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On recursive bounds for the exceptional values in speed-up

Douglas Bridges, Cristian Calude
1994 Theoretical Computer Science  
Calude, On recursive bounds for the exceptional values in speed-up, Theoretical Computer Science 132 (1994) 3877394.  ...  This note contains a proof that there is no recursive function of the initial index that gives a bound for the exceptional values in Blum speed-up, but that there is a recursive bounding function of the  ...  The authors thank Manuel Blum, whose suggestions [3] led them to this research and to whom Theorem 2 should be ascribed. They also thank Marius Zimand for his valuable comments on the paper.  ... 
doi:10.1016/0304-3975(94)00050-6 fatcat:fuwkuqjdcnayjej65cty7wntxi

Page 77 of Mathematical Reviews Vol. 53, Issue 2 [page]

1977 Mathematical Reviews  
Finally, it is shown that no self-constructable pyramid can be the “least upper boundfor a speed-up pyramid, in the sense that for any function s with speed-up and any self- constructable functions f  ...  -The “a.e.” term in the compression theorem can be specified in terms of Theorem 3; If t is any recur- sive function, then there is a 0-1 valued recursive c such that g,=c implies S,(x)2t(x) for all but  ... 

Easy Constructions in Complexity Theory: Gap and Speed-Up Theorems

Paul Young
1973 Proceedings of the American Mathematical Society  
Perhaps the two most basic phenomena discovered by the recent application of recursion theoretic methods to the developing theories of computational complexity have been Blum's speed-up phenomena, with  ...  We also present an improved proof of the Blum speed-up theorem which has a straightforward generalization to obtain operator speed-ups. The proofs of this paper are new; the results are not.  ...  The speed-up theorem of [2] is actually slightly stronger than Theorem 1 because, in [2] , fis taken to be zero-one valued.  ... 
doi:10.2307/2039484 fatcat:3dqobrleabgqvc66pgqeu7up4m

Easy constructions in complexity theory: Gap and speed-up theorems

Paul Young
1973 Proceedings of the American Mathematical Society  
Perhaps the two most basic phenomena discovered by the recent application of recursion theoretic methods to the developing theories of computational complexity have been Blum's speed-up phenomena, with  ...  We also present an improved proof of the Blum speed-up theorem which has a straightforward generalization to obtain operator speed-ups. The proofs of this paper are new; the results are not.  ...  The speed-up theorem of [2] is actually slightly stronger than Theorem 1 because, in [2] , fis taken to be zero-one valued.  ... 
doi:10.1090/s0002-9939-1973-0312768-7 fatcat:7ggtyrtj2fgqxgxl5kis27cgee

Effective category and measure in abstract complexity theory

Cristian Calude, Marius Zimand
1996 Theoretical Computer Science  
It is also shown that all complexity classes of recursive predicates have effective measure zero in the space of recursive predicates and, on the other hand, the class of predicates with almost everywhere  ...  Strong variants of the Operator Speed-up Theorem, Operator Gap Theorem and Compression Theorem are obtained using an effective Version of Baire Category Theorem.  ...  Acknowledgements The authors thank the anonymous referee whose valuable comments led them to get stronger results.  ... 
doi:10.1016/0304-3975(95)00066-6 fatcat:b277wpq37fe7ja5c5l44wer654

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

Chung-Chih Li
2009 Theory of Computing Systems  
A classic result known as the speed-up theorem in machineindependent complexity theory shows that there exist some computable functions that do not have best programs for them [2, 3].  ...  We also argue that a type-2 analog of the operator speed-up theorem [18] does not hold, which suggests that this curious speed-up phenomenon disappears in higher-typed computations beyond type-2.  ...  We maintain a global cancelation set C u,x for each u, x ∈ N. The cancelation set, C u,x , determines the value of ϕ e (u, x). C u,x is defined recursively based on: 1.  ... 
doi:10.1007/s00224-009-9182-x fatcat:hppfousmmjegthbdan2go6xxwi

Speed-Up Theorems in Type-2 Computation [chapter]

Chung-Chih Li
2007 Lecture Notes in Computer Science  
Theorem 1 (The Speed-up Theorem [2, 3]). For any recursive function r, there exists a recursive function f such that The original remarks were translated in [7], pages 82-83.  ...  More discussion about the relation between the computational speed-up phenomena and Gödel's speed-up results in logic can be found in [21] . 2 The negation of "for all but finitely many" is "exist infinitely  ...  Then, on input (f, a), the value of f (0) only affects the speed of computing F (f, a). Thus, F (f, a) = 0 for any f ∈ T , and hence (∅, a) is the minimal locking fragment of F on (f, a).  ... 
doi:10.1007/978-3-540-73001-9_50 fatcat:nxfwzmuobjbnjiaup5cyyogfpe

Page 949 of Mathematical Reviews Vol. 55, Issue 3 [page]

1978 Mathematical Reviews  
The author also proves that in general there can be no recursive upper bound on the cardinality of the finite set of exceptions. The paper also studies the nature of lower bounds on computa- tion.  ...  When memory is less expensive than computing time, it is common practice to use tables of function values to speed up function evaluation.  ... 

