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NASA NTRS2008

Automatic Testcase Generation for Flight Software

The TacSat3 project is applying Integrated Systems Health Management (ISHM) technologies to an Air Force spacecraft for operational evaluation in space. The experiment will demonstrate the effectiveness and cost of ISHM and vehicle systems management (VSM) technologies through onboard operation for extended periods. We present two approaches to automatic testcase generation for ISHM: 1) A blackbox approach that views the system as a blackbox, and uses a grammar-based specification of the system's inputs to automatically generate *all* inputs that satisfy the specifications (up to prespecified limits); these inputs are then used to exercise the system. 2) A whitebox approach that performs analysis and testcase generation directly on a representation of the internal behaviour of the system under test. The enabling technologies for both these approaches are model checking and symbolic execution, as implemented in the Ames' Java PathFinder (JPF) tool suite. Model checking is an automated technique for software verification. Unlike simulation and testing which check only some of the system executions and therefore may miss errors, model checking exhaustively explores all possible executions. Symbolic execution evaluates programs with symbolic rather than concrete values and represents variable values as symbolic expressions. We are applying the blackbox approach to generating input scripts for the Spacecraft Command Language (SCL) from Interface and Control Systems. SCL is an embedded interpreter for controlling spacecraft systems. TacSat3 will be using SCL as the controller for its ISHM systems. We translated the SCL grammar into a program that outputs scripts conforming to the grammars. Running JPF on this program generates all legal input scripts up to a prespecified size. Script generation can also be targeted to specific parts of the grammar of interest to the developers. These scripts are then fed to the SCL Executive. ICS's in-house coverage tools will be run to measure code coverage. Because the scripts exercise all parts of the grammar, we expect them to provide high code coverage. This blackbox approach is suitable for systems for which we do not have access to the source code. We are applying whitebox test generation to the Spacecraft Health INference Engine (SHINE) that is part of the ISHM system. In TacSat3, SHINE will execute an on-board knowledge base for fault detection and diagnosis. SHINE converts its knowledge base into optimized C code which runs onboard TacSat3. SHINE can translate its rules into an intermediate representation (Java) suitable for analysis with JPF. JPF will analyze SHINE's Java output using symbolic execution, producing testcases that can provide either complete or directed coverage of the code. Automatically generated test suites can provide full code coverage and be quickly regenerated when code changes. Because our tools analyze executable code, they fully cover the delivered code, not just models of the code. This approach also provides a way to generate tests that exercise specific sections of code under specific preconditions. This capability gives us more focused testing of specific sections of code.

Bushnell, David Henry↗

NASA NTRS2007

Smooth Phase Interpolated Keying

Smooth phase interpolated keying (SPIK) is an improved method of computing smooth phase-modulation waveforms for radio communication systems that convey digital information. SPIK is applicable to a variety of phase-shift-keying (PSK) modulation schemes, including quaternary PSK (QPSK), octonary PSK (8PSK), and 16PSK. In comparison with a related prior method, SPIK offers advantages of better performance and less complexity of implementation. In a PSK scheme, the underlying information waveform that one seeks to convey consists of discrete rectangular steps, but the spectral width of such a waveform is excessive for practical radio communication. Therefore, the problem is to smooth the step phase waveform in such a manner as to maintain power and bandwidth efficiency without incurring an unacceptably large error rate and without introducing undesired variations in the amplitude of the affected radio signal. Although the ideal constellation of PSK phasor points does not cause amplitude variations, filtering of the modulation waveform (in which, typically, a rectangular pulse is converted to a square-root raised cosine pulse) causes amplitude fluctuations. If a power-efficient nonlinear amplifier is used in the radio communication system, the fluctuating-amplitude signal can undergo significant spectral regrowth, thus compromising the bandwidth efficiency of the system. In the related prior method, one seeks to solve the problem in a procedure that comprises two major steps: phase-value generation and phase interpolation. SPIK follows the two-step approach of the related prior method, but the details of the steps are different. In the phase-value-generation step, the phase values of symbols in the PSK constellation are determined by a phase function that is said to be maximally smooth and that is chosen to minimize the spectral spread of the modulated signal. In this step, the constellation is divided into two groups by assigning, to information symbols, phase values that result in equal numbers of clockwise and counter-clockwise phase rotations for equally likely symbols. The purpose served by assigning phase values in this way is to prevent unnecessary generation of spectral lines and prevent net shifts of the carrier signal. In the phase-interpolation step, the smooth phase values are interpolated over a number, n, of consecutive symbols (including the present symbol) by means of an unconventional spline curve fit.

