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The Sublogarithmic Alternating Space World

Maciej Liśkiewicz, Rüdiger Reischuk
1996 SIAM journal on computing (Print)  
Furthermore, this separation is extended to space classes defined by ATMs with a nonconstant alternation bound A provided that the product A · S grows sublogarithmically.  ...  Finally, for sublogarithmic bounded ATMs we give a separation between the weak and strong space measure, and prove a logarithmic lower space bound for the recognition of nonregular contextfree languages  ...  This result gives a complete and best possible separation for the sublogarithmic space world, except for the first level k = 1.  ... 
doi:10.1137/s0097539793252444 fatcat:csvph7zvnjc3pa2oiyazr4uyri

Sublogarithmic Bounds on Space and Reversals

Viliam Geffert, Carlo Mereghetti, Giovanni Pighizzini
1998 SIAM journal on computing (Print)  
This also separates determinism from the higher levels of the alternating hierarchy.  ...  For any (arbitrarily slow growing) unbounded monotone recursive function f (n), a nonregular unary language is presented that can be accepted by a middle ⇧ 1 alternating Turing machine in s(n) space and  ...  The authors wish to thank an anonymous referee for helpful comments and remarks.  ... 
doi:10.1137/s0097539796301306 fatcat:xzvfcejmjvd4jhotxrloi2pyim

Page 4503 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
Logic 73 (1995), no. 2, 171-190; MR 961:03034). 97g:68077 68Q15 68Q05 68Q10 Liskiewicz, Maciej (PL-WROC-C; Wroclaw); Reischuk, Riidiger The sublogarithmic alternating space world.  ...  Denote by x, Space(s) [resp. 1, Space(s)] the complexity classes defined by s-space-bounded alternating Turing machines which alternate at most kK —1 times and start in an existential [resp. universal]  ... 

A correction to Andersson's fusion tree construction

Željko Vrba, Pål Halvorsen, Carsten Griwodz
2014 Theoretical Computer Science  
We revisit the fusion tree [1] data structure as presented by Andersson et al. [2] . We show that Andersson's ranking algorithm has a subtle flaw and we present a revised algorithm.  ...  guarantees sublogarithmic amortized cost of inserts and deletes.  ...  in [2] , where they explicitly described an alternate way of constructing and querying nodes.  ... 
doi:10.1016/j.tcs.2013.09.028 fatcat:auetka2t3nhejnrekszx7iyudi

Page 2074 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
with sublogarithmic space (55-63); Tsunehiro Yoshinaga and Katsushi Inoue, Alternation for two-way (inkdot) multi-counter automata with sublinear space (64-72); Takashi Tabe and Thomas Zeugmann, Two variations  ...  World Scientific Publishing Co., Inc., River Edge, NJ, 1995. xii+360 pp. $106.00. ISBN 981-02-2129-0 {The First Conference has been reviewed [MR 91e:30001].} Contents: B.  ... 

Transdichotomous Results in Computational Geometry, I: Point Location in Sublogarithmic Time

Timothy M. Chan, Mihai Ptraşcu
2009 SIAM journal on computing (Print)  
The same space and query bound hold for 2-d nearest neighbor queries (also known as the static "post office" problem).  ...  Point location in sublogarithmic time * This work is based on a combination of two conference papers that appeared in Proc. 47th IEEE Sympos. Found. Comput.  ...  Alternative Bounds We now describe some alternative bounds which depend on the universe size and the space.  ... 
doi:10.1137/07068669x fatcat:2xvbqapx5fgo3blyl3dpak7vlu

Page 1745 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
hierarchy for sublogarithmic space is infinite.  ...  It is proved that, for space complexities lying between loglog and log, permitting more alternations always strictly increases the sets of recognizable languages.  ... 

