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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

AlgaeOrtho, a bioinformatics tool for processing ortholog inference results in algae

Introduction: Microalgae constitute a prominent feedstock for producing biofuels and biochemicals by virtue of their prolific reproduction, high bioproduct accumulation, and the ability to grow in brackish and saline water. However, naturally occurring wild type algal strains are rarely optimal for industrial use; therefore, bioengineering of algae is necessary to generate superior performing strains that can address production challenges in industrial settings, particularly the bioenergy and bioproduct sectors. One of the crucial steps in this process is deciding on a bioengineering target: namely, which gene/protein to differentially express. These targets are often orthologs which are defined as genes/proteins originating from a common ancestor in divergent species. Although bioinformatics tools for the identification of protein orthologs already exist, processing the output from such tools is nontrivial, especially for a researcher with little or no bioinformatics experience. Methods: The present study introduces AlgaeOrtho, a user-friendly tool that builds upon the SonicParanoid orthology inference tool (based on an algorithm that identifies potential protein orthologs based on amino acid sequences) and the PhycoCosm database from JGI (Joint Genome Institute) to help researchers identify orthologs of their proteins of interest in multiple diverse algal species. Results: The output of this application includes a table of the putative orthologs of their protein of interest, a heatmap showing sequence similarity (%), and an unrooted tree of the putative protein orthologs. Notably, the tool would be instrumental in identifying novel bioengineering targets in different algal strains, including targets in not-fully annotated algal species, since it does not depend on existing protein annotations. We tested AlgaeOrtho using three case studies, for which orthologs of proteins relevant to bioengineering targets, were identified from diverse algal species, demonstrating its ease of use and utility for bioengineering researchers. Discussion: This tool is unique in the protein ortholog identification space as it can visualize putative orthologs, as desired by the user, across several algal species.

09 BIOMASS FUELS↗
NASA NTRS2003

An in silico assessment of gene function and organization of the phenylpropanoid pathway metabolic networks in Arabidopsis thaliana and limitations thereof

The Arabidopsis genome sequencing in 2000 gave to science the first blueprint of a vascular plant. Its successful completion also prompted the US National Science Foundation to launch the Arabidopsis 2010 initiative, the goal of which is to identify the function of each gene by 2010. In this study, an exhaustive analysis of The Institute for Genomic Research (TIGR) and The Arabidopsis Information Resource (TAIR) databases, together with all currently compiled EST sequence data, was carried out in order to determine to what extent the various metabolic networks from phenylalanine ammonia lyase (PAL) to the monolignols were organized and/or could be predicted. In these databases, there are some 65 genes which have been annotated as encoding putative enzymatic steps in monolignol biosynthesis, although many of them have only very low homology to monolignol pathway genes of known function in other plant systems. Our detailed analysis revealed that presently only 13 genes (two PALs, a cinnamate-4-hydroxylase, a p-coumarate-3-hydroxylase, a ferulate-5-hydroxylase, three 4-coumarate-CoA ligases, a cinnamic acid O-methyl transferase, two cinnamoyl-CoA reductases) and two cinnamyl alcohol dehydrogenases can be classified as having a bona fide (definitive) function; the remaining 52 genes currently have undetermined physiological roles. The EST database entries for this particular set of genes also provided little new insight into how the monolignol pathway was organized in the different tissues and organs, this being perhaps a consequence of both limitations in how tissue samples were collected and in the incomplete nature of the EST collections. This analysis thus underscores the fact that even with genomic sequencing, presumed to provide the entire suite of putative genes in the monolignol-forming pathway, a very large effort needs to be conducted to establish actual catalytic roles (including enzyme versatility), as well as the physiological function(s) for each member of the (multi)gene families present and the metabolic networks that are operative. Additionally, one key to identifying physiological functions for many of these (and other) unknown genes, and their corresponding metabolic networks, awaits the development of technologies to comprehensively study molecular processes at the single cell level in particular tissues and organs, in order to establish the actual metabolic context.

