Search NASA⌕ Search

SEARCH · Search NASA

Results for “Boolean 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 91 records · Page 5

Inverse Design of Plasma Metamaterial Devices for Optical Computing

We apply inverse-design methods to produce two-dimensional plasma metamaterial (PMM) devices. Backpropagated finite-difference frequency-domain (FDFD) simulations are used to design waveguides and demultiplexers operating under both TE and TM modes. Demultiplexing and waveguiding are demonstrated for devices composed of plasma elements with reasonable plasma densities of approximately 7 GHz, allowing for future in situ training and experimental realization of these designs. We also explore the possible applicability of PMMs to nonlinear boolean operations for use in optical computing. Functionally complete logical connectives (or and and) are achieved in the TM mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A representational basis for the development of a distributed expert system for Space Shuttle flight control

A new representation of malfunction procedure logic which permits the automation of these procedures using Boolean normal forms is presented. This representation is discussed in the context of the development of an expert system for space shuttle flight control including software and hardware implementation modes, and a distributed architecture. The roles and responsibility of the flight control team as well as previous work toward the development of expert systems for flight control support at Johnson Space Center are discussed. The notion of malfunction procedures as graphs is introduced as well as the concept of hardware-equivalence.

Helly, J. J., Jr.↗

Learning Delayed Influences of Biological Systems

Boolean networks are widely used model to represent gene interactions and global dynamical behavior of gene regulatory networks. To understand the memory effect involved in some interactions between biological components, it is necessary to include delayed influences in the model. In this paper, we present a logical method to learn such models from sequences of gene expression data. This method analyzes each sequence one by one to iteratively construct a Boolean network that captures the dynamics of these observations. To illustrate the merits of this approach, we apply it to learning real data from bioinformatic literature. Using data from the yeast cell cycle, we give experimental results and show the scalability of the method. We show empirically that using this method we can handle millions of observations and successfully capture delayed influences of Boolean networks.

60 APPLIED LIFE SCIENCES↗

Obstacles to quantum annealing in a planar embedding of XORSAT

We introduce a planar embedding of the k-regular k-XORSAT problem, in which solutions are encoded in the ground state of a classical statistical mechanics model of reversible logic gates arranged on a square grid and acting on bits that represent the Boolean variables of the problem. The special feature of this embedding is that the resulting model lacks a finite-temperature phase transition, thus bypassing the first-order thermodynamic transition known to occur in the random graph representation of XORSAT. In spite of this attractive feature, the thermal relaxation into the ground state displays remarkably slow glassy behavior. The question addressed in this paper is whether this planar embedding can afford an efficient path to solution of k-regular k-XORSAT via quantum adiabatic annealing. We first show that our model bypasses an avoided level crossing and consequent exponentially small gap in the limit of small transverse fields. We then present quantum Monte Carlo results for our embedding of the k-regular k-XORSAT that strongly support a picture in which second-order and first-order transitions develop at a finite transverse field for k = 2 and k = 3, respectively. Furthermore, this translates into power-law and exponential dependences in the scaling of energy gaps with system size, corresponding to times-to-solution which are, respectively, polynomial and exponential in the number of variables. We conclude that neither classical nor quantum annealing can efficiently solve our reformulation of XORSAT, even though the original problem can be solved in polynomial time by Gaussian elimination.

2-dimensional systems↗

Logic hazards in threshold networks.

Logic hazards detection in threshold gate networks, discussing hazard free network synthesis based on Boolean functions and tree method

Coates, C. L.↗

Runtime Verification of C Programs

We present in this paper a framework, RMOR, for monitoring the execution of C programs against state machines, expressed in a textual (nongraphical) format in files separate from the program. The state machine language has been inspired by a graphical state machine language RCAT recently developed at the Jet Propulsion Laboratory, as an alternative to using Linear Temporal Logic (LTL) for requirements capture. Transitions between states are labeled with abstract event names and Boolean expressions over such. The abstract events are connected to code fragments using an aspect-oriented pointcut language similar to ASPECTJ's or ASPECTC's pointcut language. The system is implemented in the C analysis and transformation package CIL, and is programmed in OCAML, the implementation language of CIL. The work is closely related to the notion of stateful aspects within aspect-oriented programming, where pointcut languages are extended with temporal assertions over the execution trace.

