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Complexity of Boolean functions on PRAMs - Lower bound techniques [chapter]

Mirosław Kutyłowski
1992 Lecture Notes in Computer Science  
Determining time necessary for computing important functions on parallel machines is one of the most important problems in complexity theory for parallel algorithms.  ...  In this survey paper, we discuss the results that have been obtained for three types of parallel random access machines (PRAMs): CREW, ROBUST and EREW. † throughout the paper, log stands for log to the  ...  The overall strategy of determining lower bounds for Boolean functions on PRAMs is the following: First a complexity measure m for Boolean functions is defined.  ... 
doi:10.1007/3-540-55488-2_34 fatcat:xryrodty2bar3faapp6jfribry

Exact lower time bounds for computing Boolean functions on CREW PRAMs

Martin Dietzfelbinger, Mirosław Kutyłowski, Rüdiger Reischuk
1994 Journal of computer and system sciences (Print)  
The time complexity of Boolean functions on abstract concurrent-read exclusive-write parallel random access machines (CREW PRAMs) is considered.  ...  lower bound valid for all Boolean functions in the bounded error model.  ...  ACKNOWLEDGMENTS The first author thanks Friedhelm Meyer auf der Heide for many discussions in the course of the development of the lower bound argument; thanks to Ilan Newman for pointing out Szegedy's  ... 
doi:10.1016/s0022-0000(05)80003-0 fatcat:5yp6wsy5uvfqdppw4iwwrkt26u

CREW PRAMS and decision trees

N. Nisan
1989 Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89  
This paper gives a full characterization of the time needed to compute a boolean function on a CREW PRAM with an unlimited number of processors.  ...  The characterization is given in terms of a new complexity measure of boolean functions: the "block sensitivity".  ...  Actually, [CDR] proved a more general result as they give a lower bound on the time needed to compute a function on a CREW PRAM in terms of the function's "sensitivity".  ... 
doi:10.1145/73007.73038 dblp:conf/stoc/Nisan89 fatcat:uzzmpa3ldbcdvl4mcj4l75z34q

CREW PRAMs and Decision Trees

Noam Nisan
1991 SIAM journal on computing (Print)  
This paper gives a full characterization of the time needed to compute a boolean function on a CREW PRAM with an unlimited number of processors.  ...  The characterization is given in terms of a new complexity measure of boolean functions: the "block sensitivity".  ...  Actually, [CDR] proved a more general result as they give a lower bound on the time needed to compute a function on a CREW PRAM in terms of the function's "sensitivity".  ... 
doi:10.1137/0220062 fatcat:umsq3apnvvcurhas76wu2wee4m

Page 5544 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
We further show that the (bounded error) probabilistic time complexity of Boolean functions on CREW PRAMs differs at most by a constant factor from the deterministic time complex- ity.  ...  .], prove a general lower bound valid for all Boolean functions in the bounded er- ror model.  ... 

Page 5448 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
n))-lower bounds for Andreev’s function, which is now the largest lower bound for the monotone circuit complexity of functions in NP.  ...  Razborov proved the first superpolynomial lower bounds on the monotone circuit complexity of functions in NP. Afterwards An- dreev proved even exponential lower bounds for other functions in NP.  ... 

Page 5373 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
(ii) Some concrete Boolean functions cannot be approximated by polynomials with a low degree. This lower bound technique was extended by the author [“A note on a theorem of Razborov”, COINS Tech.  ...  The idea of his paper was to show a superpolynomial lower bound on the above-mentioned Boolean circuits with AND, OR, and XOR gates by proving the following two facts: (i) Each Boolean function computable  ... 

Limits on the Power of Parallel Random Access Machines with Weak Forms of Write Conflict Resolution

Faith E. Fich, Russell Impagliazzo, Bruce Kapron, Valerie King, Mirosław Kutyłowski
1996 Journal of computer and system sciences (Print)  
We prove a lower bound on the time required by the ROBUST PRAM to compute Boolean functions in terms of the number of different values each memory cell of the PRAM can contain and the degree of the function  ...  We extend our result to obtain a lower bound, depending on the number of processors, for computing Boolean functions on the ROBUST PRAM, even with memory cells of unbounded size. A article no. 0052  ...  This work was supported by the Natural Sciences and Engineering Research Council of Canada, the Information Technology Research Centre of Ontario, the Defense Advanced Research Projects Agency of the United  ... 
doi:10.1006/jcss.1996.0052 fatcat:quyrmsi5fbbjjhjpyyatmtyw4a

