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An Introduction to Logic for Students of Physics and Engineering

A physicist with an engineering background, the author presents a brief tutorial on logic. In his work at NASA and in his encounters with students, he has often found that a firm grounding in basic logic is lacking - perhaps because there are so many other demands on people that time simply cannot be taken to really examine the roots of human reasoning. This report provides an overview of this all-too-important subject with the dual hope that it will suffice insofar as it goes and that it will spur at least some to further study.

Kolecki, Joseph C.↗

The Strengths and Weaknesses of Logic Formalisms to Support Mishap Analysis

The increasing complexity of many safety critical systems poses new problems for mishap analysis. Techniques developed in the sixties and seventies cannot easily scale-up to analyze incidents involving tightly integrated software and hardware components. Similarly, the realization that many failures have systemic causes has widened the scope of many mishap investigations. Organizations, including NASA and the NTSB, have responded by starting research and training initiatives to ensure that their personnel are well equipped to meet these challenges. One strand of research has identified a range of mathematically based techniques that can be used to reason about the causes of complex, adverse events. The proponents of these techniques have argued that they can be used to formally prove that certain events created the necessary and sufficient causes for a mishap to occur. Mathematical proofs can reduce the bias that is often perceived to effect the interpretation of adverse events. Others have opposed the introduction of these techniques by identifying social and political aspects to incident investigation that cannot easily be reconciled with a logic-based approach. Traditional theorem proving mechanisms cannot accurately capture the wealth of inductive, deductive and statistical forms of inference that investigators routinely use in their analysis of adverse events. This paper summarizes some of the benefits that logics provide, describes their weaknesses, and proposes a number of directions for future research.

Johnson, C. W.↗

Risk-Based Prioritization of Research for Aviation Security Using Logic-Evolved Decision Analysis

The National Aeronautics and Space Administration is developing advanced technologies to reduce terrorist risk for the air transportation system. Decision support tools are needed to help allocate assets to the most promising research. An approach to rank ordering technologies (using logic-evolved decision analysis), with risk reduction as the metric, is presented. The development of a spanning set of scenarios using a logic-gate tree is described. Baseline risk for these scenarios is evaluated with an approximate reasoning model. Illustrative risk and risk reduction results are presented.

Eisenhawer, S. W.↗

Ferritin-Templated Quantum-Dots for Quantum Logic Gates

Quantum logic gates (QLGs) or other logic systems are based on quantum-dots (QD) with a stringent requirement of size uniformity. The QD are widely known building units for QLGs. The size control of QD is a critical issue in quantum-dot fabrication. The work presented here offers a new method to develop quantum-dots using a bio-template, called ferritin, that ensures QD production in uniform size of nano-scale proportion. The bio-template for uniform yield of QD is based on a ferritin protein that allows reconstitution of core material through the reduction and chelation processes. One of the biggest challenges for developing QLG is the requirement of ordered and uniform size of QD for arrays on a substrate with nanometer precision. The QD development by bio-template includes the electrochemical/chemical reconsitution of ferritins with different core materials, such as iron, cobalt, manganese, platinum, and nickel. The other bio-template method used in our laboratory is dendrimers, precisely defined chemical structures. With ferritin-templated QD, we fabricated the heptagonshaped patterned array via direct nano manipulation of the ferritin molecules with a tip of atomic force microscope (AFM). We also designed various nanofabrication methods of QD arrays using a wide range manipulation techniques. The precise control of the ferritin-templated QD for a patterned arrangement are offered by various methods, such as a site-specific immobilization of thiolated ferritins through local oxidation using the AFM tip, ferritin arrays induced by gold nanoparticle manipulation, thiolated ferritin positioning by shaving method, etc. In the signal measurements, the current-voltage curve is obtained by measuring the current through the ferritin, between the tip and the substrate for potential sweeping or at constant potential. The measured resistance near zero bias was 1.8 teraohm for single holoferritin and 5.7 teraohm for single apoferritin, respectively.

Choi, Sang H.↗

Interference Path Loss Prediction in A319/320 Airplanes Using Modulated Fuzzy Logic and Neural Networks

In this paper, neural network (NN) modeling is combined with fuzzy logic to estimate Interference Path Loss measurements on Airbus 319 and 320 airplanes. Interference patterns inside the aircraft are classified and predicted based on the locations of the doors, windows, aircraft structures and the communication/navigation system-of-concern. Modeled results are compared with measured data. Combining fuzzy logic and NN modeling is shown to improve estimates of measured data over estimates obtained with NN alone. A plan is proposed to enhance the modeling for better prediction of electromagnetic coupling problems inside aircraft.

Jafri, Madiha J.↗

Programmable Logic Application Notes

This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter will continue a series of notes concentrating on analysis techniques with this issue's section discussing: Digital Timing Analysis Tools and Techniques. Articles in this issue include: SX and SX-A Series Devices Power Sequencing; JTAG and SXISX-AISX-S Series Devices; Analysis Techniques (i.e., notes on digital timing analysis tools and techniques); Status of the Radiation Hard reconfigurable Field Programmable Gate Array Program, Input Transition Times; Apollo Guidance Computer Logic Study; RT54SX32S Prototype Data Sets; A54SX32A - 0.22 micron/UMC Test Results; Ramtron FM1608 FRAM; and Analysis of VHDL Code and Synthesizer Output.

