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Unambiguous Computation: Boolean Hierarchies and Sparse Turing-Complete Sets

Lane A. Hemaspaandra, Jörg Rothe
1997 SIAM journal on computing (Print)  
Karp and Lipton proved that if nondeterministic polynomial time has sparse Turing-complete sets, then the polynomial hierarchy collapses.  ...  As examples regarding UP, we have the following: NP has ≤ p m -complete sets, but UP does not robustly possess ≤ p m -complete sets [22] or even ≤ p T -complete sets [31]; NP positively relativizes, in  ...  Sparse Turing-complete and Turing-hard sets for UP. In this section, we show some consequences of the existence of sparse Turing-complete and Turinghard sets for UP.  ... 
doi:10.1137/s0097539794261970 fatcat:rsxr4m5o3bh35bqicrmwx4upx4

Generalized Sparse Learning of Linear Models Over the Complete Subgraph Feature Set

Ichigaku Takigawa, Hiroshi Mamitsuka
2017 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Supervised learning over graphs is an intrinsically difficult problem: simultaneous learning of relevant features from the complete subgraph feature set, in which enumerating all subgraph features occurring  ...  learning studies, such as Adaboost, LPBoost, and LARS/LASSO, can be viewed as variations of a branch-and-bound algorithm with simple bounds, which we call Morishita-Kudo bounds; 2) We present a direct sparse  ...  CONCLUSIONS In terms of sparse learning over the complete subgraph feature set, our contributions were the three points as mentioned in Introduction.  ... 
doi:10.1109/tpami.2016.2567399 pmid:27187949 fatcat:t2ypdcvfafhxpbl32irnoebhae

Sparse Conic Reformulation of Structured QCQPs based on Copositive Optimization with Applications in Stochastic Optimization [article]

Markus Gabl
2022 arXiv   pre-print
The reformulation rests on a generalization of the set-completely positive matrix cone.  ...  can then be approximated via inner and out approximations in order to obtain upper and lower bounds, which potentially close the optimality gap, and hence can give a certificate of exactness for these sparse  ...  This is significant, since for a sparse relaxation to be exact it suffices that its optimal set contains just one appropriately completable matrix.  ... 
arXiv:2101.06219v2 fatcat:gza2kwhf6zfzlfemakw4htgbfm

Optimal Proof Systems and Sparse Sets [chapter]

Harry Buhrman, Steve Fenner, Lance Fortnow, Dieter van Melkebeek
2000 Lecture Notes in Computer Science  
We also examine under what reductions NP n SPARSE can have complete sets. We show a close connection between these issues and red uctions from sparse to tally sets.  ...  We exhibit a relativized world where NP n SPARSE has no complete sets. This gives the first relativized world where no optimal proof systems exist.  ...  The techniques used for relativized results on NP n SPARSE-complete sets also apply to the question of reducing sparse sets to tally sets. We show several results along these lines as well.  ... 
doi:10.1007/3-540-46541-3_34 fatcat:iombfkqz3fd5pgazv4tklwclfq

Page 7322 of Mathematical Reviews Vol. , Issue 90M [page]

1990 Mathematical Reviews  
For deterministic exponential-time (E) complete sets, L. Berman proved that any polynomial-time many- one complete set is polynomial-time one-one complete.  ...  In section 4 we settle this question, showing that for NE any many- one complete set is one-one complete.  ... 

A note on sparse oracles for NP

Timothy J. Long
1982 Journal of computer and system sciences (Print)  
Our single construction yields Mahaney's result for sparse <c-complete sets for NP and also the corresponding result for co-sparse &complete sets for NP.  ...  Consequently, if NP has either a sparse or co-sparse <T-complete set, then the polynomial-time hierarchy collapses to AC. S.  ...  This paper is concerned with the implications of having a (co-)sparse <P,-complete set for NP as opposed to having a (co-)sparse <L-complete set for NP.  ... 
doi:10.1016/0022-0000(82)90050-2 fatcat:zi4czk5rhfaptpladdtwnbt6zi

Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis

Stephen R. Mahaney
1982 Journal of computer and system sciences (Print)  
The main result of this paper is that if there is a sparse NP-complete set under polynomial-time many-one reductions, then P= NP.  ...  All known NP-complete sets, such as SAT, are polynomialtime isomorphic and are not sparse.  ...  Under many-one reductions, a sparse NP(or coNP)-complete set implies P = NP.  ... 
doi:10.1016/0022-0000(82)90002-2 fatcat:tixr36kigfbi3hp6hqsl2cf4ne

A View of Structural Complexity Theory [chapter]

