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Fine hierarchies and m-reducibilities in theoretical computer science

Victor L. Selivanov
2008 Theoretical Computer Science  
This is a survey of results about versions of fine hierarchies and many-one reducibilities that appear in different parts of theoretical computer science.  ...  We try not only to present the corresponding notions and facts from the particular fields but also to identify the unifying notions, techniques and ideas.  ...  In contrast, in this section we have different reducibilities for the different bases (and for the fine hierarchies over these bases).  ... 
doi:10.1016/j.tcs.2008.06.031 fatcat:canuexaafjau3i4mcdpdu4oibe

Page 6534 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
Finally the authors consider classes Y consisting of the c.e. sets in a single r-degree. For any reducibility besides <7 and <q, any incomplete c.e. degree is bounded in that sense. A c.e.  ...  If B is a hierarchy, e.g., PH, then one types a term in accord with the level in the hierarchy which is the domain of its variables. 03 MATHEMATICAL LOGIC AND FOUNDATIONS 6534 Theorem 4.1.  ... 

Page 3372 of Mathematical Reviews Vol. , Issue 92f [page]

1992 Mathematical Reviews  
and the low hierarchy in NP.  ...  context of a PTIME relation that de- fines L.  ... 

Degrees of Transducibility [chapter]

Jörg Endrullis, Jan Willem Klop, Aleksi Saarela, Markus Whiteland
2015 Lecture Notes in Computer Science  
However, in this hierarchy, all the computable streams are identified in the bottom degree.  ...  In contrast with the degrees of unsolvability, very little is known about the structure of degrees obtained from finite state transducers or Mealy Machines.  ...  embedded in the hierarchy?  ... 
doi:10.1007/978-3-319-23660-5_1 fatcat:57hl6axxanbi7gqagwhifm5dru

Fine-grained I/O Complexity via Reductions: New Lower Bounds, Faster Algorithms, and a Time Hierarchy

Erik D. Demaine, Andrea Lincoln, Quanquan C. Liu, Jayson Lynch, Virginia Vassilevska Williams, Marc Herbstritt
2018 Innovations in Theoretical Computer Science  
We also prove the existence of a time hierarchy for the I/O model, which motivates the fine-grained reductions.  ...  Using fine-grained reductions, we give an algorithm for distinguishing 2 vs. 3 diameter and radius that runs in O(|E| 2 /(M B)) cache misses, which for sparse graphs improves over the previous O(|V | 2  ...  We thank the anonymous reviewers for their helpful suggestions.  ... 
doi:10.4230/lipics.itcs.2018.34 dblp:conf/innovations/DemaineLLLW18 fatcat:dwdccig625e2zfrm6yxrxrnor4

Page 1767 of Mathematical Reviews Vol. 54, Issue 6 [page]

1977 Mathematical Reviews  
Boone [Ann. of Math. (2) 84 (1966), 49-84; MR 34 #1382], who devised a parallel construction for the Turing degrees of non-recursive sets in place of the Grzegorczyk hierarchy.  ...  Lecture Notes in Comput. Sci., Vol. 33, Springer, Berlin, 1975. Let E, denote the nth class of recursive functions in the Grzegorczyk hierarchy.  ... 

Page 5134 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
In particular, let Aver(P, ¥)‘") be the class of randomized problems (D,) with u € ¥ which are av- erage polynomial-time (with respect to 4) Turing reducible to (E,v), and let (NP, ¥)‘”) be the class of  ...  if it is polynomial time Turing reducible to itself while querying only strings whose length is shorter than the input.  ... 

AFET: Automatic Fine-Grained Entity Typing by Hierarchical Partial-Label Embedding

Xiang Ren, Wenqi He, Meng Qu, Lifu Huang, Heng Ji, Jiawei Han
2016 Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing  
Distant supervision has been widely used in current systems of fine-grained entity typing to automatically assign categories (entity types) to entity mentions.  ...  This paper proposes a novel embedding method to separately model "clean" and "noisy" mentions, and incorporates the given type hierarchy to induce loss functions.  ...  The views and conclusions contained in this paper are those of the authors and should not be interpreted as representing any funding agencies.  ... 
doi:10.18653/v1/d16-1144 dblp:conf/emnlp/RenHQHJH16 fatcat:a3wionpxcbfmlhchxal6i2iitm

Page 4568 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
In particular, we show that logspace self-reducible sets are DLOG self-witnessing.  ...  This modification admits an average-case time hierarchy which is independent of distribu- tions and is as tight as the Hartmanis-Sterns hierarchy for the worst-case deterministic time.  ... 

