Bounded Variable Logic, Parameterized Logarithmic Space, and Savitch’s Theorem

2014 ◽  
pp. 183-195 ◽  
Author(s):  
Yijia Chen ◽  
Moritz Müller
Keyword(s):  
Logarithmic Space ◽  
Variable Logic

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.

scholarly journals An Effective Characterization of the Alternation Hierarchy in Two-Variable Logic

2017 ◽  
Vol 18 (4) ◽  
pp. 1-22
Author(s):  
Andreas Krebs ◽  
Howard Straubing
Keyword(s):  
Variable Logic

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.

scholarly journals One-variable logic meets Presburger arithmetic

2020 ◽  
Vol 802 ◽  
pp. 141-146
Author(s):  
Bartosz Bednarczyk
Keyword(s):  
Presburger Arithmetic ◽  
Variable Logic
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