Borah, Deva K.↗

NASA NTRS2006

Sequence Detection for PPM Optical Communication With ISI

A method of sequence detection has been proposed to mitigate the effects of inter-slot interference and inter-symbol interference (both denoted ISI) in the reception of M-ary pulse-position modulation (PPM) optical signals. The method would make it possible to reduce the error rate for a given slot duration, to use a shorter slot duration (and, hence, to communicate at a higher rate) without exceeding a given error rate, or to use a lower-bandwidth (and, hence, less-expensive) receiver to receive a signal of a given slot width without exceeding a given error rate. In M-ary PPM, a symbol period is divided into M time slots, each of duration T(sub s), and a symbol consists of a binary sequence ones and zeros represented by pulses or the absence of pulses, respectively, in the time slots. At the transmitter, the bit stream is used to modulate a laser, the output of which is constant (either full power or zero power, representing 1 or 0, respectively) during each time slot. However, the signal becomes attenuated (signal photons are lost) in propagation from the transmitter to the receiver and noise enters at the receiver, complicating the problem of determining the timing of the symbol periods and slots and identifying the symbols.

Moision, Bruce↗

NASA NTRS2011

Methodology and method and apparatus for signaling with capacity optimized constellations

Communication systems having transmitter, includes a coder configured to receive user bits and output encoded bits at an expanded output encoded bit rate, a mapper configured to map encoded bits to symbols in a symbol constellation, a modulator configured to generate a signal for transmission via the communication channel using symbols generated by the mapper. In addition, the receiver includes a demodulator configured to demodulate the received signal via the communication channel, a demapper configured to estimate likelihoods from the demodulated signal, a decoder that is configured to estimate decoded bits from the likelihoods generated by the demapper. Furthermore, the symbol constellation is a capacity optimized geometrically spaced symbol constellation that provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes d.sub.min.

Barsoum, Maged F.↗

NASA NTRS2005

Multiple-Bit Differential Detection of OQPSK

A multiple-bit differential-detection method has been proposed for the reception of radio signals modulated with offset quadrature phase-shift keying (offset QPSK or OQPSK). The method is also applicable to other spectrally efficient offset quadrature modulations. This method is based partly on the same principles as those of a multiple-symbol differential-detection method for M-ary QPSK, which includes QPSK (that is, non-offset QPSK) as a special case. That method was introduced more than a decade ago by the author of the present method as a means of improving performance relative to a traditional (two-symbol observation) differential-detection scheme. Instead of symbol-by-symbol detection, both that method and the present one are based on a concept of maximum-likelihood sequence estimation (MLSE). As applied to the modulations in question, MLSE involves consideration of (1) all possible binary data sequences that could have been received during an observation time of some number, N, of symbol periods and (2) selection of the sequence that yields the best match to the noise-corrupted signal received during that time. The performance of the prior method was shown to range from that of traditional differential detection for short observation times (small N) to that of ideal coherent detection (with differential encoding) for long observation times (large N).

Simon, Marvin↗

NASA NTRS2014

Qualitative Event-Based Fault Isolation under Uncertain Observations

For many systems, automatic fault diagnosis is critical to ensuring safe and efficient operation. Fault isolation is performed by analyzing measured signals from the system, and reasoning over the system behavior to determine which faults have occurred, based on models of predicted faulty behavior. For dynamic systems, reasoning may be performed using qualitative analysis of the differences between measured signals and their predicted values, in which observations take the form of qualitative symbols. Such an approach is quick to isolate faults, but depends critically on correct generation of the qualitative symbols from the signals. In this paper, we develop an approach to qualitative event-based fault isolation for dynamic systems that is robust to incorrect qualitative observations. Observations are treated as uncertain, where multiple interpretations of an observation, each with its own probability, are considered. By interpreting observed symbols in a probabilistic manner, the approach degrades gracefully as the number of incorrectly-generated symbols increases. The approach is demonstrated on an electrical power system testbed, and experiments using real data obtained from the hardware demonstrate the improved fault isolation performance in the presence of incorrect symbol generation.