NASA Program Fundamental Space Biology↗
DOE OSTI2024

Human Host Cellular Response to HCoV-229E Infection Proteomics (ACS-JM-DP2)

The purpose of this experiment was to evaluate the human host cellular response to wild-type Human coronavirus strain 229E (HCoV-229E) infection. Sample data was obtained for mock and infected immortalized human lung epithelial cells (A549) (MOI 5) nuclear extracts, immortalized human lung fibroblasts cells (MRC5) (MOI5) nuclear extracts, and primary human airway epithelial (HAE) (MOI 3) cells from lung tissue and processed for proteome analysis. Processed datasets are openly accessible from the download button and contain secondary processed proteomic results files and supporting metadata materials. Experimental proteomics samples were prepared using Limited Proteolysis (LiP) methods for Label-free quantification (LFQ) and global proteomic evaluation. Sample data was acquired using a Q-Exactive HF-X mass spectrometer and was processed and compiled using MaxQuant software (v.1.6.17.0). Processed proteomic data downloads include a sample naming key, processed MaxQuant results/parameters, and protein annotated relative abundance files. See corresponding primary data accessions below and Viral Experiment LiP Analysis source code supporting data transparency and reuse. Experimental transcriptomics samples were collected in parallel and processed for RNA sequencing (RNA-Seq) as summarized under ACS-DP1 (https://data.pnnl.gov/group/nodes/dataset/34069).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

MVP: a modular viromics pipeline to identify, filter, cluster, annotate, and bin viruses from metagenomes

While numerous computational frameworks and workflows are available for recovering prokaryote and eukaryote genomes from metagenome data, only a limited number of pipelines are designed specifically for viromics analysis. With many viromics tools developed in the last few years alone, it can be challenging for scientists with limited bioinformatics experience to easily recover, evaluate quality, annotate genes, dereplicate, assign taxonomy, and calculate relative abundance and coverage of viral genomes using state-of-the-art methods and standards. Here, we describe Modular Viromics Pipeline (MVP) v.1.0, a user-friendly pipeline written in Python and providing a simple framework to perform standard viromics analyses. MVP combines multiple tools to enable viral genome identification, characterization of genome quality, filtering, clustering, taxonomic and functional annotation, genome binning, and comprehensive summaries of results that can be used for downstream ecological analyses. Overall, MVP provides a standardized and reproducible pipeline for both extensive and robust characterization of viruses from large-scale sequencing data including metagenomes, metatranscriptomes, viromes, and isolate genomes. As a typical use case, we show how the entire MVP pipeline can be applied to a set of 20 metagenomes from wetland sediments using only 10 modules executed via command lines, leading to the identification of 11,656 viral contigs and 8,145 viral operational taxonomic units (vOTUs) displaying a clear beta-diversity pattern. Further, acting as a dynamic wrapper, MVP is designed to continuously incorporate updates and integrate new tools, ensuring its ongoing relevance in the rapidly evolving field of viromics. MVP is available at https://gitlab.com/ccoclet/mvp and as versioned packages in PyPi and Conda.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Coupling Metabolic Source Isotopic Pair Labeling and Genome Wide Association for Metabolite and Gene Annotation in Plants (Final Technical Report)

In this project, we applied our labeling pipeline to Arabidopsis and sorghum by feeding tissues with isotopically labeled versions of commercially available amino acids to identify all metabolite features that incorporate the label. In sorghum, we fed five accessions, sampled across the diversity of sorghum, to identify the precursor-of-origin for metabolites that vary between accessions as well as those that may be missing from a single reference genotype. This provided us with precursor-of-origin annotation for thousands of unknown metabolites. We then used GWA to map genes responsible for the synthesis of precursor-of-origin classified metabolites. For sorghum leaf and root ducible metabolites, we performed untargeted metabolomics on leaf and root tissues from 300 diverse genotyped sorghum inbred lines. The amino acid precursor-of-origin metabolite library were then used to identify the corresponding metabolites in the GWA data sets and to identify novel gene-metabolite associations. Finally, we utilized existing and newly generated sequenced EMS mutants of sorghum to validate the predicted gene-metabolite relationships that our labelling analysis identified. In parallel, we conducted similar feeding experiments in Arabidopsis to categorize metabolites based on precursor-of-origin, identify those that vary across our existing Arabidopsis metabolite GWA dataset, and identify genes required for the synthesis of each metabolite. To provide an independent test of gene annotation and pathway involvement, we tested the GWA gene-metabolite associations in Arabidopsis by analyzing the metabolic phenotypes of gene knockouts. Genes of particular interest from both sorghum and Arabidopsis were studied in detail by directly measuring the activity of the corresponding enzymes following heterologous expression. In summary, this work classified as-yet-unknown amino acid-derived metabolites and identified genes involved in their production generated through “omics” technologies. This information was used to validate gene function and identify new metabolism in Arabidopsis and sorghum.

