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On recursive bounds for the exceptional values in speed-up

1994
*
Theoretical Computer Science
*

Calude,

doi:10.1016/0304-3975(94)00050-6
fatcat:fuwkuqjdcnayjej65cty7wntxi
*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. ...##
###
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*bound*”*for*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

1973
*
Proceedings of the American Mathematical Society
*

Perhaps

doi:10.2307/2039484
fatcat:3dqobrleabgqvc66pgqeu7up4m
*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*. ...##
###
Easy constructions in complexity theory: Gap and speed-up theorems

1973
*
Proceedings of the American Mathematical Society
*

Perhaps

doi:10.1090/s0002-9939-1973-0312768-7
fatcat:7ggtyrtj2fgqxgxl5kis27cgee
*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*. ...##
###
Effective category and measure in abstract complexity theory

1996
*
Theoretical Computer Science
*

It is also shown that all complexity classes of

doi:10.1016/0304-3975(95)00066-6
fatcat:b277wpq37fe7ja5c5l44wer654
*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. ...##
###
Speed-Up Theorems in Type-2 Computations Using Oracle Turing Machines

2009
*
Theory of Computing Systems
*

A classic result known as

doi:10.1007/s00224-009-9182-x
fatcat:hppfousmmjegthbdan2go6xxwi
*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. ...##
###
Speed-Up Theorems in Type-2 Computation
[chapter]

2007
*
Lecture Notes in Computer Science
*

Theorem 1 (

doi:10.1007/978-3-540-73001-9_50
fatcat:nxfwzmuobjbnjiaup5cyyogfpe
*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). ...##
###
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]

2020
*
arXiv
*
pre-print

Our extensive evaluation

arXiv:2010.11497v1
fatcat:w3ge474m45cizp6rf2n43nnb4u
*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. ...##
###
Arithmetic with Limited Exponentiation
[article]

2016
*
arXiv
*
pre-print

We present and analyze a natural hierarchy of weak theories, develop analysis

arXiv:1612.05941v1
fatcat:e5uceyudnfghvocs3xcydolbgi
*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 ...##
###
Multi-core and SIMD architecture based implementation of recursive digital filtering algorithms

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% ...

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

2012
*
Lecture Notes in Computer Science
*

Experimental evaluation shows good run time

doi:10.1007/978-3-642-27694-1_9
fatcat:q6nnuuhrd5h4hlelg2bovtikje
*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. ...##
###
Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots

2008
*
Nonlinear Analysis: Modelling and Control
*

average

doi:10.15388/na.2008.13.3.14557
fatcat:uminhm4qofh3le7qbha55ve6ly
*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 ...##
###
Expected time analysis of a simple recursive Poisson random variate generator

1991
*
Computing
*

Despite

doi:10.1007/bf02239170
fatcat:7k42bg5rbvhptjwckpmlbj3x5u
*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.). ...##
###
Engineering Multi-Level Overlay Graphs for Shortest-Path Queries

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. ...

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