RMOR↗

Applying Incremental, Inductive Model Checking to the Modal Mu Calculus

This work aims to demonstrate that an incremental inductive model checking algorithm built on top of Boolean satisfiability (SAT) solvers can be extended to support modal mu calculus (MMC) formulas. The resulting algorithm, called modal mu calculus model checking using myopic constraints (MC3), solves MMC model checking problems over Boolean labeled transition systems (LTSs). MMC subsumes simple invariance/reachability (as solved by the IC3 algorithm), linear temporal logic (LTL, as solved by the fair algorithm), computation tree logic (CTL, as solved by IICTL), and CTL* (which in turn subsumes LTL and CTL, but was not previously supported by any incremental inductive algorithm). The algorithm is implemented in a prototype solver, mc3.

97 MATHEMATICS AND COMPUTING↗

Organic Relay Carry Generator and Logic Gates

Our letter demonstrates that a single organic micrometer-scale relay can easily generate a carry for four input bits and perform basic Boolean operations for two input bits.

42 ENGINEERING↗

Machine Learning–Guided Boolean Matrix Inference for Real-Time O-RAN Conflict Detection

Open Radio Access Networks (O-RAN) are emerging, software-driven cellular architectures that promote flexibility by enabling components from different vendors to interoperate. Multiple control applications called xApps can independently adjust network parameters in near real time, often without awareness of each other's actions. This creates a system highly prone to unintended conflicts and performance degradation due to the inherent complexity of such openness. To model such systems and ultimately prevent or mitigate xApp conflicts, it is essential to understand the dynamic relationships between xApps (A), the control parameters they adjust (P), and the resulting KPI responses (K). While the mappings from A to P and from K to A can often be derived from xApp specifications, the relationship from P to K is typically hidden within the system’s dynamics and must be inferred from observed data. We propose a novel data-driven Boolean inference framework that uncovers the hidden P?K dependencies using machine learning and interpretable rule induction. Continuous parameters and KPIs are first binarized using decision tree classifiers, and a binary influence matrix L is then inferred by solving Boolean matrix equations over time. This compact representation improves interpretability and enables real-time tracking of dynamically evolving parameter-KPI dependencies. We demonstrate the effectiveness of our method in a realistic mobile handover scenario, where it accurately recovers the underlying logic and enables proactive conflict detection.

42 - ENGINEERING↗

Revisiting separation: Algorithms and complexity

Abstract Linear temporal logic (LTL) with Since and Until modalities is expressively equivalent, over the class of complete linear orders, to a fragment of first-order logic known as FOMLO (first-order monadic logic of order). It turns out that LTL, under some basic assumptions, is expressively complete if and only if it has the property, called separation, that every formula is equivalent to a Boolean combination of formulas that each refer only to the past, present or future. Herein we present simple algorithms and their implementations to perform separation of the LTL with Since and Until, over discrete and complete linear orders, and translation from FOMLO formulas into equivalent temporal logic formulas. We additionally show that the separation of a certain fragment of LTL results in at most a double exponential size growth.

Oliveira, Daniel↗

Additively manufacturable micro-mechanical logic gates

Early examples of computers were almost exclusively based on mechanical devices. Although electronic computers became dominant in the past 60 years, recent advancements in three-dimensional micro-additive manufacturing technology provide new fabrication techniques for complex microstructures which have rekindled research interest in mechanical computations. Here we propose a new digital mechanical computation approach based on additively-manufacturable micro-mechanical logic gates. The proposed mechanical logic gates (i.e., NOT, AND, OR, NAND, and NOR gates) utilize multi-stable micro-flexures that buckle to perform Boolean computations based purely on mechanical forces and displacements with no electronic components. A key benefit of the proposed approach is that such systems can be additively fabricated as embedded parts of microarchitected metamaterials that are capable of interacting mechanically with their surrounding environment while processing and storing digital data internally without requiring electric power.