09 BIOMASS FUELS↗
DOE OSTI2026

The small protein SbtC is a functional component of the CO 2 concentrating mechanism in Synechocystis sp. PCC 6803

Oxygenic phototrophs fix CO 2 via the enzyme ribulose-1,5-bisphosphate carboxylase/oxygenase (RubisCO), which shows relatively low CO 2 affinity and specificity. To circumvent low and fluctuating CO 2 concentrations in aquatic systems, cyanobacteria and algae have evolved sophisticated inorganic carbon (Ci) concentrating mechanisms (CCMs). Bicarbonate transporters such as SbtA play a crucial role in the cyanobacterial CCM and hence display multiple layers of tight regulation. Control of sbtA gene expression and corresponding transporter activity involves the PII-like protein SbtB, whose gene is frequently co-transcribed with sbtA. A previously non-annotated gene located upstream of the sbtAB operon in the model Synechocystis sp. PCC 6803 encodes the small protein SbtC, composed of 80 amino acids. Presence of SbtC was confirmed by immunoblotting of the sbtC-coding sequence fused to a Flag-tag. Similar to sbtAB , transcription of the sbtC locus is induced by low CO 2 availability; however, it is controlled independently. Mutation of the sbtC locus in a wild-type background produced only a mild phenotype, even under low CO 2 , but impaired diurnal growth resembled that of the mutant ΔsbtB . Biochemical analysis indicated a trimeric SbtABC complex in the membrane. Bicarbonate leakage from cells was strongly elevated when either sbtB or sbtC was deleted from recombinant Synechocystis strains harboring only SbtA as single Ci uptake system. Here, our results provide evidence that SbtC contributes to the formation of the SbtAB complex, thereby regulating bicarbonate exchange at the cytoplasmic membrane. Well-conserved SbtC-like proteins encoded in the neighborhood of sbtAB exist in many cyanobacterial genomes, pointing toward an important role in the cyanobacterial CCM.

Walke, Peter [Univ. of Rostock (Germany)] (ORCID:0↗
NASA NTRS2003

The Thiamin Pyrophosphate-Motif

Using databases the authors have identified a common thiamin pyrophosphate (TPP)-motif in the family of functionally diverse TPP-dependent enzymes. This common motif consists of multimeric organization of subunits, two catalytic centers, common amino acid sequence, and specific contacts to provide a flip-flop, or alternate site, mechanism of action. Each catalytic center [PP:PYR] is formed at the interface of the PP-domain binding the magnesium ion, pyrophosphate and aminopyrimidine ring of TPP, and the PYR-domain binding the aminopyrimidine ring of that cofactor. A pair of these catalytic centers constitutes the catalytic core [PP:PYR]* within these enzymes. Analysis of the structural elements of this catalytic core reveals novel definition of the common amino acid sequences, which are GX@&(G)@XXGQ, and GDGX25-30 within the PP- domain, and the E&(G)@XXG@ within the PYR-domain, where Q, corresponds to a hydrophobic amino acid. This TPP-motif provides a novel tool for annotation of TPP-dependent enzymes useful in advancing functional proteomics.

Dominiak, Paulina M.↗
DOE OSTI2024

Building a FAIR data ecosystem for incorporating single-cell transcriptomics data into agricultural genome to phenome research