Katz, Richard↗

Universal programmable logic gate and routing method

An universal and programmable logic gate based on G.sup.4-FET technology is disclosed, leading to the design of more efficient logic circuits. A new full adder design based on the G.sup.4-FET is also presented. The G.sup.4-FET can also function as a unique router device offering coplanar crossing of signal paths that are isolated and perpendicular to one another. This has the potential of overcoming major limitations in VLSI design where complex interconnection schemes have become increasingly problematic.

Fijany, Amir↗

A Safety Conundrum Illustrated: Logic, Mathematics, and Science Are Not Enough

In an ideal world, conversations about whether a particular system is safe, or whether a particular method or tool enhances safety, would be emotion-free discussions concentrating on the level of safety required, available evidence, and coherent logical, mathematical, or scientific arguments based on that evidence. In the real world, discussions about safety are often not emotion-free. Political and economic arguments may play a bigger role than logical, mathematical, and scientific arguments, and psychological factors may be as important, or even more important, than purely technical factors. This paper illustrates the conundrum that can result from this clash of the ideal and the real by means of an imagined conversation among a collection of fictional characters representing various types of people who may be participating in a safety discussion.

Holloway, C. M.↗

Simulation and Verification of Synchronous Set Relations in Rewriting Logic

This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property veri cation of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure consists of an ordersorted rewrite theory in Maude, a rewriting logic system, that enables the synchronous execution of a set relation provided by the user. By using the infrastructure, existing algorithm veri cation techniques already available in Maude for traditional asynchronous rewriting, such as reachability analysis and model checking, are automatically available to synchronous set rewriting. The use of the infrastructure is illustrated with an executable operational semantics of a simple synchronous language and the veri cation of temporal properties of a synchronous system.

Rocha, Camilo↗

Nonlinear Aerodynamic Modeling From Flight Data Using Advanced Piloted Maneuvers and Fuzzy Logic

Results of the Aeronautics Research Mission Directorate Seedling Project Phase I research project entitled "Nonlinear Aerodynamics Modeling using Fuzzy Logic" are presented. Efficient and rapid flight test capabilities were developed for estimating highly nonlinear models of airplane aerodynamics over a large flight envelope. Results showed that the flight maneuvers developed, used in conjunction with the fuzzy-logic system identification algorithms, produced very good model fits of the data, with no model structure inputs required, for flight conditions ranging from cruise to departure and spin conditions.

Brandon, Jay M.↗

Automated Translation of Safety Critical Application Software Specifications into PLC Ladder Logic

The numerous benefits of automatic application code generation are widely accepted within the software engineering community. A few of these benefits include raising the abstraction level of application programming, shorter product development time, lower maintenance costs, and increased code quality and consistency. Surprisingly, code generation concepts have not yet found wide acceptance and use in the field of programmable logic controller (PLC) software development. Software engineers at the NASA Kennedy Space Center (KSC) recognized the need for PLC code generation while developing their new ground checkout and launch processing system. They developed a process and a prototype software tool that automatically translates a high-level representation or specification of safety critical application software into ladder logic that executes on a PLC. This process and tool are expected to increase the reliability of the PLC code over that which is written manually, and may even lower life-cycle costs and shorten the development schedule of the new control system at KSC. This paper examines the problem domain and discusses the process and software tool that were prototyped by the KSC software engineers.

Leucht, Kurt W.↗

Logic Model Checking of Unintended Acceleration Claims in Toyota Vehicles

Part of the US Department of Transportation investigation of Toyota sudden unintended acceleration (SUA) involved analysis of the throttle control software, JPL Laboratory for Reliable Software applied several techniques including static analysis and logic model checking, to the software; A handful of logic models were build, Some weaknesses were identified; however, no cause for SUA was found; The full NASA report includes numerous other analyses

sudden unintended acceleration↗

DejaVu: A Monitoring Tool for First-Order Temporal Logic

Runtime Verification (rv) is aimed at analyzing individual execution traces and temporal behaviors observed from running programs and systems. Its traditional purpose is in detecting the lack of conformance with respect to a formal specification. While very early rv systems were based on specifications given in some form of propositional temporal logic, recent efforts have focused on monitoring so-called parametric specifications over events that carry data. Since a monitor for such specifications has to store observed data, the challenge is to have an efficient representation and manipulation of data. The fundamental problem is that the actual values of the data are not necessarily bounded or provided in advance. In this paper, we describe our monitoring tool, DejaVu, which implements our algorithm [HPU17] for monitoring first-order past linear-time temporal logic over a sequence of events that carry data. We propose the use of Binary Decision Diagrams (bdds) [Bry86] for representing and manipulating sets of observed data since (1) bdds provide highly compact representations, (2) operations over bdds, in particular complementation, are very efficient, and (3) the monitor construction for the propositional case shown in [HR02] naturally extends to bdds. Our experiments show a substantial improvement in performance compared to a related tool.

Ulus, Dogan↗

Logical shadow tomography: Efficient estimation of error-mitigated observables

We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting into the codespace as in subspace expansion and taking powers of the density matrix as in virtual distillation. Relative to subspace expansion which requires Ω (2^((n-1)k) samples to estimate a Pauli observable with an [[n; k]] stabilizer code, our technique requires only Ө(2^k) samples. Relative to virtual distillation, our technique can compute powers of the density matrix without implementing additional copies of quantum states the quantum computer. We present numerical results using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only 10^5 samples under 1% depolarizing noise.

quantum computing↗