36 MATERIALS SCIENCE↗

Data Analysis

Analysis of the material protection, control, and accountability (MPC&A) system is necessary to understand the limits and vulnerabilities of the system to internal threats. A self-appraisal helps the facility be prepared to respond to internal threats and reduce the risk of theft or diversion of nuclear material. The material control and accountability (MC&A) system effectiveness tool (MSET) fault tree was developed to depict the failure of the MPC&A system as a result of poor practices and random failures in the MC&A system. It can also be employed as a basis for assessing deliberate threats against a facility. MSET uses fault tree analysis, which is a top-down approach to examining system failure. The analysis starts with identifying a potential undesirable event called a 'top event' and then determining the ways it can occur (e.g., 'Fail To Maintain Nuclear Materials Under The Purview Of The MC&A System'). The analysis proceeds by determining how the top event can be caused by individual or combined lower level faults or failures. These faults, which are the causes of the top event, are 'connected' through logic gates. The MSET model uses AND-gates and OR-gates and propagates the effect of event failure using Boolean algebra. To enable the fault tree analysis calculations, the basic events in the fault tree are populated with probability risk values derived by conversion of questionnaire data to numeric values. The basic events are treated as independent variables. This assumption affects the Boolean algebraic calculations used to calculate results. All the necessary calculations are built into the fault tree codes, but it is often useful to estimate the probabilities manually as a check on code functioning. The probability of failure of a given basic event is the probability that the basic event primary question fails to meet the performance metric for that question. The failure probability is related to how well the facility performs the task identified in that basic event over time (not just one performance or exercise). Fault tree calculations provide a failure probability for the top event in the fault tree. The basic fault tree calculations establish a baseline relative risk value for the system. This probability depicts relative risk, not absolute risk. Subsequent calculations are made to evaluate the change in relative risk that would occur if system performance is improved or degraded. During the development effort of MSET, the fault tree analysis program used was SAPHIRE. SAPHIRE is an acronym for 'Systems Analysis Programs for Hands-on Integrated Reliability Evaluations.' Version 1 of the SAPHIRE code was sponsored by the Nuclear Regulatory Commission in 1987 as an innovative way to draw, edit, and analyze graphical fault trees primarily for safe operation of nuclear power reactors. When the fault tree calculations are performed, the fault tree analysis program will produce several reports that can be used to analyze the MPC&A system. SAPHIRE produces reports showing risk importance factors for all basic events in the operational MC&A system. The risk importance information is used to examine the potential impacts when performance of certain basic events increases or decreases. The initial results produced by the SAPHIRE program are considered relative risk values. None of the results can be interpreted as absolute risk values since the basic event probability values represent estimates of risk associated with the performance of MPC&A tasks throughout the material balance area (MBA). The RRR for a basic event represents the decrease in total system risk that would result from improvement of that one event to a perfect performance level. Improvement of the basic event with the greatest RRR value produces a greater decrease in total system risk than improvement of any other basic event. Basic events with the greatest potential for system risk reduction are assigned performance improvement values, and new fault tree calculations show the improvement in total system risk. The operational impact or cost-effectiveness from implementing the performance improvements can then be evaluated. The improvements being evaluated can be system performance improvements, or they can be potential, or actual, upgrades to the system. The RIR for a basic event represents the increase in total system risk that would result from failure of that one event. Failure of the basic event with the greatest RIR value produces a greater increase in total system risk than failure of any other basic event. Basic events with the greatest potential for system risk increase are assigned failure performance values, and new fault tree calculations show the increase in total system risk. This evaluation shows the importance of preventing performance degradation of the basic events. SAPHIRE identifies combinations of basic events where concurrent failure of the events results in failure of the top event.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Two mechanisms for the spontaneous emergence, execution, and reprogramming of chemical logic circuits

A key question in origin-of-life research is how primitive life or life-like systems obtained reusable and reprogrammable machinery of processing information to respond to various environmental and internal stimuli. One strategy to approach this question is to view living systems as universal chemical computers. This approach focuses upon uncovering how reusable and reprogrammable chemical NOT, AND, and OR logic gates could appear under prebiotically possible scenarios where simple chemicals and second- or lower-order reactions are more frequent than macromolecules and higher-order reactions. In this article, we theoretically model two generic mechanisms of forming Boolean gates based on geochemically plausible reaction systems that could have preceded complex biopolymers. The mechanisms exploit simple bistable autocatalytic systems to encode binary variables and use heterogeneous dilution rates to differentially activate or deactivate autocatalysis in different reactors. We found that NOT, AND, and OR gates, as well as more complex logic circuits, can spontaneously arise from connected, well-mixed flow reactors based on (i) catalysis by a heterodimer between mutually inhibitory autocatalysts or (ii) selectively permeable tunnels connecting reactors. Our results suggest that simple machinery can support the prebiotic emergence of complex chemical logic circuits and provide new guides for experimentally actualizing chemical computation.