New lower bounds for parallel computation

Ming Li, Yaacov Yesha
1989 Journal of the ACM  
Lower bounds are proven on the parallel-time complexity of several basic functions on the most powerful concurrent-read concurrent-write PRAM with unlimited shared memory and unlimited power of individual  ...  The simulation technique is of independent interest since it can serve as a general tool to translate circuit lower bounds into PRAM lower bounds.  ...  Q(log n) Lower Bound on the Bit Complexity of ADDITION and Related Functions Recently, Fich et al [9] and Meyer auf der Heide and Wigderson [22] proved several important lower bounds on PRIORITY(w)  ... 
doi:10.1145/65950.65959 fatcat:3ehin4j34vb65hnyqu22jvrlbq

On separating the EREW and CREW PRAM models

Eli Gafni, Joseph Naor, Prabhakar Ragde
1989 Theoretical Computer Science  
This problem defines a partial function, that is, one that is defined only on a restricted set of inputs.  ...  Here we solve this problem by generalizing the Selection Problem to a derision tree problem which is defined on a full domain and to which Snir's lower bound applies.  ...  It is easy to see that the complexity of problem (S) on a CREW PRAM is O(1), and Snir [6] proved a O(x/~g n) upper ar_d ',,r~er bound on solving the problem in the EREW model.  ... 
doi:10.1016/0304-3975(89)90169-2 fatcat:gwzkjumgnjfeliogznkgiddde4

Optimal bounds for decision problems on the CRCW PRAM

P. Beame, J. Hastad
1987 Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87  
We prove optimal R(log n/log log n) lower bounds on the time for CRCW PRAM's with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems.  ...  We also exhibit a strict time hierarchy of explicit Boolean functions of n bits on such machines which holds up to O(log n/ log log n) time.  ...  We also prove a tight O(logn) lower bound on the time to compute almost all n-bit Boolean functions on CRCW PRAM's with polynomial numbers of processors.  ... 
doi:10.1145/28395.28405 dblp:conf/stoc/BeameH87 fatcat:kepq6msierfdtixy4vvshmnzlm

Optimal bounds for decision problems on the CRCW PRAM

Paul Beame, Johan Hastad
1989 Journal of the ACM  
We prove optimal R(log n/log log n) lower bounds on the time for CRCW PRAM's with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems.  ...  We also exhibit a strict time hierarchy of explicit Boolean functions of n bits on such machines which holds up to O(log n/ log log n) time.  ...  We also prove a tight O(logn) lower bound on the time to compute almost all n-bit Boolean functions on CRCW PRAM's with polynomial numbers of processors.  ... 
doi:10.1145/65950.65958 fatcat:tja3jvt6yrckncrkqzouzi7vxi

Page 1964 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
Lower bound techniques are investigated which behave multiplica- tively for functions defined on direct sums of sets.  ...  It may be of interest especially for re- searchers working in proving lower bounds on complexity.  ... 

Page 3948 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
{For the entire collection see MR 91¢:68005.} 92g:68047 68Q10 68Q25 Kutylowski, Mirostaw (PL-WROC-C) Time complexity of Boolean functions on CREW PRAMs. SIAM J. Comput. 20 (1991), no. 5, 824-833.  ...  It follows that the time required by the logical ‘or’ of n variables is at least log,n. We present an essentially different method of estimating PRAM complexity of Boolean functions.  ... 

Separating the power of EREW and CREW PRAMs with small communication width [chapter]

Paul Beame, Faith E. Fich, Rakesh K. Sinha
1993 Lecture Notes in Computer Science  
We prove that evaluating a Boolean decision tree of height h requires 0(hÂ(m+log*h)) time on any EREW PRAM with communication width m and any number of processors.  ...  Since this function can be easily computed in time O(-h) on a CREW PRAM with communication width 1 using 2 O(h) processors, this gives a separation between the two models whenever the EREW PRAM has communication  ...  For example, the technique in the lower bound result for the OR function on CREW(1) PRAMs [VW85, Bea86] is very similar to the technique that Kuty*owski [Kut91] eventually used in his optimal bound  ... 
doi:10.1007/3-540-57155-8_245 fatcat:2sxnhzzbnjfd7aw2wb4xgi3aea
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