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NASA NTRS2006

Symbolic Constraint Maintenance Grid

Version 3.1 of Symbolic Constraint Maintenance Grid (SCMG) is a software system that provides a general conceptual framework for utilizing pre-existing programming techniques to perform symbolic transformations of data. SCMG also provides a language (and an associated communication method and protocol) for representing constraints on the original non-symbolic data. SCMG provides a facility for exchanging information between numeric and symbolic components without knowing the details of the components themselves. In essence, it integrates symbolic software tools (for diagnosis, prognosis, and planning) with non-artificial-intelligence software. SCMG executes a process of symbolic summarization and monitoring of continuous time series data that are being abstractly represented as symbolic templates of information exchange. This summarization process enables such symbolic- reasoning computing systems as artificial- intelligence planning systems to evaluate the significance and effects of channels of data more efficiently than would otherwise be possible. As a result of the increased efficiency in representation, reasoning software can monitor more channels and is thus able to perform monitoring and control functions more effectively.

James, Mark↗

NASA NTRS2014

Statistical Symbolic Execution with Informed Sampling

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

Reliability↗

NASA NTRS2005

Noncoherent Symbol Synchronization Techniques

Traditional methods for establishing symbol synchronization (sync) in digital communication receivers assume that carrier sync has already been established, i.e., the problem is addressed at the baseband level assuming that a 'perfect' estimate of carrier phase is available. We refer to this approach as coherent symbol sync. Since, for NRZ signaling, a suppressed carrier sync loop such as an I-Q Costas loop includes integrate-and-dump (I and D) filters in its in-phase (1) and quadrature (Q) arms, the traditional approach is to first track the carrier in the absence of symbol sync information, then feed back the symbol sync estimate to these filters, and then iterate between the two to a desirable operating level In this paper, we revisit the symbol sync problem by examining methods for obtaining such sync in the absence of carrier phase information, i.e., so-called noncoherent symbol sync loops. We compare the performance of these loops with that of a well-known coherent symbol sync loop and examine the conditions under which one is preferable over the other.

digital communications↗

NASA NTRS1983

Symbol synchronization for the TDRSS decoder

Each 8 bits out of the Viterbi decoder correspond to one symbol of the R/S code. Synchronization must be maintained here so that each 8-bit symbol delivered to the R/S decoder corresponds to an 8-bit symbol from the R/S encoder. Lack of synchronization, would cause an error in almost every R/S symbol since even a - 1-bit sync slip shifts every bit in each 8-bit symbol by one position, therby confusing the mapping betweeen 8-bit sequences and symbols. The error correcting capability of the R/S code would be exceeded. Possible ways to correcting this condition include: (1) designing the R/S decoder to recognize the overload and shifting the output sequence of the inner decoder to establish a different sync state; (2) using the characteristics of the inner decoder to establish symbol synchronization for the outer code, with or without a deinterleaver and an interleaver; and (3) modifying the encoder to alternate periodically between two sets of generators.

Costello, D. J., Jr.↗

NASA NTRS1989

Multiple symbol differential detection of uncoded and trellis coded MPSK

A differential detection for MPSK, which uses a multiple symbol observation interval, is presented and its performance analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. As such the performance of this multiple symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases, M, and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded and trellis coded MPSK.

Divsalar, Dariush↗

NASA NTRS1990

Multiple-symbol differential detection of MPSK

A differential detection technique for MPSK (multiple-phase shift keying), which uses a multiple-symbol observation interval, is presented, and its performance is analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. Thus, the performance of this multiple-symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases M and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded MPSK.

Divsalar, Dariush↗

NASA NTRS1991

A comparison of Manchester symbol tracking loops for block 5 applications

The linearized tracking errors of three Manchester (biphase coded) symbol tracking loops are compared to determine which is appropriate for Block 5 receiver applications. The first is a nonreturn to zero (NRZ) symbol synchronizer loop operating at twice the symbol rate (NRZ x 2) so that it operates on half symbols. The second near optimally processes the mid-symbol transitions and ignores the between symbol transitions. In the third configuration, the first two approaches are combined as a hybrid to produce the best performance. Although this hybrid loop is the best at low symbol signal to noise ratios (SNRs), it has about the same performance as the NRZ x 2 loop at higher SNRs (greater than 0-dB E sub s/N sub 0). Based on this analysis, it is tentatively recommended that the hybrid loop be implemented for Manchester data in the Block 5 receiver. However, the high data rate case and the hardware implications of each implementation must be understood and analyzed before the hybrid loop is recommended unconditionally.