Zhen Peng↗

SEQ-GEN: A comprehensive multimission sequencing system

SEQ-GEN is a user-interactive computer program used to plan and generate a sequence of commands for spacecraft. Desired activities are specified by the user of SEQ-GEN; SEQ-GEN in turn expands these activities, deriving the spacecraft commands necessary to accomplish the desired activities. SEQ-GEN models the effects on the spacecraft of the commands, predicting the state as a function of time, flagging any conflicts and rule violations. These states, conflicts, and violations are viewable both graphically and textually at the user's request. SEQ-GEN also displays the entire sequence graphically, showing each requested activity as a bar on its graphical timeline. SEQ-GEN immediately revalidates the sequence, updating its models and calculations along with its displays based on these changes. Because it has the ability to recalculate spacecraft states immediately, the user is able to perform 'what-if' sessions easily. SEQ-GEN, a multimission tool, is adaptable to any flight project. A flight project writes its adaptation files containing project unique information including in its simplest form, only spacecraft commands. For more involved projects the adaptation files may also contain flight and mission rules, description of the spacecraft and ground models, and the definition of activities. SEQ-GEN operates at whatever level of detail the adaptation files imply. Simple adaptations are straight forward to do. There is, however, no limit to the complexity of activity definitions or of spacecraft models: both may involve unlimited logical decision points. Commands and activities may involve any number of parameters of a wide variety of data types, including integer, float, time, boolean, and character strings. SEQ-GEN will be used by the Mars Pathfinder, Cassini, and VIM (Voyager Interstellar Mission) project in an effort to speed up adaptation time and to keep sequence generation costs down. SEQ-GEN is hosted on UNIX workstations. It uses MOTIF and X for windowing, and was designed and coded in an object-oriented style in the language C++.

Salcedo, Jose↗

Development of Boolean calculus and its applications

The development of Boolean calculus for its application to developing digital system design methodologies that would reduce system complexity, size, cost, speed, power requirements, etc., is discussed. Synthesis procedures for logic circuits are examined particularly asynchronous circuits using clock triggered flip flops.

Tapia, M. A.↗

Superior model for fault tolerance computation in designing nano-sized circuit systems

As CMOS technology scales nano-metrically, reliability turns out to be a decisive subject in the design methodology of nano-sized circuit systems. As a result, several computational approaches have been developed to compute and evaluate reliability of desired nano-electronic circuits. The process of computing reliability becomes very troublesome and time consuming as the computational complexity build ups with the desired circuit size. Therefore, being able to measure reliability instantly and superiorly is fast becoming necessary in designing modern logic integrated circuits. For this purpose, the paper firstly looks into the development of an automated reliability evaluation tool based on the generalization of Probabilistic Gate Model (PGM) and Boolean Difference-based Error Calculator (BDEC) models. The Matlab-based tool allows users to significantly speed-up the task of reliability analysis for very large number of nano-electronic circuits. Secondly, by using the developed automated tool, the paper explores into a comparative study involving reliability computation and evaluation by PGM and, BDEC models for different implementations of same functionality circuits. Based on the reliability analysis, BDEC gives exact and transparent reliability measures, but as the complexity of the same functionality circuits with respect to gate error increases, reliability measure by BDEC tends to be lower than the reliability measure by PGM. The lesser reliability measure by BDEC is well explained in this paper using distribution of different signal input patterns overtime for same functionality circuits. Simulation results conclude that the reliability measure by BDEC depends not only on faulty gates but it also depends on circuit topology, probability of input signals being one or zero and also probability of error on signal lines.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Atomic effect algebras with compression bases

Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Geometric Structure and Transversal Logic of Quantum Reed–Muller Codes

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. Here, in this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2 k Z -rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.

Reed–Muller (RM) codes↗