Ronald V. BOOK, Osamu WATANABE
1993 Current Trends in Theoretical Computer Science  
Every complete set in C is in some sense a hardest set in C; but ≤ P m -complete sets are more difficult than ≤ P 1-tt -complete sets, and so on.  ...  In other words, we can conjecture that no ≤ P r -hard set for C (thus, no ≤ P r -complete set for C) is sparse.  ... 
doi:10.1142/9789812794499_0034 dblp:series/wsscs/Book093 fatcat:jcrj2u7caveejeojt6w6ouzqvq

Robustness of PSPACE-complete sets

A. Pavan, Fengming Wang
2007 Information Processing Letters  
We study the robustness of complete languages in PSPACE and prove that they are robust against P-selective sparse sets.  ...  Earlier similar results are known for EXPcomplete sets [3] and NP-complete sets [7] .  ...  Since many-one complete sets for EXP are complete via one-to-one and length-increasing reductions [2] , it easily follows that they are robust against every sparse set in P.  ... 
doi:10.1016/j.ipl.2007.02.018 fatcat:fh4dp5duirapzahrzaoes6yeda

Improving Selection Efficiency of Crop Breeding With Genomic Prediction Aided Sparse Phenotyping

Sang He, Yong Jiang, Rebecca Thistlethwaite, Matthew J. Hayden, Richard Trethowan, Hans D. Daetwyler
2021 Frontiers in Plant Science  
Whether sparse phenotyping resulted in more selection response depended on the correlations of phenotypes between environments.  ...  The breeders' main interest – response to selection – was directly simulated to evaluate the effectiveness of the sparse genomic phenotyping method in a wheat and a rice data set.  ...  DISCUSSION Our study investigated the potential of a genomics-assisted sparse phenotyping method via simulated selection responses based on a wheat and a rice data set.  ... 
doi:10.3389/fpls.2021.735285 pmid:34691111 pmcid:PMC8526887 fatcat:2q4bwhemqzcqnltpywrf5ilnfy

Space-efficient recognition of sparse self-reducible languages

Lane A. Hemaspaandra, Mitsunori Ogihara, Seinosuke Toda
1994 Computational Complexity  
Mahaney and others have shown that sparse self-reducible sets have timeefficient algorithms, and have concluded that it is unlikely that NP has sparse complete sets.  ...  This paper shows that sparse self-reducible sets have space-efficient algorithms, and concludes that it is unlikely that NL, NCk, LOG(DCFL), LOG(CFL), or P have complete (or even Turing-hard) sets oflow  ...  Acknowledgements We are very grateful to Ron Book for making our col1aboration possible, and to Juris Hartmanis and Joel Seiferas for helpful suggestions on presentation.  ... 
doi:10.1007/bf01206639 fatcat:pej3x4kho5avdoykfoc2isenvu

Computation times of NP sets of different densities

J. Hartmanis, Y. Yesha
1984 Theoretical Computer Science  
We show that the detemlinistic computation time for sets in NP can depend on their density if and only if there is a collapse or partial collapse of the corresponding higher nondeterministic and deterministic  ...  We show also that for NP sets of different densities there exist complrete sets of the corresponding density under polynomial time Turing reductions.  ...  On many-one complete sparse sets The existence of a tally set SO in NP such that all other sparse sets in NP are in P%p raises the question whether there exists a tally set which is many-one polynomial  ... 
doi:10.1016/0304-3975(84)90111-7 fatcat:t7z5662iyvchjbubcrgbgardva

Page 642 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
In particular it proves that NL has sparse logspace many-one complete sets if and only if L=NL, and that the same result holds for logspace many-one hard sets.  ...  For example, if there are sparse NP-complete sets then clearly not all NP-complete sets are polynomial-time many-one isomorphic, as SAT is quite dense, and thus cannot be polynomial-time many-one isomorphic  ... 

Page 3121 of Mathematical Reviews Vol. , Issue 85g [page]

1985 Mathematical Reviews  
Yesha, Yaacov (3-TRNT-C) 85g:68024 On certain polynomial-time truth-table reducibilities of complete sets to sparse sets. SIAM J. Comput. 12 (1983), no. 3, 411-425.  ...  , hard or complete sets for reduction types more general than the many-one reductions.  ... 

An effective crosswell seismic traveltime-estimation approach for quasi-continuous reservoir monitoring

Adeyemi Arogunmati, Jerry M. Harris
2012 Geophysics  
This approach involves recording sparse data sets frequently, rather than complete data sets infrequently.  ...  The series of recorded time-lapse data sets is then used to estimate missing, unrecorded data in the sparse data sets. The approach was tested on synthetic and field crosswell traveltime data sets.  ...  ACKNOWLEDGMENTS Special thanks go to the Global Climate and Energy Project (GCEP) for supporting this research and the sponsors of the Seismic Tomography Project at Stanford University for providing the field data set  ... 
doi:10.1190/geo2011-0197.1 fatcat:xb65t6gervbpdkeog7ngsn6cfa
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