Ordering of implicants.
Correspondence between logical relations of Boolean function implicants and numerical relations between identifiers
BOOLEAN ALGEBRA↗
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Boolean differentiation and integration using Karnaugh maps
Algorithms are presented for differentiation and integration of Boolean functions by means of Karnaugh maps. The algorithms are considered simple when the number of variables is six or less; in this case Boolean differentiation and integration is said to be as easy as the Karnaugh map method of simplifying switching functions. It is suggested that the algorithms would be useful in the analysis of faults in combinational systems and in the synthesis of asynchronous sequential systems which utilize edge-sensitive flip-flops.
Tucker, J. H.↗
Trajectory Optimization: OTIS 4
The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.
Riehl, John P.↗
Methods of minimization and construction of bridge structures for relay devices
Minimization of Boolean function, and construction of bridge structures for relay devices
RELAY↗
Improving Search Properties in Genetic Programming
With the advancing computer processing capabilities, practical computer applications are mostly limited by the amount of human programming required to accomplish a specific task. This necessary human participation creates many problems, such as dramatically increased cost. To alleviate the problem, computers must become more autonomous. In other words, computers must be capable to program/reprogram themselves to adapt to changing environments/tasks/demands/domains. Evolutionary computation offers potential means, but it must be advanced beyond its current practical limitations. Evolutionary algorithms model nature. They maintain a population of structures representing potential solutions to the problem at hand. These structures undergo a simulated evolution by means of mutation, crossover, and a Darwinian selective pressure. Genetic programming (GP) is the most promising example of an evolutionary algorithm. In GP, the structures that evolve are trees, which is a dramatic departure from previously used representations such as strings in genetic algorithms. The space of potential trees is defined by means of their elements: functions, which label internal nodes, and terminals, which label leaves. By attaching semantic interpretation to those elements, trees can be interpreted as computer programs (given an interpreter), evolved architectures, etc. JSC has begun exploring GP as a potential tool for its long-term project on evolving dextrous robotic capabilities. Last year we identified representation redundancies as the primary source of inefficiency in GP. Subsequently, we proposed a method to use problem constraints to reduce those redundancies, effectively reducing GP complexity. This method was implemented afterwards at the University of Missouri. This summer, we have evaluated the payoff from using problem constraints to reduce search complexity on two classes of problems: learning boolean functions and solving the forward kinematics problem. We have also developed and implemented methods to use additional problem heuristics to fine-tune the searchable space, and to use typing information to further reduce the search space. Additional improvements have been proposed, but they are yet to be explored and implemented.
Janikow, Cezary Z.↗
Optimal ranging codes.
Optimum encoding of transmitted signal in ranging system, using boolean functions of component sequences
RANGE MEASUREMENT↗
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.↗
Formulation of a telemetry computer program, supplement 1 Final report
Fast algorithm for minimization of Boolean functions to two level and-or form
Hill, K. H.↗
Formulation of a telemetry computer program, supplement 2 Final report
Algorithm for simultaneous minimization of multiple Boolean functions with application to telemetry system
Hill, K. H.↗
Feedback in sequential machine realizations.
A method is described for determining the realizability of a sequential machine with trigger or set-reset flip-flop memory elements when the feedback of the machine is given by a Boolean function. Feedbacks in several types of sequential machines with different memory elements are compared, showing the memory specifications allowing the realization of such machines.
Harlow, C. A.↗
Model checking
Automatic formal verification methods for finite-state systems, also known as model-checking, successfully reduce labor costs since they are mostly automatic. Model checkers explicitly or implicitly enumerate the reachable state space of a system, whose behavior is described implicitly, perhaps by a program or a collection of finite automata. Simple properties, such as mutual exclusion or absence of deadlock, can be checked by inspecting individual states. More complex properties, such as lack of starvation, require search for cycles in the state graph with particular properties. Specifications to be checked may consist of built-in properties, such as deadlock or 'unspecified receptions' of messages, another program or implicit description, to be compared with a simulation, bisimulation, or language inclusion relation, or an assertion in one of several temporal logics. Finite-state verification tools are beginning to have a significant impact in commercial designs. There are many success stories of verification tools finding bugs in protocols or hardware controllers. In some cases, these tools have been incorporated into design methodology. Research in finite-state verification has been advancing rapidly, and is showing no signs of slowing down. Recent results include probabilistic algorithms for verification, exploitation of symmetry and independent events, and the use symbolic representations for Boolean functions and systems of linear inequalities. One of the most exciting areas for further research is the combination of model-checking with theorem-proving methods.