Daigle, Matthew↗

DOE OSTI2014

A stochastic analysis of steady and transient heat conduction in random media using a homogenization approach

We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total number N. Both steady and transient solutions T are expressed in terms of the homogenized solution (symbol) and its spatial derivatives (equation), where homogenized solution (symbol) is obtained by solving the homogenized equation with effective thermal conductivity. Both mean and variance of stochastic solutions can be obtained analytically for K field consisting of independent identically distributed (i.i.d) random variables. The mean and variance of T are shown to be dependent only on the mean and variance of these i.i.d variables, not the particular form of probability distribution function of i.i.d variables. Variance of temperature field T can be separated into two contributions: the ensemble contribution (through the homogenized temperature (symbol)); and the configurational contribution (through the random variable Ln(x)Ln(x)). The configurational contribution is shown to be proportional to the local gradient of (symbol). Large uncertainty of T field was found at locations with large gradient of (symbol) due to the significant configurational contributions at these locations. Numerical simulations were implemented based on a direct Monte Carlo method and good agreement is obtained between numerical Monte Carlo results and the proposed stochastic analysis.

99 GENERAL AND MISCELLANEOUS↗

NASA NTRS2014

Feedback-Driven Dynamic Invariant Discovery

Program invariants can help software developers identify program properties that must be preserved as the software evolves, however, formulating correct invariants can be challenging. In this work, we introduce iDiscovery, a technique which leverages symbolic execution to improve the quality of dynamically discovered invariants computed by Daikon. Candidate invariants generated by Daikon are synthesized into assertions and instrumented onto the program. The instrumented code is executed symbolically to generate new test cases that are fed back to Daikon to help further re ne the set of candidate invariants. This feedback loop is executed until a x-point is reached. To mitigate the cost of symbolic execution, we present optimizations to prune the symbolic state space and to reduce the complexity of the generated path conditions. We also leverage recent advances in constraint solution reuse techniques to avoid computing results for the same constraints across iterations. Experimental results show that iDiscovery converges to a set of higher quality invariants compared to the initial set of candidate invariants in a small number of iterations.

Daikon↗

DOE OSTI2019

All two-loop MHV remainder functions in multi-Regge kinematics

We introduce a method to extract the symbol of the coefficient of (2πi) 2 of MHV remainder functions in planar N = 4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics. At two loops this symbol can be uplifted to the full function in a unique way, without any beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV amplitudes at function level in all kinematic regions with different energy signs in multi-Regge kinematics. We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exchange of a three-Reggeon composite state starting from two loops and eight points in certain kinematic regions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Bootstrapping two-loop Feynman integrals for planar $ \mathcal{N}=4 $ sYM

We derive analytic results for the symbol of certain two-loop Feynman integrals relevant for seven- and eight-point two-loop scattering amplitudes in planar $ \mathcal{N}=4 $ super-Yang-Mills theory. We use a bootstrap inspired strategy, combined with a set of second-order partial differential equations that provide powerful constraints on the symbol ansatz. When the complete symbol alphabet is not available, we adopt a hybrid approach. Instead of the full function, we bootstrap a certain discontinuity for which the alphabet is known. Then we write a one-fold dispersion integral to recover the complete result. At six and seven points, we find that the individual Feynman integrals live in the same space of functions as the amplitude, which is described by the 9- and 42-letter cluster alphabets respectively. Starting at eight points however, the symbol alphabet of the MHV amplitude is insufficient for individual integrals. In particular, some of the integrals require algebraic letters involving four-mass box square-root singularities. We point out that these algebraic letters are relevant at the amplitude level directly starting with N2MHV amplitudes even at one loop.