The complexity world below logarithmic space

M. Liskiewicz, R. Reischuk
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory  
This method cannot be applied in the sublogarithmic space world.  ...  Let us nally investigate the relation between the sublogarithmic space world and context-free languages.  ...  For this purpose, let us denote by the set of all nontrivial sublogarithmic space bounds. 2 How Does the Sublogarithmic Space World Look like?  ... 
doi:10.1109/sct.1994.315816 dblp:conf/coco/LiskiewiczRR94 fatcat:nwfzezmrbnhidpdo5xxohliela

Spatially embedded random networks

L. Barnett, E. Di Paolo, S. Bullock
2007 Physical Review E  
for scale free degree distributions and the existence of small-world spatial networks.  ...  Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc.  ...  ACKNOWLEDGMENT This study has been supported by the Spatially Embedded Complex Systems Engineering ͑SECSE͒ project, EPSRC Grant No. EP/C51632X/1.  ... 
doi:10.1103/physreve.76.056115 pmid:18233726 fatcat:myo3dog23nfdjm64dmsmuinppi

Social networks spread rumors in sublogarithmic time

Benjamin Doerr, Mahmoud Fouz, Tobias Friedrich
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
This is the first time that a sublogarithmic broadcast time is proven for a natural setting.  ...  to Θ(log n/ log log n), which is the diameter of the graph.  ...  Acknowledgments We are thankful to the reviewers for helpful comments that improved the presentation of the results significantly.  ... 
doi:10.1145/1993636.1993640 dblp:conf/stoc/DoerrFF11 fatcat:jv56bakusrhf7ffbkk3cjz4miy

Social Networks Spread Rumors in Sublogarithmic Time

Benjamin Doerr, Mahmoud Fouz, Tobias Friedrich
2011 Electronic Notes in Discrete Mathematics  
This is the first time that a sublogarithmic broadcast time is proven for a natural setting.  ...  to Θ(log n/ log log n), which is the diameter of the graph.  ...  Acknowledgments We are thankful to the reviewers for helpful comments that improved the presentation of the results significantly.  ... 
doi:10.1016/j.endm.2011.09.050 fatcat:vm4tmbutnzboxgy3r5lnoczmpe

On space-bounded synchronized alternating Turing machines

Oscar H. Ibarra, Nicholas Q. Trân
1992 Theoretical Computer Science  
Howwr. the alternating Turing machine is not a realistic model for real-world parallel c~~mputers. because it dots not allow any communication among its processus.  ...  The first lemma shows that synchronization cannot be replaced by nondeterminism, modified acceptance, off-line capability and sublogarithmic space combined. Lemma3.1.  ...  Note that if U( lS.4 TM (log(n))) = Y'( 1 A TM (log(n))) then alternating Turing machines use space optimally, and hence P= NP (see [S] ).  ... 
doi:10.1016/0304-3975(92)90351-f fatcat:eu4yogf3wjcydc2dhugo2yau3q

Dynamic Orthogonal Range Searching on the RAM, Revisited

Timothy M. Chan, Konstantinos Tsakalidis, Marc Herbstritt
2017 International Symposium on Computational Geometry  
We present a new data structure achieving O log n log log n + k optimal query time and O log 2/3+o(1) n update time (amortized) in the word RAM model, where n is the number of data points and k is the  ...  In the case of 3-sided queries, our update time reduces to O log 1/2+ε n , improving Wilkinson's previous bound [ESA 2014] of O log 2/3+ε n .  ...  space bound.  ... 
doi:10.4230/lipics.socg.2017.28 dblp:conf/compgeom/ChanT17 fatcat:qgdqfi2u3bcmhlgk7fdihglztm

Efficient Low-Contention Parallel Algorithms

Phillip B. Gibbons, Yossi Matias, Vijaya Ramachandran
1996 Journal of computer and system sciences (Print)  
These logarithmic or sublogarithmic time algorithms considerably improve upon the best known EREW PRAM algorithms for these problems, while avoiding the high-contention steps typical of CRCW PRAM algorithms  ...  For the Kendall Square KSR1, the contention properties can be approximated by the concurrent-read, queue-write rule.  ...  ( j) n space.  ... 
doi:10.1006/jcss.1996.0079 fatcat:yvkouuxtyrhr3eyn3htpem3dwy

Optimal Simulations between Unary Automata

Carlo Mereghetti, Giovanni Pighizzini
2001 SIAM journal on computing (Print)  
Further results on simulating unary one-way alternating finite automata are also discussed.  ...  ends of the input tape.  ...  The authors wish to thank anonymous referees for helpful comments and remarks. Moreover, the authors kindly acknowledge Viliam Geffert for stimulating discussions.  ... 
doi:10.1137/s009753979935431x fatcat:g6vikbqczrfghbgaetwwuyicaq
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