Introduction The agriculture genomics community has numerous data submission standards available, but the standards for describing and storing single-cell (SC, e.g., scRNA- seq) data are comparatively underdeveloped. Methods To bridge this gap, we leveraged recent advancements in human genomics infrastructure, such as the integration of the Human Cell Atlas Data Portal with Terra, a secure, scalable, open-source platform for biomedical researchers to access data, run analysis tools, and collaborate. In parallel, the Single Cell Expression Atlas at EMBL-EBI offers a comprehensive data ingestion portal for high-throughput sequencing datasets, including plants, protists, and animals (including humans). Developing data tools connecting these resources would offer significant advantages to the agricultural genomics community. The FAANG data portal at EMBL-EBI emphasizes delivering rich metadata and highly accurate and reliable annotation of farmed animals but is not computationally linked to either of these resources. Results Herein, we describe a pilot-scale project that determines whether the current FAANG metadata standards for livestock can be used to ingest scRNA-seq datasets into Terra in a manner consistent with HCA Data Portal standards. Importantly, rich scRNA-seq metadata can now be brokered through the FAANG data portal using a semi-automated process, thereby avoiding the need for substantial expert curation. We have further extended the functionality of this tool so that validated and ingested SC files within the HCA Data Portal are transferred to Terra for further analysis. In addition, we verified data ingestion into Terra, hosted on Azure, and demonstrated the use of a workflow to analyze the first ingested porcine scRNA-seq dataset. Additionally, we have also developed prototype tools to visualize the output of scRNA-seq analyses on genome browsers to compare gene expression patterns across tissues and cell populations. This JBrowse tool now features distinct tracks, showcasing PBMC scRNA-seq alongside two bulk RNA-seq experiments. Discussion We intend to further build upon these existing tools to construct a scientist-friendly data resource and analytical ecosystem based on Findable, Accessible, Interoperable, and Reusable (FAIR) SC principles to facilitate SC-level genomic analysis through data ingestion, storage, retrieval, re-use, visualization, and comparative annotation across agricultural species.

Genetics & Heredity↗
DOE OSTI2024

RolyPoly (rp) v0.1.0

The Rolypoly pipeline is designed to process raw RNA-seq data and identify potential RNA viral sequences. It is split into several self contained steps: 1. input data filtering and QC, 2. Genome assembly and refinement, 3. Assembly filtering, 4. Mapping to known RNA viral genomes, 5. Searching for RNA viral marker genes. 6. Genome functional and structural annotation. 6. Report preparation and potential downstream analysis The last module, may include taxonomic assignment, host range estimation, and phenotypic prediction. There are many similar software, but they focus on human related viruses, and lack the downstream applications or differ in their sensitivity. The initial user base are non-computational microbial ecologists who wish to better understand the potential RNA viruses in their own generated samples.

Neri, Uri↗
DOE OSTI2026

Database of virus genomes from ultra-deep sequencing of wastewater

Researchers at University of Missouri have conducted ultra-deep RNA sequencing of viral concentrates from wastewater (1 billion Illumina reads per sample). The resulting dataset spans 321 samples collected weekly from 11 cities between 2023-2025. As part of a tri-lab collaboration, scientists at LLNL and LANL cleaned, assembled, and annotated this metagenomic data, identifying nearly 200,000 viral genomes. Careful data curation resulted in a database containing 21,015 high-quality, near-complete viral genomes from wastewater. This database contains viruses predicted to infect a range of hosts including bacteria (most common viruses), plants (most abundant viruses), and vertebrates (rarest viruses). There are also numerous novel viruses that could not be well identified and whose host(s) are unknown. Just 7% of all genomes in the wastewater virus database had genus-level matches in the public NCBI database, and 17% matched to a recently created metagenomic virus database at that level (metaVR). The database will provide baseline information about viruses in wastewater that may be used to additional identify novel viruses during ongoing monitoring

Allen, Jonathan [Lawrence Livermore National Labor↗
NASA NTRS2019

Local frustration around enzyme active sites

Conflicting biological goals often meet in the specification of protein sequences for structure and function. Overall, strong energetic conflicts are minimized in folded native states according to the principle of minimal frustration, so that a sequence can spontaneously fold, but local violations of this principle open up the possibility to encode the complex energy landscapes that are required for active biological functions. We survey the local energetic frustration patterns of all protein enzymes with known structures and experimentally annotated catalytic residues. In agreement with previous hypotheses, the catalytic sites themselves are often highly frustrated regardless of the protein oligomeric state, overall topology, and enzymatic class. At the same time a secondary shell of more weakly frustrated interactions surrounds the catalytic site itself. We evaluate the conservation of these energetic signatures in various family members of major enzyme classes, showing that local frustration is evolutionarily more conserved than the primary structure itself.

