that exhibit a fractional magnetoelectric effect. However, we emphasize the form of all results in the physically relevant $\textit{d}$ = 3 dimensions, and discuss a few applications to topological magnetic conductors like Mn 3 Sn and Pr 2 Ir 2 O 7 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Gauge invariance and Ward identities in nonlinear response theory

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