Speed-Up of Turing Machines with One Work Tape and a Two-Way Input Tape

1987 ◽  
Vol 16 (1) ◽  
pp. 195-202 ◽  
Author(s):  
Wolfgang Maass ◽  
Amir Schorr
Keyword(s):  
Turing Machines ◽  
Input Tape ◽  
Speed Up

Computational speed-up by effective operators

1972 ◽  
Vol 37 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Albert R. Meyer ◽  
Patrick C. Fischer
Keyword(s):  
Turing Machine ◽  
Computable Function ◽  
Turing Machines ◽  
Complexity Measures ◽  
Computational Speed ◽  
Partial Recursive Functions ◽  
Speed Up ◽  
Recursive Equations ◽  
Computable Functions ◽  
Effective Operators

The complexity of a computable function can be measured by considering the time or space required to compute its values. Particular notions of time and space arising from variants of Turing machines have been investigated by R. W. Ritchie [14], Hartmanis and Stearns [8], and Arbib and Blum [1], among others. General properties of such complexity measures have been characterized axiomatically by Rabin [12], Blum [2], Young [16], [17], and McCreight and Meyer [10].In this paper the speed-up and super-speed-up theorems of Blum [2] are generalized to speed-up by arbitrary total effective operators. The significance of such theorems is that one cannot equate the complexity of a computable function with the running time of its fastest program, for the simple reason that there are computable functions which in a very strong sense have no fastest programs.Let φi be the ith partial recursive function of one variable in a standard Gödel numbering of partial recursive functions. A family Φ0, Φ1, … of functions of one variable is called a Blum measure on computation providing(1) domain (φi) = domain (Φi), and(2) the predicate [Φi(x) = m] is recursive in i, x and m.Typical interpretations of Φi(x) are the number of steps required by the ith Turing machine (in a standard enumeration of Turing machines) to converge on input x, the space or number of tape squares required by the ith Turing machine to converge on input x (with the convention that Φi(x) is undefined even if the machine fails to halt in a finite loop), and the length of the shortest derivation of the value of φi(x) from the ith set of recursive equations.

Linear speed-up does not hold on Turing machines with tree storages

1993 ◽  
Vol 47 (6) ◽  
pp. 313-318 ◽  
Author(s):  
Martin Hühne
Keyword(s):  
Turing Machines ◽  
Linear Speed ◽  
Speed Up

THE EFFECT OF INKDOTS FOR TWO-DIMENSIONAL AUTOMATA

1995 ◽  
Vol 09 (05) ◽  
pp. 777-796 ◽  
Author(s):  
AKIRA ITO ◽  
KATSUSHI INOUE ◽  
ITSUO TAKANAMI ◽  
YUE WANG
Keyword(s):  
Turing Machine ◽  
Open Problem ◽  
Complexity Classes ◽  
Two Dimensional ◽  
Turing Machines ◽  
Input Tape ◽  
One Dimensional ◽  
Finite State ◽  
Relationship Of ◽  
The Relationship

Recently, related to the open problem of whether deterministic and nondeterministic space (especially lower-level) complexity classes are separated, the inkdot Turing machine was introduced. An inkdot machine is a conventional Turing machine capable of dropping an inkdot on a given input tape for a landmark, but not to pick it up nor further erase it. In this paper, we introduce a finite state version of the inkdot machine as a weak recognizer of the properties of digital pictures, rather than a Turing machine supplied with a one-dimensional working tape. We first investigate the sufficient spaces of three-way Turing machines to simulate two-dimensional inkdot finite automaton, as preliminary results. Next, we investigate the basic properties of two-dimensional inkdot automaton, i.e. the hierarchy based on the number of inkdots and the relationship of two-dimensional inkdot automata to other conventional two-dimensional automata. Finally, we investigate the recognizability of connected pictures of two-dimensional inkdot finite machines.

Speed-Up Theorems in Type-2 Computations Using Oracle Turing Machines

2009 ◽  
Vol 45 (4) ◽  
pp. 880-896
Author(s):  
Chung-Chih Li
Keyword(s):  
Turing Machines ◽  
Speed Up

SAFE TURING MACHINES, GRZEGORCZYK CLASSES AND POLYTIME

1996 ◽  
Vol 07 (03) ◽  
pp. 241-252 ◽  
Author(s):  
SALVATORE CAPORASO
Keyword(s):  
Turing Machines ◽  
Input Tape ◽  
Machine Model

We introduce a class of safe Turing machines which execute structured while, if-then- else programs and operate on stacks and on a read-only input tape. A hierarchy is obtained by taking as Si the class of all functions computed by programs of loop-depth i. The main result is that S1 equals Lintime and S2 equals Polytime while, for i≥3, we have that Si equals the i-th Grzegorczyk class. By adding to the language a non-deterministic construct choose we take S2 into a class equivalent to NP. This gives a syntactical characterization in a pure-machine model of the mentioned classes.