Maria I. Freiberger↗
DOE OSTI2024

Fungal diversity and function in metagenomes sequenced from extreme environments

Fungi are increasingly recognized as key players in various extreme environments. Here we present an analysis of publicly-sourced metagenomes from global extreme environments, focusing on fungal taxonomy and function. The majority of 855 selected metagenomes contained scaffolds assigned to fungi. Relative abundance of fungi was as high as 10% of protein-coding genes with taxonomic annotation, with up to 289 fungal genera per sample. Despite taxonomic clustering by environment, fungal communities were more dissimilar than archaeal and bacterial communities, both for within- and between-environment comparisons. Relatively abundant fungal classes in extreme environments included Dothideomycetes, Eurotiomycetes, Leotiomycetes, Pezizomycetes, Saccharomycetes, and Sordariomycetes. Broad generalists and prolific aerial spore formers were the most relatively abundant fungal genera detected in most of the extreme environments, bringing up the question of whether they are actively growing in those environments or just surviving as spores. More specialized fungi were common in some environments, such as zoosporic taxa in cryosphere water and hot springs. Relative abundances of genes involved in adaptation to general, thermal, oxidative, and osmotic stress were greatest in soda lake, acid mine drainage, and cryosphere water samples.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Strategies for community-sourced biocuration in bioinformatics: a case study on MIBiG 4.0

Biocuration is essential to transform molecular sequence data into standardized, machine-readable resources. Such curated datasets enable comparative analysis, predictive modeling, and data integration across bioinformatics platforms. While professional biocuration is resource-intensive and usually limited to institutional settings, community-driven approaches can mobilize large-scale annotation of specialized datasets and are more resilient to disruptions in scientific funding. Here, we present a model for community-powered curation applied to the Minimum Information about a Biosynthetic Gene Cluster (MIBiG) repository. Through a framework of workflows for metadata capture, annotation validation, and contributor coordination, the MIBiG 4.0 initiative recruited 267 scientists across 178 institutions from 33 countries, volunteering an estimated 4000 h of work. These efforts expanded the MIBiG repository by 22% and enhanced its usability in downstream molecular data analyses in comparative genomic analyses, natural product discovery, and machine learning applications. We provide strategies and actionable lessons for adopting this model, supporting the sustainability of curated bioinformatics resources central to nucleic acid research and related fields.

biocuration↗
DOE OSTI2025

Pangenomes suggest ecological-evolutionary responses to experimental soil warming

ABSTRACT Below-ground carbon transformations that contribute to healthy soils represent a natural climate change mitigation, but newly acquired traits adaptive to climate stress may alter microbial feedback mechanisms. To better define microbial evolutionary responses to long-term climate warming, we study microorganisms from an ongoing in situ soil warming experiment where, for over three decades, temperate forest soils are continuously heated at 5°C above ambient. We hypothesize that across generations of chronic warming, genomic signatures within diverse bacterial lineages reflect adaptations related to growth and carbon utilization. From our bacterial culture collection isolated from experimental heated and control plots, we sequenced genomes representing dominant taxa sensitive to warming, including lineages of Actinobacteria, Alphaproteobacteria, and Betaproteobacteria. We investigated genomic attributes and functional gene content to identify signatures of adaptation. Comparative pangenomics revealed accessory gene clusters related to central metabolism, competition, and carbon substrate degradation, with few functional annotations explicitly associated with long-term warming. Trends in functional gene patterns suggest genomes from heated plots were relatively enriched in central carbohydrate and nitrogen metabolism pathways, while genomes from control plots were relatively enriched in amino acid and fatty acid metabolism pathways. We observed that genomes from heated plots had less codon bias, suggesting potential adaptive traits related to growth or growth efficiency. Codon usage bias varied for organisms with similar 16S rrn operon copy number, suggesting that these organisms experience different selective pressures on growth efficiency. Our work suggests the emergence of lineage-specific trends as well as common ecological-evolutionary microbial responses to climate change. IMPORTANCE Anthropogenic climate change threatens soil ecosystem health in part by altering below-ground carbon cycling carried out by microbes. Microbial evolutionary responses are often overshadowed by community-level ecological responses, but adaptive responses represent potential changes in traits and functional potential that may alter ecosystem function. We predict that microbes are adapting to climate change stressors like soil warming. To test this, we analyzed the genomes of bacteria from a soil warming experiment where soil plots have been experimentally heated 5°C above ambient for over 30 years. While genomic attributes were unchanged by long-term warming, we observed trends in functional gene content related to carbon and nitrogen usage and genomic indicators of growth efficiency. These responses may represent new parameters in how soil ecosystems feedback to the climate system.