1/N Expansion↗

DOE OSTI2018

Periodic p-adic Gibbs Measures of q-State Potts Model on Cayley Trees I: The Chaos Implies the Vastness of the Set of p-Adic Gibbs Measures

We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts–Bethe mapping over ℚ{sub p} for the prime numbers p≡1 (mod 3). In fact, for 0<|θ−1|{sub p}<|q|{sub p}{sup 2}<1 where θ=exp{sub p} (J) and J is a coupling constant, there exists a subsystem that is isometrically conjugate to the full shift on three symbols. Meanwhile, for 0<|q|{sub p}{sup 2}≤|θ−1|{sub p}<|q|{sub p}<1, there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r≥4. However, these subshifts on r symbols are all topologically conjugate to the full shift on three symbols. The p-adic Gibbs measures of the same model for the prime numbers p=2,3 and the corresponding Potts–Bethe mapping are also discussed. On the other hand, for 0<|θ−1|{sub p}<|q|{sub p}<1, we remark that the Potts–Bethe mapping is not chaotic when p=3 and p≡2 (mod 3) and we could not conclude the vastness of the set of the periodic p-adic Gibbs measures. In a forthcoming paper with the same title, we will treat the case 0<|q|{sub p}≤|θ−1|{sub p}<1 for all prime numbers p.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Synthesis and characterization of d{sup 10} metal complexes with mixed 1,3-di(1H-imidazol-4-yl)benzene and multicarboxylate ligands

Seven new coordination polymers [Zn(H{sub 2}L)(mbdc)] (1), [Zn(H{sub 3}L)(btc)] (2), [Zn(H{sub 2}L)(Hbtc)] (3), [Zn(H{sub 2}L)(Hbtc)]·H{sub 2}O (4), [Zn{sub 2}(H{sub 2}L)(btc)(μ{sub 2}-OH)] (5), [Cd(H{sub 2}L)(mbdc)] (6) and [Cd{sub 3}(H{sub 2}L){sub 2}(btc){sub 2}(H{sub 2}O)]·5H{sub 2}O (7) were synthesized by reactions of the corresponding metal salt with rigid ligand 1,3-di(1H-imidazol-4-yl)benzene (H{sub 2}L) and different carboxylic acids of 1,3-benzenedicarboxylic acid (H{sub 2}mbdc) and benzene-1,3,5-tricarboxylic acid (H{sub 3}btc), respectively. The results of X-ray crystallographic analysis indicate that complex 1 is 1D chain while 2 is a (3,3)-connected 2D network with Point (Schläfli) symbol of (4,8{sup 2}). Complexes 3 and 6 are 2D networks, 4 is a 3-fold interpenetrating 3D framework with Point (Schläfli) symbol of (6{sup 5},8) and 5 is a (3,8)-connected 2D network with Point (Schläfli) symbol of (3,4{sup 2}){sub 2}(3{sup 4},4{sup 6},5{sup 6},6{sup 8},7{sup 3},8), while 7 is a (3,10)-connected 3D net with Schläfli symbol of (3,4,5){sub 2}(3{sup 4},4{sup 8},5{sup 18},6{sup 12},7{sup 2},8). The thermal stability and photoluminescence of the complexes were investigated. Furthermore, DFT calculations were performed for 2–4 to discuss the temperature controlled self-assembly of the complexes. - Graphical abstract: Seven new coordination polymers with multicarboxylate and rigid ditopic 4-imidazole containing ligands have been obtained and found to show different structures and topologies. - Highlights: • Metal complexes with diverse structures of 1D chain, 2D network and 3D framework. • Mixed ligands of 1,3-di(1H-imidazol-4-yl)benzene and multicarboxylate. • Photoluminescence property.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Synthesis, crystal structures and luminescent properties of zinc(II) metal–organic frameworks constructed from terpyridyl derivative ligand

