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Automaton Logic
 International Journal of Theoretical Physics
, 1996
"... The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1 ..."
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Cited by 79 (47 self)
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The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1
Partition logics, orthoalgebras and automata
 Helvetica Physica Acta
, 1995
"... We investigate the orthoalgebras of certain nonBoolean models which have a classical realization. Our particular concern will be the partition logics arising from the investigation of the empirical propositional structure of Moore and Mealy type automata. 1 ..."
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Cited by 13 (9 self)
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We investigate the orthoalgebras of certain nonBoolean models which have a classical realization. Our particular concern will be the partition logics arising from the investigation of the empirical propositional structure of Moore and Mealy type automata. 1
Halting probability amplitude of quantum computers
 Journal of Universal Computer Science
, 1995
"... The classical halting probability to quantum computations. introduced by Chaitin is generalized Chaitin's [1,2,3] is a magic number. It is a measure for arbitrary programs to take a nite number of execution steps and then halt. It contains the solution for all halting problems, and hence to question ..."
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Cited by 9 (7 self)
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The classical halting probability to quantum computations. introduced by Chaitin is generalized Chaitin's [1,2,3] is a magic number. It is a measure for arbitrary programs to take a nite number of execution steps and then halt. It contains the solution for all halting problems, and hence to questions codable into halting problems, such asFermat's theorem. It contains the solution for the question of whether or not a particular exponential Diophantine equation has in nitely many ora nite number of solutions. And, since is provable \algorithmically incompressible," it is MartinLof/Chaitin/Solovay random. Therefore, is both: a mathematicians \fair coin, " and a formalist's nightmare. Here, is generalized to quantum computations. Consider a (not necessarily universal) quantum computer C and its ith program pi, which, at time t 2 Z, can be described by a quantum state [4, 5,6,7,
Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Cited by 8 (7 self)
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
Automatic Differentiation, Tangent Linear Models, and (Pseudo)Adjoints
 PREPRINT MCSP4721094, MATHEMATICS AND COMPUTER SCIENCE DIVISION, ARGONNE NATIONAL LABORATORY
, 1994
"... This paper provides a brief introduction to automatic differentiation and relates it to the tangent linear model and adjoint approaches commonly used in meteorology. After a brief review of the forward and reverse mode of automatic differentiation, the ADIFOR automatic differentiation tool is int ..."
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Cited by 7 (6 self)
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This paper provides a brief introduction to automatic differentiation and relates it to the tangent linear model and adjoint approaches commonly used in meteorology. After a brief review of the forward and reverse mode of automatic differentiation, the ADIFOR automatic differentiation tool is introduced, and initial results of a sensitivityenhanced version of the MM5 PSU/NCAR mesoscale weather model are presented. We also present a novel approach to the computation of gradients that uses a reverse mode approach at the time loop level and a forward mode approach at every time step. The resulting "pseudoadjoint" shares the characteristic of an adjoint code that the ratio of gradient to function evaluation does not depend on the number of independent variables. In contrast to a true adjoint approach, however, the nonlinearity of the model plays no role in the complexity of the derivative code.
Large Limits to Software Estimation
, 2001
"... Algorithmic (KCS) complexity results can be interpreted as indicating some limits to software estimation. While these limits are abstract they nevertheless contradict enthusiastic claims occasionally made by commercial software estimation advocates. Specifically, if it is accepted that algorithmic c ..."
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Cited by 7 (0 self)
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Algorithmic (KCS) complexity results can be interpreted as indicating some limits to software estimation. While these limits are abstract they nevertheless contradict enthusiastic claims occasionally made by commercial software estimation advocates. Specifically, if it is accepted that algorithmic complexity is an appropriate definition of the complexity of a programming project, then claims of purely objective estimation of project complexity, development time, and programmer productivity are necessarily incorrect.
NonBoolean Descriptions for MindMatter Problems
"... A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmat ..."
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Cited by 6 (0 self)
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A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmatter distinction. Such a description in terms of a locally Boolean but globally nonBoolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely nonBoolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a nonBoolean structure and can be encompassed into a single nonBoolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.
Speedup in Quantum Computation is Associated With Attenuation of Processing Probability
"... Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it is shown that, although in principle correct, any speed ..."
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Cited by 4 (1 self)
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Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it is shown that, although in principle correct, any speedup is accompanied by an associated attenuation of detection rates. Thus, on the average, no effective speedup is obtained relative to classical (nondeterministic) devices. 1 Recent findings in quantum complexity theory suggest an exponential speedup of discrete logarithms and factoring [1] and the travelling salesman problem [2] with respect to classical complexity. (The best classical estimate for the computing time for factoring is e cn 1/3 , where n is the number of bits in the number to be factored and c is a constant; the travelling salesman problem is NPcomplete). At the heart of these types of speedups is quantum parallelism. Roughly stated, quantum parallelism assures that a ...
How real are virtual realities, how virtual is reality? The constructive reinterpretation of physical undecidability
"... constructive reinterpretation of physical undecidability ..."
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Cited by 4 (4 self)
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constructive reinterpretation of physical undecidability
Complexity: A LanguageTheoretic Point of View
, 1995
"... this paper (see the discussion in [51, 58, 70, 126, 127, 120, 121, 130]); in what follows we shall superficially review this topic in connection with the related question: can computers think? ..."
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Cited by 2 (0 self)
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this paper (see the discussion in [51, 58, 70, 126, 127, 120, 121, 130]); in what follows we shall superficially review this topic in connection with the related question: can computers think?