Choudoir, Mallory J. (ORCID:0000000291175150)↗
NASA NTRS2003

The Thiamin Pyrophosphate-Motif

Using databases the authors have identified a common thiamin pyrophosphate (TPP)-motif in the family of functionally diverse TPP-dependent enzymes. This common motif consists of multimeric organization of subunits and two catalytic centers. Each catalytic center (PP:PYR) is formed at the interface of the PP-domain binding the magnesium ion, pyrophosphate and amhopyrimidine ring of TPP, and the PYR-domain binding the aminopyrimidine ring of that cofactor. A pair of these catalytic centers constitutes the catalytic core (PP:PYR)(sub 2) within these enzymes. Analysis of the structural elements of this catalytic core reveals novel definition of the common amino acid sequences, which are GXPhiX(sub 4)(G)PhiXXGQ and GDGX(sub 25-30)NN in the PP-domain, and the EX(sub 4)(G)PhiXXGPhi in the PYR-domain, where Phi corresponds to a hydrophobic amino acid. This TPP-motif provides a novel tool for annotation of TPP-dependent enzymes useful in advancing functional proteomics.

Dominiak, P.↗
DOE OSTI2026

LibraryX: A Framework for Cross-Library-Call Optimization

Scientific applications utilize performance libraries as a software engineering concept: these libraries encapsulate important and well-understood (mathematical) operations, allow for reuse, and are implemented and tuned by experts. Domain scientists then implement complex algorithms based on these domainspecific libraries. While individual library calls are optimized, larger performance gains across sequences of calls—sometimes spanning multiple libraries—are often unrealized, forcing a trade-off between performance and implementation complexity.To overcome this issue, we propose LibraryX, an approach and a system that allows for cross-library-call optimization even when library calls stem from multiple performance libraries. LibraryX annotates library calls with semantic information and optimizes entire directed acyclic graphs (DAGs) of calls dynamically using the SPIRAL code generation system. We demonstrate its effectiveness across a range of memory bound workloads, achieving significant speedups on Nvidia, AMD, and Intel accelerators compared to code using native libraries without cross-call optimization.

Rao, Sanil [Carnegie Mellon University,Department ↗
DOE OSTI2026

Finding the missing pieces: filling gaps that impede the translation of omics data into models

High-throughput omics technologies such as DNA sequencing have made the sequencing and computational assembly of microbial genomes recovered from the environment relatively routine. Computational inference of the protein products encoded by these genomes, and the associated biochemical functions, should enable the accurate prediction and modeling of microbial metabolism, organismal interactions, and ecosystem processes. However, a lack of scalable, probabilistic protein annotation tools limits the full potential of modeling for understanding the metabolism and biogeochemical cycles of microbial communities. Our approach to improve inference of protein annotations and metabolic models relied on learning from and emulating expert manual curation, leveraging software engineering and data science best practices to scale up the throughput and accuracy of annotations and metabolic model construction, building software to objectively evaluate different annotation strategies, and more closely linking the protein annotation and metabolic model inference process. Outcomes of this research include several improved or new computational tools, including DRAM (Distilled and Refined Annotation of Metabolism) for annotating microbial genomes with protein function and metabolic traits, CAMPER (Curated Annotations for Microbial Polyphenol Enzymes and Reactions) for annotating key polyphenol metabolisms, EC-Bench for comprehensive and unbiased benchmarking of annotation tools, and several apps available via the DOE Systems Biology Knowledgebase (KBase) for building genome-scale metabolic models. We demonstrate that these tools allow us to scalably annotate and understand thousands of genomes for microbial communities from a variety of systems and test cases, including rivers, thawing permafrost, and gut microbiomes. All of these computational tools are available as open-source software, with most broadly and easily accessible to the scientific community via KBase apps.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1983

Verification of Numerical Algorithms

The following strategy is suggested for specification and proof: (1) Defer the construction of a formal program specification with respect to I/O assertions unit the correctness of the program with respect to an abstract mathematical model of program intent is demonstrated. (2) Prove that an abstract machine (using infinite precision arithmetic) would compute that object exactly. (3) Prove that the computational sequences of arithmetic operations that occur in the abstract machine must be precisely the same at every step as those occurring on an actual machine (with finite precision arithmetic), executing the same program. (4) Use a Verification Conditions VC-generator that knows about the semantics of arithmetic operations to annotate the program with assertions that bound (or in some circumstances estimate) the difference between the actual machine state variables and the corresponding ones of the abstract machine. Construct the formal program specification by combining the verification conditions into theorems about computational error that can be proved with mechanical assistance.

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