Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICAL LOGIC”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Investigating Formal Methods Tools and their Applicability for Hardware Vulnerability Remediation

Formal methods use mathematical logic and equations to prove that a system or code is secure. In this poster, I examine existing formal methods tools and their application for projects working to remediate vulnerabilities in hardware and hardware description language. This poster is focused on the tools ReWire and AutoGenILA and I hope to evaluate their benefits and weaknesses with the intention of creating an internal report on the application and weaknesses of existing formal methods tools and identifying gaps for future formal methods tool creation.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Properties of Existentially Closed Companions

Necessary and sufficient conditions are stated for an arbitrary theory to be an elementary theory for a class of its existentially closed models. Conditions are given under which some existentially closed model simultaneously realizes one maximal existential type and omits another. We also prove a theorem on a prime existentially closed model over a maximal existential type. Considerable complexity of existentially closed structures and their theories was noted by A. Macintyre. Therefore, the examples of existentially closed companions having any finite or countable number of pairwise non elementarily equivalent existentially closed models constructed here are of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Continuous solutions to a class of first-order fuzzy differential equations with discontinuous coefficients

In this paper, we study the continuity of solution functions to a class of fuzzy differential equations (FDEs) in the form y{sup ′}(t)=((φ(t))/((t−α){sup p}))⊙y(t)+ψ(t), where the coefficient function ((φ(t))/((t−α){sup p})) is a discontinuous function at the point t=α and α is an inner point of the interval under study. At first, the continuity of solutions for the crisp case of the problem is investigated and those results are extended to the fuzzy case of the problem from the view point of strongly generalized differentiability (G-differentiability). Next, we obtain explicit formulas of solutions and the conditions of their existence for a special class of these problems. Finally, the results are illustrated by solving some examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment

The objective of this paper is to focus on multi-attribute decision-making for interval-valued intuitionistic fuzzy set environment based on set pair analysis (SPA). For it, the major component of the SPA known as connection number has been constructed based on the set pairs between two preference values consists of every attribute and ideal pairs of it. Based on these connection numbers, an extension of technique for order of preference by similarity to ideal solution method is developed by combining the proposed connection number for IVIFSs and hence finding the best alternative(s) using relative degree of closeness coefficient. An illustrative example has been given for demonstrating the approach and compares their performance with some existing measures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Runge–Kutta method for solving fuzzy differential equations under generalized differentiability

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. The Runge–Kutta approximation method is implemented and its error analysis, which guarantees pointwise convergence, is given. The method applicability is illustrated by solving a linear first-order fuzzy differential equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

TOPSIS with similarity measure for MADM applied to network selection

In this article, a new method is introduced to handle fuzzy multi-attribute decision-making problems. The method preserves fuzziness in the preference technique to avoid the drawbacks of defuzzification. The study modifies the technique of order preference by similarity to an ideal solution (TOPSIS) for interval-valued fuzzy numbers. The traditional TOPSIS uses the relative degree of closeness to rank the alternatives. Instead, a similarity measure based on map distance is used for preference. The degree of similarity between each attribute of an alternative and the ideal solution is computed, and a similarity matrix is formed. Then, the total degree of similarity for all the attributes of an alternative is used for ranking. The alternative corresponding to the one norm of the similarity matrix is the best alternative. Thus, the comparison is done on a fuzzy basis to avoid the loss of information due to converting the elements of the weighted normalized decision matrix to crisp values by defuzzification. An illustrative example is given to demonstrate the approach. A practical example in network selection to optimize vertical hand offs is solved where both user preferences and network parameters are treated as interval-valued fuzzy numbers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Designing Secure and Resilient Cyber-Physical Systems Using Formal Models

This work-in-progress paper proposes a design methodology that addresses the complexity and heterogeneity of cyber-physical systems (CPS) while simultaneously proving resilient control logic and security properties. The design methodology involves a formal methods-based approach by translating the complex control logic and security properties of a water flow CPS into timed automata. Timed automata are a formal model that describes system behaviors and properties using mathematics-based logic languages with precision. Due to the semantics that are used in developing the formal models, verification techniques, such as theorem proving and model checking, are used to mathematically prove the specifications and security properties of the CPS. This work-in-progress paper aims to highlight the need for formalizing plant models by creating a timed automata of the physical portions of the water flow CPS. Extending the time automata with control logic, network security, and privacy control processes is investigated. The final model will be formally verified to prove the design specifications of the water flow CPS to ensure efficacy and security.

42 ENGINEERING↗
DOE OSTI2018

On the Depth of k-Valued Logic Functions Over Arbitrary Bases

The behavior of the Shannon function of the depth of k-valued logic functions realized by circuits over an arbitrary complete basis is examined. For all k, k ≥ 3, for an arbitrary basis of k-valued logic functions, the existence of the asymptotic behavior of the Shannon function of the depth is established. The asymptotic behavior is linear for finite bases and it is constant or logarithmic for infinite bases. Thus, the complete picture of asymptotic behavior of the Shannon function of the depth is obtained for all k, k ≥ 2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Cosmic logic: a computational model