Dill, David L.↗
Adaptable Constrained Genetic Programming: Extensions and Applications
An evolutionary algorithm applies evolution-based principles to problem solving. To solve a problem, the user defines the space of potential solutions, the representation space. Sample solutions are encoded in a chromosome-like structure. The algorithm maintains a population of such samples, which undergo simulated evolution by means of mutation, crossover, and survival of the fittest principles. Genetic Programming (GP) uses tree-like chromosomes, providing very rich representation suitable for many problems of interest. GP has been successfully applied to a number of practical problems such as learning Boolean functions and designing hardware circuits. To apply GP to a problem, the user needs to define the actual representation space, by defining the atomic functions and terminals labeling the actual trees. The sufficiency principle requires that the label set be sufficient to build the desired solution trees. The closure principle allows the labels to mix in any arity-consistent manner. To satisfy both principles, the user is often forced to provide a large label set, with ad hoc interpretations or penalties to deal with undesired local contexts. This unfortunately enlarges the actual representation space, and thus usually slows down the search. In the past few years, three different methodologies have been proposed to allow the user to alleviate the closure principle by providing means to define, and to process, constraints on mixing the labels in the trees. Last summer we proposed a new methodology to further alleviate the problem by discovering local heuristics for building quality solution trees. A pilot system was implemented last summer and tested throughout the year. This summer we have implemented a new revision, and produced a User's Manual so that the pilot system can be made available to other practitioners and researchers. We have also designed, and partly implemented, a larger system capable of dealing with much more powerful heuristics.
Janikow, Cezary Z.↗
Logical activation functions for training arbitrary probabilistic Boolean operations
Not Available
96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
On the fundamental structure of Galois switching functions
It is shown that the fundamental structure of Galois switching functions follows naturally from that of Boolean switching functions. An expanded formula for deriving multimomial Galois switching functions is provided with illustrations of its application.
Benjauthrit, B.↗
K-Spin Hamiltonian for Quantum-Resolvable Markov Decision Processes
The Markov decision process is the mathematical formalization underlying the modern field of reinforcement learning when transition and reward functions are unknown. We derive a pseudo-Boolean cost function that is equivalent to a K-spin Hamiltonian representation of the discrete, finite, discounted Markov decision process with infinite horizon. This K-spin Hamiltonian furnishes a starting point from which to solve for an optimal policy using heuristic quantum algorithms such as adiabatic quantum annealing and the quantum approximate optimization algorithm on near-term quantum hardware. In arguing that the variational minimization of our Hamiltonian is approximately equivalent to the Bellman optimality condition for a prevalent class of environments we establish an interesting analogy with classical field theory. Along with proof-of-concept calculations to corroborate our formulation by simulated and quantum annealing against classical Q-Learning, we analyze the scaling of physical resources required to solve our Hamiltonian on quantum hardware.
Hamiltonian↗
Simulation of Mariner Mars 1971 spacecraft
Preparation for the Mariner Mars 1971 mission is reported, including an extensive training program for operations personnel during which the primary source of spacecraft data was a computer program simulating the spacecraft. The objectives of a simulation model for training purposes differed from objectives appropriate to a design or analysis model. Model subsystems were designed to provide realistic telemetry data reflecting changes due both to commands and environmental parameters affecting the spacecraft at various times during the mission. The spacecraft is modeled along two separate functional lines. Boolean operations are concentrated in the spacecraft logic model, which determines the spacecraft state or mode, while mathematical operations or algorithms are executed in computational subsystem models. Although logic parameters are interrogated as a part of each computational pass, actual logic model processing occurs only when a change-of-state input is generated by the operations organization. The program design, some of the special characteristics of each of the modeled subsystems, and how the model was used in support of mission operations training are presented.
Ausman, N. E., Jr.↗
Logical Activation Functions v.1.1
SAND2024-01501O Logical Activation Functions software is a PyTorch implementation from the paper, "Logical Activation Functions for Training Arbitrary Probabilistic Boolean Logic." The activation functions approximate logit-space marginalization of probabilistic truth tables from probabilistic interpretations of inputs. They also provide a general methodology to approximate logical relationships between abstract antecedents and consequents for machine learning architectures. They do not target any specific application or use-case. By training probabilistic truth tables, these activation functions can capture more expressive relationships in a neural network than typical elementwise activation functions. This code is only designed for a single compute node with a GPU and is limited to machine learning architectures than can fit within the memory of a single GPU. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Duersch, Jed↗
Defining of the BDX930 Assembly Language
A definition of the BDX930 assembly language is presented. Various definition problems and suggested solutions are included. A class of defined recognizers based on boolean valued nowrecursive functions is employed in preprocessing.
Boyer, R. S.↗