Holmes, J. K.↗

DOE OSTI2022

GSoFa: Scalable Sparse Symbolic LU Factorization on GPUs

Decomposing a matrix $\mathbf {A}$ into a lower matrix $\mathbf {L}$ and an upper matrix $\mathbf {U}$, which is also known as LU decomposition, is an essential operation in numerical linear algebra. For a sparse matrix, LU decomposition often introduces more nonzero entries in the $\mathbf {L}$ and $\mathbf {U}$ factors than in the original matrix. A symbolic factorization step is needed to identify the nonzero structures of $\mathbf {L}$ and $\mathbf {U}$ matrices. Attracted by the enormous potentials of the Graphics Processing Units (GPUs), an array of efforts have surged to deploy various LU factorization steps except for the symbolic factorization, to the best of our knowledge, on GPUs. This article introduces gSoFa, the first GPU-based symbolic factorization design with the following three optimizations to enable scalable LU symbolic factorization for nonsymmetric pattern sparse matrices on GPUs. First, here we introduce a novel fine-grained parallel symbolic factorization algorithm that is well suited for the Single Instruction Multiple Thread (SIMT) architecture of GPUs. Second, we tailor supernode detection into a SIMT friendly process and strive to balance the workload, minimize the communication and saturate the GPU computing resources during supernode detection. Third, we introduce a three-pronged optimization to reduce the excessive space consumption problem faced by multi-source concurrent symbolic factorization. Taken together, gSoFa achieves up to 31× speedup from 1 to 44 Summit nodes (6 to 264 GPUs) and outperforms the state-of-the-art CPU project, on average, by 5×. Notably, gSoFa also achieves up to 47 percent of the peak memory throughput of a V100 GPU in the Summit Supercomputer.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2014

Improving Coverage of Test Cases Generated by Symbolic PathFinder for Programs with Loops

Symbolic execution is a program analysis technique that is used for many purposes, one of which is test-case generation. For loop-free programs, this generates a test-set that achieves path coverage. Program loops, however, imply exponential growth of the number of paths in the best case and non-termination in the worst case. In practice, the number of loop unwindings needs to be bounded for analysis. We consider symbolic execution in the context of the tool Symbolic Pathfinder. This tool extends the model-checker Java Pathfinder and relies on its bounded state-space exploration for termination. We present an implementation of k-bounded loop unwinding, which increases the amount of user-control over the symbolic execution of loops. Bounded unwinding can be viewed as a naive way to prune paths through loops. When using symbolic execution for test-case generation, naively pruning paths is likely at the cost of coverage. In order to improve coverage of branches within a loop body, we present a technique that semi-automatically concretizes variables used in a loop. The basic technique is limited and we therefore present annotations to manually steer symbolic execution towards certain branches, as well as ideas on how the technique can be extended to be more widely applicable.

Programs With Loops↗

DOE OSTI2015

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4, 7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the 7 ll 6 collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the threeloop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n > 6.

1/N Expansion↗

DOE OSTI2023

Language model-accelerated deep symbolic optimization

Symbolic optimization methods have been used to solve varied challenging and relevant problems such as symbolic regression and neural architecture search. However, the current state of the art typically learns each problem from scratch and is unable to leverage pre-existing knowledge and datasets that are available for many applications. Here, inspired by the similarity between sequence representations learned in natural language processing and the formulation of symbolic optimization as a discrete sequence optimization problem, we propose language model-accelerated deep symbolic optimization (LA-DSO), a method that leverages language models to learn symbolic optimization solutions more efficiently. We demonstrate LA-DSO in two tasks: symbolic regression, which allows us to perform extensive experimentation due to its low computation requirements, and computational antibody optimization, which shows that our proposal accelerates learning in challenging real-world problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1971

Applications of symbolic computing methods to the dynamic analysis of large systems

Since the symbolic computing language is very well suited to the operations with algebraic equations, techniques use the transfer function concept as a tool for the analysis of large linear dynamic systems. Techniques were coded in the experimental symbolic computer language FORMAC. The first of these approaches, REDUCE 1, establishes the techniques and a computer program to symbolically reduce arbitrary block diagrams associated with large systems for desired transfer functions. Symbolic closed form solutions are determined in several forms including an expanded form in terms of the driving frequencies and system constants. Programs are also written to numerically evaluate the symbolic solutions. A second computer program, REDUCE 2, is also based on the use of symbolic computing methods and was written to accommodate large engineering systems.

Lorenzo, C. F.↗

NASA NTRS1986

Antenna arraying of Voyager telemetry signals by symbol stream combining

Telemetry signals received from the Voyager 2 spacecraft at Deep Space Stations at Parkes and Canberra, Australia, on February 6, 1986, were combined by the method of symbol stream combining. This second demonstration of symbol stream combining followed the International Cometary Explorer (ICE) demonstration at Giacobini-Zinner encounter in September 1985. The Voyager demonstration was at a symbol rate of 43.2 ksymb/s, compared to 2 ksymb/s for ICE. Recording, playback, and combining at this higher rate were demonstrated. The average symbol signal-to-noise ratio (SNR) of the combined data was 2.84 dB, or 0.23 dB less than the sum of the SNRs of the two imput symbol streams. This 0.23 loss from ideal combining was due to use of 4-bit quantization of the input symbol stream and imperfect scaling. A practical implementation with 8-bit quantization could achieve combining losses of under 0.05 dB over a wide dynamic range of input signal levels.