We initiate a formal study of logical inferences in context of the measure problem in cosmology or what we call cosmic logic. We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized cosmological systems. The construction is based on a particular model of computation, developed by Alan Turing, with cosmic observers (CO), cosmic measures (CM) and cosmic symmetries (CS) described by Turing machines. CO machines always start with a blank tape and CM machines take CO's Turing number (also known as description number or Gödel number) as input and output the corresponding probability. Similarly, CS machines take CO's Turing number as input, but output either one if the CO machines are in the same equivalence class or zero otherwise. We argue that CS machines are more fundamental than CM machines and, thus, should be used as building blocks in constructing CM machines. We prove the non-computability of a CS machine which discriminates between two classes of CO machines: mortal that halts in finite time and immortal that runs forever. In context of eternal inflation this result implies that it is impossible to construct CM machines to compute probabilities on the set of all CO machines using cut-off prescriptions. The cut-off measures can still be used if the set is reduced to include only machines which halt after a finite and predetermined number of steps.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A note on the logistic equation subject to uncertainties in parameters

This paper discusses the logistic equation subject to uncertainties in the intrinsic growth rate, α, in the initial population density, N{sub 0}, and in the environmental carrying capacity, K. These parameters are treated as independent random variables. The random variable transformation method is applied to compute the first probability density function of the time–population density, N(t), and of its inflection point, t{sup ∗}. Results for the density functions of N(t), for a fixed t>0, and t{sup ∗} are also provided for α, N{sub 0} and K uniformly distributed. Finally, numerical experiments illustrate the proposed theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Applications of Fuzzy Logic for Tritium Sensing Technology

Fuzzy Logic is a mathematical method that can represent human-like decisions by analyzing vagueness. The project is a practical approach for evaluating sensors using a fuzzy group best-worst method. Results What is the best sensor? The fuzzy logic methods give an answer to that through a selection system. The relationship between the inputs and the outputs gives consumers an understanding of how the best sensor was found through a scoring of each quality/criteria and their corresponding sub-criteria through expert opinion.

Holman, Allyson↗
DOE OSTI2021

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput—83% of theoretical peak—on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.

Data refactoring↗
DOE OSTI2021

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput—83% of theoretical peak—on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.

Chen, Jieyang↗
DOE OSTI2018

A methodology to analyze photovoltaic tracker uptime

A metric is developed to analyze the daily performance of single-axis photovoltaic (PV) trackers. The metric relies on comparing correlations between the daily time series of the PV power output and an array of simulated plane-of-array irradiances for the given day. Mathematical thresholds and a logic sequence are presented, so the daily tracking metric can be applied in an automated fashion on large-scale PV systems. The results of applying the metric are visually examined against the time series of the power output data for a large number of days and for various systems. The visual inspection results suggest that overall, the algorithm is accurate in identifying stuck or functioning trackers on clear-sky days. Visual inspection also shows that there are days that are not classified by the metric where the power output data may be sufficient to identify a stuck tracker. Based on the daily tracking metric, uptime results are calculated for 83 different inverters at 34 PV sites. The mean tracker uptime is calculated at 99% based on 2 different calculation methods. The daily tracking metric clearly has limitations, but as there is no existing metrics in the literature, it provides a valuable tool for flagging stuck trackers.

14 SOLAR ENERGY↗
DOE OSTI2018

Minimax theorems in fuzzy metric spaces

A minimax theorem is a theorem providing conditions which guarantee that the max–min inequality is also an equality. The first theorem in this sense is von Neumann’s minimax theorem, which was considered the starting point of game theory. Since then, several alternative generalizations of von Neumann’s original theorem have appeared in the literature. Variational inequality and minimax problems are of fundamental importance in modern non-linear analysis. They are widely applied in mechanics, differential equations, control theory, mathematical economics, game theory, and optimization. The purpose of this paper is first to establish a minimax theorem for mixed lower–upper semi-continuous functions in fuzzy metric spaces which extends the minimax theorems of many von Neumann types. As applications, we utilize this result to study the existence problems of solutions for abstract variational inequalities and quasi-variational inequalities in fuzzy metric spaces and to study the coincidence problems and saddle problems in fuzzy metric spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Design of quantum optical experiments with logic artificial intelligence

Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to mathematical conjectures can be encoded into these clauses and solved by checking their satisfiability (SAT). In contrast to machine learning approaches where the results can be approximations or local minima, Logic AI delivers formal and mathematically exact solutions to those problems. In this work, we propose the use of logic AI for the design of optical quantum experiments. We show how to map into a SAT problem the experimental preparation of an arbitrary quantum state and propose a logic-based algorithm, called Klaus, to find an interpretable representation of the photonic setup that generates it. We compare the performance of Klaus with the state-of-the-art algorithm for this purpose based on continuous optimization. We also combine both logic and numeric strategies to find that the use of logic AI significantly improves the resolution of this problem, paving the path to developing more formal-based approaches in the context of quantum physics experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Demand Curve Estimation of Locally Produced Woody Biomass Products

Abstract. The goal of the Waste-to-Wisdom project is to produce and sell value-added products derived from post-harvest forest residues including wood briquettes, torrefied briquettes, and biochar. The consumer demand for these products (i.e., market size) determines the success of manufacturers especially when the location of production is far away from a population center and the producer is a price taker. Consumers are often scattered and transportation costs from the factory to retail stores lower the net sales revenue at the plant. The objective of this study was to estimate the demand curves and the associated revenue functions of the bioenergy products in five case locations applying a market-based analysis. We first estimated the size of the potential market for the products in each location and then assumed a market penetration rate to estimate consumer demand. This information was used to develop a set of mathematical functions based on deductive logic. Plugging presumable values based on scenario assumptions into the models contributes to the economic feasibility studies. Keywords: Biochar, Forest products marketing, Market penetration rate, Price skimming strategy, Wood briquette.

Agriculture↗