Five zinc(II) metal–organic frameworks, [Zn{sub 3}(344-pytpy){sub 2}Cl{sub 6}]{sub n}·n(H{sub 2}O) (1), [Zn(344-pytpy)(ox)]{sub n} (2), [Zn{sub 2}(344-pytpy)(bdc){sub 2}]{sub n}·1.5n(H{sub 2}O) (3), [Zn{sub 2}(344-pytpy){sub 2} (sfdb){sub 2}]{sub n}·1.5n(H{sub 2}O) (4) and [Zn{sub 3}(344-pytpy){sub 2}(btc){sub 2}]{sub n}·2n(H{sub 2}O) (5), (344-pytpy=4′-(3-pyridyl)-4,2′:6′,4″-terpyridine, H{sub 2}ox=oxalic acid, H{sub 2}bdc=1,4-benzenedi-carboxylic acid, H{sub 2}sfdb=4,4′-sulfonyldibenzoic acid and H{sub 3}btc=1,3,5-benzene-tricarboxylic acid) have been prepared by hydrothermal reactions. Compound 1 is a 1D chain structure, in which 344-pytpy ligand links three Zn{sup II} centers through three of terminal N-donors. Compound 2 is a 4-connected 3D framework with the dia topological net and the Schläfli symbol of 6{sup 6}. Compound 3 displays a unusual 3-fold interpenetrating 3D coordination network which exhibits a new intriguing (3,3,4)-connected topological net with the Schläfli symbol of (4.8{sup 2})(4.8{sup 5})(8{sup 3}). Compound 4 features a two-fold interpenetrating 4-connected 2D framework with the sql topological net and the Schläfli symbol of (4{sup 4}.6{sup 2}). Compound 5 is a new self-interpenetrating (3,3,4,4)-connected topological net with the Schläfli symbol of (6.8{sup 2}){sub 2}(6{sup 2}.8{sup 2}.10.12)(6{sup 2}.8{sup 3}.10){sub 2}(6{sup 2}.8){sub 2}. The luminescence properties of 1–5 have been investigated by emission spectra and they possess great thermal stabilities which can be stable up to around 400 °C. - Graphical abstract: Five new Zn(II) metal–organic frameworks based on dicarboxylate and terpyridyl derivative ligands have been synthesized by hydrothermal reactions, giving networks from 1D to 3D structures. The thermal stability and luminescent property have been investigated. - Highlights: • Five zinc(II) metal–organic frameworks have been prepared under hydrothermal conditions. • Their crystal and topological structures have been investigated. • The luminescent properties have been investigated. • They possess great thermal stabilities which can be stable up to around 400 °C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1980

Spectral characteristics of convolutionally coded digital signals

The power spectral density of the output symbol sequence of a convolutional encoder is computed for two different input symbol stream source models, namely, an NRZ signaling format and a first-order Markov source. The effects of alternate symbol inversion on this spectrum are also considered. The mathematical results are illustrated with many examples corresponding to optimal performance codes. It is demonstrated that only for the case of a purely random input source (e.g., NRZ data with equiprobable symbols) and a particular class of codes is the output spectrum identical to the input spectrum except for a frequency scaling (expansion) by the reciprocal of the code rate.

Divsalar, D.↗

NASA NTRS1985

Test Sequences for Reed-Solomon Encoders

Theory of Reed-Solomon codes yields sequences of input test symbols. Two specific sequences worked out for codes of 8 bits per symbol with 223 information symbols and 32 parity check symbols per code words. Test patterns also used for decoders.

Lee, J. J.↗

NASA NTRS1983

On the probability of undetected error for the maximum distance separable codes

The performance of maximum-distance-separable codes with symbols from GF(1) when they are used for pure error detection or for simultaneous error correction and detection is investigated. These codes are good for symbol error detection. Their probability of undetected error is upper bounded by q to the -r and decreases monotonically as the symbol error probability epsilon decreases from (q-1)/q to 0, where r is the number of parity-check symbols of a code.

Kasami, T.↗

NASA NTRS1984

On the probability of undetected error for the maximum distance separable codes

Kasami, T.↗

NASA NTRS1986

Single-Chip VLSI Reed-Solomon Encoder

Reed-Solomon (RS) encoder based on Berlekamp bit-serial multiplier algorithm. RS code standard, based on code words of 255 8-bit symbols, of which 223 symbols convey information and remaining 32 are check symbols. This code enables correction of up to 16 erroneous information symbols per word. Berlekamp algorithm based on code-generating polynomial with 32 roots that occur in reciprocal pairs. Choice of algorithm permits compact design.

Truong, T. K.↗