Hurd, W. J.↗

NASA NTRS2012

Memoized Symbolic Execution

This paper introduces memoized symbolic execution (Memoise), a novel approach for more efficient application of forward symbolic execution, which is a well-studied technique for systematic exploration of program behaviors based on bounded execution paths. Our key insight is that application of symbolic execution often requires several successive runs of the technique on largely similar underlying problems, e.g., running it once to check a program to find a bug, fixing the bug, and running it again to check the modified program. Memoise introduces a trie-based data structure that stores the key elements of a run of symbolic execution. Maintenance of the trie during successive runs allows re-use of previously computed results of symbolic execution without the need for re-computing them as is traditionally done. Experiments using our prototype embodiment of Memoise show the benefits it holds in various standard scenarios of using symbolic execution, e.g., with iterative deepening of exploration depth, to perform regression analysis, or to enhance coverage.

Yang, Guowei↗

NASA NTRS2010

Symbolic Analysis of Concurrent Programs with Polymorphism

The current trend of multi-core and multi-processor computing is causing a paradigm shift from inherently sequential to highly concurrent and parallel applications. Certain thread interleavings, data input values, or combinations of both often cause errors in the system. Systematic verification techniques such as explicit state model checking and symbolic execution are extensively used to detect errors in such systems [7, 9]. Explicit state model checking enumerates possible thread schedules and input data values of a program in order to check for errors [3, 9]. To partially mitigate the state space explosion from data input values, symbolic execution techniques substitute data input values with symbolic values [5, 7, 6]. Explicit state model checking and symbolic execution techniques used in conjunction with exhaustive search techniques such as depth-first search are unable to detect errors in medium to large-sized concurrent programs because the number of behaviors caused by data and thread non-determinism is extremely large. We present an overview of abstraction-guided symbolic execution for concurrent programs that detects errors manifested by a combination of thread schedules and data values [8]. The technique generates a set of key program locations relevant in testing the reachability of the target locations. The symbolic execution is then guided along these locations in an attempt to generate a feasible execution path to the error state. This allows the execution to focus in parts of the behavior space more likely to contain an error.

Rungta, Neha Shyam↗

DOE OSTI2013

MINING NUCLEAR TRANSIENT DATA THROUGH SYMBOLIC CONVERSION

Dynamic Probabilistic Risk Assessment (DPRA) methodologies generate enormous amounts of data for a very large number of simulations. The data contain temporal information of both the state variables of the simulator and the temporal status of specific systems/components. In order to measure system performances, limitations and resilience, such data need to be carefully analyzed with the objective of discovering the correlations between sequence/timing of events and system dynamics. A first approach toward discovering these correlations from data generated by DPRA methodologies has been performed by organizing scenarios into groups using classification or clustering based algorithms. The identification of the correlations between system dynamics and timing/sequencing of events is performed by observing the temporal distribution of these events in each group of scenarios. Instead of performing “a posteriori” analysis of these correlations, this paper shows how it is possible to identify the correlations implicitly by performing a symbolic conversion of both continuous (temporal profiles of simulator state variables) and discrete (status of systems and components) data. Symbolic conversion is performed for each simulation by properly quantizing both continuous and discrete data and then converting them as a series of symbols. After merging both series together, a temporal phrase is obtained. This phrase preserves duration, coincidence and sequence of both continuous and discrete data in a uniform and consistent manner. In this paper it is also shown that by using specific distance measures, it is still possible to post-process such symbolic data using clustering and classification techniques but in considerably less time since the memory needed to store the data is greatly reduced by the symbolic conversion.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series

We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Here, our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to elliptic polylogarithms and iterated integrals of modular forms. We illustrate how to use our formalism to derive relations among elliptic polylogarithms, in complete analogy with the non-elliptic case. We then analyze the symbol alphabet of elliptic polylogarithms evaluated at rational points, and we observe that it is given by Eisenstein series for a certain congruence subgroup. We apply our formalism to hypergeometric functions that can be expressed in terms of elliptic polylogarithms and show that they can equally be written in terms of iterated integrals of Eisenstein series. Finally, we present the symbol of the equal-mass sunrise integral in two space-time dimensions. The symbol alphabet involves Eisenstein series of level six and weight three, and we can easily integrate the symbol in terms of iterated integrals of Eisenstein series.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Spread Spectrum Symbol Detection With Blind Interference Suppression in FBMC-SS

Recent works have demonstrated Filter Bank Multicarrier Spread Spectrum (FBMC-SS) to be a robust communication scheme in the presence of high-power interferers. Existing FBMC-SS symbol detector designs based on analysis filter banks (AFB) suggest using an optimal combining scheme to suppress the interferers, necessitating some noise/interference power estimation method. In this paper, we introduce a symbol detector with blind interference suppression by extending a recently developed packet detection method. We then provide an analysis to show that the existing AFB-based symbol detector and the one proposed in this paper are equivalent in typical usage scenarios. A fully-fledged receiver design is proposed utilizing this symbol detector, with specifics presented for estimation of the channel impulse response and carrier frequency offset (CFO). We also outline a method of iterating upon the channel and CFO estimations to improve the quality of both parameters. Moreover, a modification to allow improved performance of the symbol detector at high SNR is provided. Finally, simulated performance results are presented to corroborate these findings and demonstrate the efficiency of this receiver design.

99 GENERAL AND MISCELLANEOUS↗