Scanning x-ray fluorescence microscopy and principal component analysis

1992 ◽  
Vol 50 (2) ◽  
pp. 1752-1753
Author(s):  
Brian Cross
Keyword(s):  
Principal Component Analysis ◽  
Fluorescence Microscopy ◽  
Spatial Resolution ◽  
High Speed ◽  
Image Acquisition ◽  
Principal Component ◽  
Fluorescence Microscope ◽  
Acquisition Rate ◽  
X Ray ◽  
Speed Up

A relatively new entry, in the field of microscopy, is the Scanning X-Ray Fluorescence Microscope (SXRFM). Using this type of instrument (e.g. Kevex Omicron X-ray Microprobe), one can obtain multiple elemental x-ray images, from the analysis of materials which show heterogeneity. The SXRFM obtains images by collimating an x-ray beam (e.g. 100 μm diameter), and then scanning the sample with a high-speed x-y stage. To speed up the image acquisition, data is acquired "on-the-fly" by slew-scanning the stage along the x-axis, like a TV or SEM scan. To reduce the overhead from "fly-back," the images can be acquired by bi-directional scanning of the x-axis. This results in very little overhead with the re-positioning of the sample stage. The image acquisition rate is dominated by the x-ray acquisition rate. Therefore, the total x-ray image acquisition rate, using the SXRFM, is very comparable to an SEM. Although the x-ray spatial resolution of the SXRFM is worse than an SEM (say 100 vs. 2 μm), there are several other advantages.

Direct measurement of electron-diffraction-pattern intensities using an energy loss spectrometer

1989 ◽  
Vol 47 ◽  
pp. 668-669
Author(s):  
A. G. Jackson ◽  
M. Rowe
Keyword(s):  
Thermal Effects ◽  
Dynamic Range ◽  
Scattering Amplitude ◽  
Dynamical Theory ◽  
Site Symmetry ◽  
Proof Of Concept ◽  
Parallel Acquisition ◽  
Kinematic Approximation ◽  
Speed Up ◽  
Structure Calculations

Diffraction intensities from intermetallic compounds are, in the kinematic approximation, proportional to the scattering amplitude from the element doing the scattering. More detailed calculations have shown that site symmetry and occupation by various atom species also affects the intensity in a diffracted beam. [1] Hence, by measuring the intensities of beams, or their ratios, the occupancy can be estimated. Measurement of the intensity values also allows structure calculations to be made to determine the spatial distribution of the potentials doing the scattering. Thermal effects are also present as a background contribution. Inelastic effects such as loss or absorption/excitation complicate the intensity behavior, and dynamical theory is required to estimate the intensity value.The dynamic range of currents in diffracted beams can be 104or 105:1. Hence, detection of such information requires a means for collecting the intensity over a signal-to-noise range beyond that obtainable with a single film plate, which has a S/N of about 103:1. Although such a collection system is not available currently, a simple system consisting of instrumentation on an existing STEM can be used as a proof of concept which has a S/N of about 255:1, limited by the 8 bit pixel attributes used in the electronics. Use of 24 bit pixel attributes would easily allowthe desired noise range to be attained in the processing instrumentation. The S/N of the scintillator used by the photoelectron sensor is about 106 to 1, well beyond the S/N goal. The trade-off that must be made is the time for acquiring the signal, since the pattern can be obtained in seconds using film plates, compared to 10 to 20 minutes for a pattern to be acquired using the digital scan. Parallel acquisition would, of course, speed up this process immensely.

How to speed up to be in time: Action-judgment dissociations in children and adults

2004 ◽  
Vol 63 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Friedrich Wilkening ◽  
Claudia Martin
Keyword(s):  
Rating Scale ◽  
Constant Speed ◽  
Linear Condition ◽  
Speed Up ◽  
Nonlinear Condition ◽  
Speed Change ◽  
Catch Up ◽  
Normative Rule ◽  
Judgment Condition ◽  
Time Linear

Children 6 and 10 years of age and adults were asked how fast a toy car had to be to catch up with another car, the latter moving with a constant speed throughout. The speed change was required either after half of the time (linear condition) or half of the distance (nonlinear condition), and responses were given either on a rating scale (judgment condition) or by actually producing the motion (action condition). In the linear condition, the data patterns for both judgments and actions were in accordance with the normative rule at all ages. This was not true for the nonlinear condition, where children’s and adults’ judgment and also children’s action patterns were linear, and only adults’ action patterns were in line with the nonlinearity principle. Discussing the reasons for the misconceptions and for the action-judgment dissociations, a claim is made for a new view on the development of children’s concepts of time and speed.

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