Theme 3: Confidence Standards for Biosignature Observations and Interpretation
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In this paper we present a semantic theory of abstractions based on viewing abstractions as interpretations between theories. This theory captures important aspects of abstractions not captured in the theory of abstractions presented by Giunchiglia and Walsh. Instead of viewing abstractions as syntactic mappings, we view abstractions as a two step process: the intended domain model is first abstracted and then a set of (abstract) formulas is constructed to capture the abstracted domain model. Viewing and justifying abstractions as model level transformations is both natural and insightful. We provide a precise characterization of the abstract theory that exactly implements the intended abstraction, and show that this theory, while being axiomatizable, is not always finitely axiomatizable. A simple corollary of the latter result disproves a conjecture made by Tenenberg that if a theory is finitely axiomatizable, then predicate abstraction of that theory leads to a finitely axiomatizable theory.
The task assignment 3 of the design and validation of digital flight control systems suitable for fly-by-wire applications is studied. Task 3 is associated with formal verification of embedded systems. In particular, results are presented that provide a methodological approach to microprocessor verification. A hierarchical decomposition strategy for specifying microprocessors is also presented. A theory of generic interpreters is presented that can be used to model microprocessor behavior. The generic interpreter theory abstracts away the details of instruction functionality, leaving a general model of what an interpreter does.
Markets are often considered superior to other global scheduling mechanisms for distributed computing systems. This claim is supported by: a casual observation from our every-day life that markets successfully equilibrate supply and demand, and the features of markets which originate in the general equilibrium theory, e.g., efficiency and the lack of necessity of 2 central controller. This paper describes why such beliefs in markets are not warranted. It does so by examining the general equilibrium theory, in terms of scope, abstraction, and interpretation. Not only does the general equilibrium theory fail to provide a satisfactory explanation of actual economies, including a computing-resource economy, it also falls short of supplying theoretical foundations for commonly held views of market desirability. This paper also points out that the argument for the desirability of markets involves circular reasoning and that the desirability can be established only vis-a-vis a scheduling goal. Finally, recasting the conclusion of Arrow's Impossibility Theorem as that for global scheduling, we conclude that there exists no market-based scheduler that is rational (in the sense defined in microeconomic theory), takes into account utility of more than one user, and yet yields a Pareto-optimal outcome for arbitrary user utility functions.
A review of the existing literature regarding the effects of different types of physical activities on the gene expression of adult skeletal muscles leads us to conclude that each type of exercise training program has, as a result, a different phenotype, which means that there are multiple mechanisms, each producing a unique phenotype. A portion of the facts which support this position is presented and interpreted here. [Abstract translated from the original French by NASA].
We explore a transformational approach to the problem of verifying simple array-manipulating programs. Traditionally, verification of such programs requires intricate analysis machinery to reason with universally quantified statements about symbolic array segments, such as "every data item stored in the segment A[i] to A[j] is equal to the corresponding item stored in the segment B[i] to B[j]." We define a simple abstract machine which allows for set-valued variables and we show how to translate programs with array operations to array-free code for this machine. For the purpose of program analysis, the translated program remains faithful to the semantics of array manipulation. Based on our implementation in LLVM, we evaluate the approach with respect to its ability to extract useful invariants and the cost in terms of code size.
Model-based diagnosis is a powerful, first-principles approach to diagnosis. The primary drawback with model-based diagnosis is that it is based on a system model, and this model might be inappropriate. The inappropriateness of models usually stems from the fundamental tradeoff between completeness and efficiency. Recently, Struss has developed an elegant proposal for diagnosis with multiple models. Struss characterizes models as relations and develops a precise notion of abstraction. He defines relations between models and analyzes the effect of a model switch on the space of possible diagnoses. In this paper we extend Struss's proposal in three ways. First, our account of diagnosis with multiple models is based on representing models as more expressive first-order theories, rather than as relations. A key technical contribution is the use of a general notion of abstraction based on interpretations between theories. Second, Struss conflates component modes with models, requiring him to define models relations such as choices which result in non-relational models. We avoid this problem by differentiating component modes from models. Third, we present a more general account of simplifications that correctly handles situations where the simplification contradicts the base theory.
The TAMPR System originated as an approach to the problem of automating the routine modifications of FORTRAN source programs required to adapt them to a variety of uses or environments. Three steps are involved: (1) A FORTRAN source program is processed by the TAMPR Recognizer, yielding essentially a parse tree called the abstract form, (2) the Transformation Interpreter applies IGT's (Intragrammatical Transformations) to the abstract form as tree operations, and (3) the abstract form is then reconverted to source program form by the Formatter. By ensuring that the transformations are applied only to the correct syntactic entities and only in the intended contexts, the use of the abstract form greatly simplifies establishing the reliability of the overall process.
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Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern. Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern.
It is found that under mild assumptions, feedback system stability can be concluded if one can 'topologically separate' the infinite-dimensional function space containing the system's dynamical input-output relations into two regions, one region containing the dynamical input-output relation of the 'feedforward' element of the system and the other region containing the dynamical output-input relation of the 'feedback' element. Nonlinear system stability criteria of both the input-output type and the state-space (Liapunov) type are interpreted in this context. The abstract generality and conceptual simplicity afforded by the topological separation perspective clarifies some of the basic issues underlying stability theory and serves to suggest improvements in existing stability criteria. A generalization of Zames' (1966) conic-relation stability criterion is proved, laying the foundation for improved multivariable generalizations of the frequency-domain circle stability criterion for nonlinear systems.
An efficient evaluation technique is examined for lazy functional programs based on combinator graph reduction. Graph reduction is widely believed to be slow and inefficient, but an abstract machine called the Threaded Interpretive Graph Reduction Engine (TIGRE) achieves a substantial speedup over previous reduction techniques. The runtime system of TIGRE is a threaded system that permits self-modifying program execution with compiler-guaranteed safety. This paper describes an implementation of TIGRE in Forth for the Harris RTX 2000 stack processor.