Unimprovable Upper Bounds on Time Complexity of Decision Trees

1997 ◽  
Vol 31 (2) ◽  
pp. 157-184 ◽  
Author(s):  
Mikhail Moshkov
Keyword(s):  
Decision Trees ◽  
Time Complexity ◽  
Upper Bounds

scholarly journals A Complexity Analysis of Functional Interpretations

2003 ◽  
Vol 10 (12) ◽  
Author(s):  
Mircea-Dan Hernest ◽  
Ulrich Kohlenbach
Keyword(s):  
Quantitative Analysis ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Upper Bounds ◽  
Weak Base ◽  
Functional Interpretation ◽  
Maximal Size ◽  
Negative Translation

We give a quantitative analysis of Gödel's functional interpretation and its monotone variant. The two have been used for the extraction of programs and numerical bounds as well as for conservation results. They apply both to (semi-)intuitionistic as well as (combined with negative translation) classical proofs. The proofs may be formalized in systems ranging from weak base systems to arithmetic and analysis (and numerous fragments of these). We give upper bounds in basic proof data on the depth, size, maximal type degree and maximal type arity of the extracted terms as well as on the depth of the verifying proof. In all cases terms of size linear in the size of the proof at input can be extracted and the corresponding extraction algorithms have cubic worst-time complexity. The verifying proofs have depth linear in the depth of the proof at input and the maximal size of a formula of this proof.

scholarly journals Bounds on Complexity when Sorting Reals

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Linear Function ◽  
Time Complexity ◽  
Upper Bounds ◽  
Data Set ◽  
Counting Sort ◽  
Sort Algorithm

We derive the upper bounds on the complexity of the counting sort algorithm applied to reals. We show that the algorithm has a time complexity O(n) for n data items distributed uniformly or exponentially. The proof is based on the fact that the use of comparison-type sorting for small portion of a given data set is bounded by a linear function of n. Some numerical demonstrations are discussed.

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