On the Computational Complexity of MapReduce [article]

Benjamin Fish and Jeremy Kun and Ádám Dániel Lelkes and Lev Reyzin and György Turán
2015 arXiv   pre-print
In addition, we prove that, conditioned on a variant of the Exponential Time Hypothesis, there are strict hierarchies within MRC so that increasing the number of rounds or the amount of time per processor  ...  We then show that the class of regular languages, and moreover all of sublogarithmic space, lies in constant round MRC. This result also applies to the MPC model of Andoni et al. (2014).  ...  In the MRC model we use in this paper, we require that every mapper and reducer arise as separate runs of the same Turing machine M .  ... 
arXiv:1410.0245v2 fatcat:bivfh5pkwnbztjqladsaiic6me

Native Chemical Computation. A Generic Application of Oscillating Chemistry Illustrated With the Belousov-Zhabotinsky Reaction. A Review

Marta Dueñas-Díez, Juan Pérez-Mercader
2021 Frontiers in Chemistry  
If so, at what levels in the hierarchy of computing complexity?  ...  We illustrate their implementation with the example of a programmable finite tape Turing machine which using the Belousov-Zhabotinsky oscillatory chemistry is capable of recognizing words in a Context  ...  for many useful conversations related to the work we have summarized here.  ... 
doi:10.3389/fchem.2021.611120 pmid:34046394 pmcid:PMC8144498 fatcat:2xtxhr2ny5g4zoljsqlf62tbde

Wadge Reducibility and Infinite Computations

Victor Selivanov
2008 Mathematics in Computer Science  
In [s94a,s95,s98] the Wagner hierarchy was related to descriptive set theory, Büchi-Landweber theorem and the fine hierarchy[s83,s95].  ...  In [s94a,s95,s98] the Wagner hierarchy was related to descriptive set theory, Büchi-Landweber theorem and the fine hierarchy[s83,s95].  ...  non-deterministic Turing machines (in fact, the same was proved also for the weaker notion of Büchi 1-counter automata).  ... 
doi:10.1007/s11786-008-0042-x fatcat:2knzkgv3rzawparll4joxfs2iu

Proper Hierarchies in Polylogarithmic Time and Absence of Complete Problems [article]

Flavio Ferrarotti, Senén González, Klaus-Dieter Schewe, José María Turull-Torres
2019 arXiv   pre-print
In this paper the descriptive complexity theory of polylogarithmic time is taken further showing that there are strict hierarchies inside each of the classes of the hierarchy.  ...  The polylogarithmic time hierarchy structures sub-linear time complexity.  ...  The research reported in this paper results from the project Higher-Order Logics and Structures supported by the Austrian Science Fund (FWF: [I2420-N31]).  ... 
arXiv:1911.13104v1 fatcat:gagdfvtm6bb55aktnqmyzs2k54

Page 442 of Metal Progress Vol. 37, Issue 4 [page]

1940 Metal Progress  
THIS IS HOW: SMO ohWD — Lowers initial cost Increases furnace capacity Reduces fuel cost Handles easier Saves time in handling and loading Reduces pot cost per hour Outlasts average cast alloy equipment  ...  cleav- age planes in a Widmanstatten pattern that is to say, related to the micrographic structure; or b) To a particular crystal- line organization (superstrue- ture), or toa special distribution lattice  ... 

Well Quasiorders and Hierarchy Theory [article]

Victor Selivanov
2018 arXiv   pre-print
While the classical hierarchies of sets usually degenerate to structures very close to ordinals, the extension of them to functions requires more complicated WQOs, and the same applies to reducibilities  ...  We discuss some applications of WQOs to several fields were hierarchies and reducibilities are the principal classification tools, notably to Descriptive Set Theory, Computability theory and Automata Theory  ...  I am grateful to Leibniz-Zentrum für Informatik for accepting and taking care of Dagstuhl Seminars 08271, 11411, 15392, 16031 which were important for promoting the topic of this paper.  ... 
arXiv:1809.02941v1 fatcat:7ztqokcr7ret3fiusnzszegyxa
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