Cluster-and-Conquer: When Randomness Meets Graph Locality [article]

George Giakkoupis
2020 arXiv   pre-print
Our extensive evaluation on real datasets shows that Cluster-and-Conquer significantly outperforms existing approaches, including LSH, yielding speed-ups of up to x4.42 while incurring only a negligible  ...  In this paper, we remove this drawback with Cluster-and-Conquer (C 2 for short).  ...  As a result, except for the smallest value of N = 500, Cluster-and-Conquer on AmazonMovies does not use recursive splitting and is immune to the impact of N . VII.  ... 
arXiv:2010.11497v1 fatcat:w3ge474m45cizp6rf2n43nnb4u

Arithmetic with Limited Exponentiation [article]

Dmytro Taranovsky
2016 arXiv   pre-print
We present and analyze a natural hierarchy of weak theories, develop analysis in them, and show that they are interpretable in bounded quantifier arithmetic IΔ_0 (and hence in Robinson arithmetic Q).  ...  recursive comprehension, and quantifier-free axiom of choice.  ...  The original theory may have an iterated exponential speed-up of proofs, but (at least if is not too small) that speed-up should only be likely for sentences that (perhaps indirectly) involve very large  ... 
arXiv:1612.05941v1 fatcat:e5uceyudnfghvocs3xcydolbgi

Multi-core and SIMD architecture based implementation of recursive digital filtering algorithms

Dong-hwan Lee, Wonyong Sung
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
for the homogeneous solutions.  ...  In this paper, parallel computation of recursive filtering equations is studied for multi-core architecture with SIMD (Single Instruction Multiple Data) arithmetic support.  ...  time 16L 2.45 4.01 7.58 Speed up 521% 659% 674% Table 3 3 Execution time of M-th order recursive filtering implemented on multi-core SIMD with 8M input samples (ms) Speed Up (DLP+TLP) 145%  ... 
doi:10.1109/icassp.2010.5495519 dblp:conf/icassp/LeeS10 fatcat:yhvfl3bf2vcyzbfanf4hdltjzq

Optimizing Inequality Joins in Datalog with Approximated Constraint Propagation [chapter]

Dario Campagna, Beata Sarna-Starosta, Tom Schrijvers
2012 Lecture Notes in Computer Science  
Experimental evaluation shows good run time speed-ups on a range of non-recursive as well as recursive programs.  ...  Furthermore, our technique improves upon the previously reported in the literature constraint magic set transformation approach.  ...  The experimental evaluation of the approach shows good run time speed-ups on a range of non-recursive as well as recursive programs.  ... 
doi:10.1007/978-3-642-27694-1_9 fatcat:q6nnuuhrd5h4hlelg2bovtikje

Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots

A. G. Akritas, A. W. Strzebonski, P. S. Vigklas
2008 Nonlinear Analysis: Modelling and Control  
average speed-up of 40 % over the original implementation using Cauchy's linear bound.  ...  on the values of the positive roots of polynomials.  ...  The average speed-up was calculated using the formula: Speed-up = 100 · (LMQ − Cauchy)/Cauchy, from which we omitted the minus sign. 3 recursively defined as: L 0 (x) = 1, L 1 (x) = 1 − x, and L n+1  ... 
doi:10.15388/na.2008.13.3.14557 fatcat:uminhm4qofh3le7qbha55ve6ly

Expected time analysis of a simple recursive Poisson random variate generator

L. Devroye
1991 Computing  
Despite the fact that the expected time is not uniformly bounded in)., the algorithm should prove useful for extremely large values of A because virtually all numerical problems associated with the evaluation  ...  The probabilistic analysis presented here is applicable in other situations as well, in which there are a random number of levels of recursion. 1980  ...  The situation gets worse when p is picked as a function of log J.. If we try to speed up matters by selecting n = cJ. with c E (0, 1), the number of recursions becomes O(log J.).  ... 
doi:10.1007/bf02239170 fatcat:7k42bg5rbvhptjwckpmlbj3x5u

Engineering Multi-Level Overlay Graphs for Shortest-Path Queries

Martin Holzer, Frank Schulz, Dorothea Wagner
2006 2006 Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments (ALENEX)  
The main contribution is a systematic experimental study where we investigate the impact of selection criteria and strategies on multi-level overlay graphs and the resulting speed-up achieved for shortest-path  ...  In particular, we consider variations of the multi-level overlay graph used in [Schulz et al. 2002 ] to speed up shortest-path computation.  ...  ACKNOWLEDGMENTS The authors would like to thank Imen Borgi, Sebastian Knopp, and Andrea Schumm for their support in parts of the implementation work.  ... 
doi:10.1137/1.9781611972863.15 dblp:conf/alenex/HolzerSW06 fatcat:ojtcix2b5neavl2ta3wpqhmufq
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