Unambiguity and fewness for logarithmic space

1991 ◽  
pp. 168-179 ◽  
Author(s):  
Gerhard Buntrock ◽  
Birgit Jenner ◽  
Klaus-Jörn Lange ◽  
Peter Rossmanith
Keyword(s):  
Logarithmic Space

Evaluation of Selected Pier-Scour Equations Using Field Data

1996 ◽  
Vol 1523 (1) ◽  
pp. 186-195 ◽  
Author(s):  
Mark N. Landers ◽  
David S. Mueller
Keyword(s):  
Field Measurements ◽  
Bridge Piers ◽  
Critical Ratio ◽  
Scour Depth ◽  
Flow Depth ◽  
Clear Water ◽  
Pier Scour ◽  
Logarithmic Space ◽  
State Highway ◽  
Federal Highway

Field measurements of channel scour at bridges are needed to improve the understanding of scour processes and the ability to accurately predict scour depths. An extensive data base of pier-scour measurements has been developed over the last several years in cooperative studies between state highway departments, the Federal Highway Administration, and the U.S. Geological Survey. Selected scour processes and scour design equations are evaluated using 139 measurements of local scour in live-bed and clear-water conditions. Pier-scour measurements were made at 44 bridges around 90 bridge piers in 12 states. The influence of pier width on scour depth is linear in logarithmic space. The maximum observed ratio of pier width to scour depth is 2.1 for piers aligned to the flow. Flow depth and scour depth were found to have a relation that is linear in logarithmic space and that is not bounded by some critical ratio of flow depth to pier width. Comparisons of computed and observed scour depths indicate that none of the selected equations accurately estimate the depth of scour for all of the measured conditions. Some of the equations performed well as conservative design equations; however, they overpredict many observed scour depths by large amounts. Some equations fit the data well for observed scour depths less than about 3 m (9.8 ft), but significantly underpredict larger observed scour depths.

Space-bounded OTMs and REG ∞

Computability ◽  
2021 ◽  
pp. 1-16
Author(s):  
Merlin Carl
Keyword(s):  
Complexity Theory ◽  
Turing Machine ◽  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Logarithmic Space ◽  
Working Space ◽  
Important Theorem

An important theorem in classical complexity theory is that REG = LOGLOGSPACE, i.e., that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs) and show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA, which is a transfinite analogue of LOGLOGSPACE ⊆ REG; the other direction, however, is easily seen to fail.

Diving into the queue

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 89-110
Author(s):  
Simon Beier ◽  
Martin Kutrib ◽  
Andreas Malcher ◽  
Matthias Wendlandt
Keyword(s):  
Finite Number ◽  
Finite Automata ◽  
Time Constraints ◽  
Membership Problem ◽  
Storage Medium ◽  
Logarithmic Space ◽  
Better Than

We introduce and study the model of diving queue automata which are basically finite automata equipped with a storage medium that is organized as a queue. Additionally, two queue heads are provided at both ends of the queue that can move in a read-only mode inside the queue. In particular, we consider suitable time constraints and the case where only a finite number of turns on the queue is allowed. As one main result we obtain a proper queue head hierarchy, that is, two heads are better than one head, and one head is better than no head. Moreover, it is shown that the model with one queue head, finitely many turns, and no time constraints as well as the model with two queue heads, possibly infinitely many turns, and time constraints is captured by P and has a P-complete membership problem. We obtain also that a subclass of the model with two queue heads is already captured by logarithmic space. Finally, we consider decidability questions and it turns out that almost nothing is decidable for the model with two queue heads, whereas we obtain that at least emptiness and finiteness are decidable for subclasses of the model with one queue head.

DFT TECHNIQUES FOR SIZE ESTIMATION OF DATABASE JOIN OPERATIONS

1999 ◽  
Vol 10 (01) ◽  
pp. 81-102 ◽  
Author(s):  
KAMİl SARAÇ ◽  
ÖMER EĞECİOĞLU ◽  
AMR EL ABBADI
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Distribution ◽  
Fourier Coefficients ◽  
Experimental Results ◽  
Direct Approach ◽  
Size Estimation ◽  
Logarithmic Space ◽  
Novel Algorithms ◽  
Special Case

Novel algorithms based on the Discrete Fourier Transform (DFT) are proposed to estimate the size of relations resulting from join operations. We start with an approach in which the frequency distribution values are transformed using the DFT and the Fourier coefficients are used to construct histograms. Our main contribution is a direct approach which uses the amplitudes of the DFT coefficients iteratively. The proposed algorithm gives the exact join size using logarithmic space for the special case of self join. A generalization to compute the join of arbitrary relations is then used to develop two tree-based techniques that provide a spectrum of algorithms which interpolate storage requirements versus accuracy of the estimation obtained. Finally, we present experimental results to exhibit the effectiveness of our approach.

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