M. Dietzfelbinger, M. Mkutylowski, and R. Reischuk, Feasible Time-optimal Algorithms for Boolean Functions on Exclusive-write Parallel Random-access Machines, SIAM J. Computing, Vol. 25, No. 6, Dec. 1996. Home/Search Document Details and Download
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On the Complexity of Some Arithmetic Problems over F2[T] - Allender, Bernasconi, Damm, .. (Correct)
....) max u#Bn # u (#) and the average sensitivity of # is s(#) 2 n X u#Bn n X i=1 #(u) #(u (i) 2 n X u#Bn # u (#) Clearly, s(#) # #(#) # n for any #. Sensitivity can be used to obtain lower bounds for the CREW PRAM complexity of Boolean functions (see [25, 18, 19, 27, 32]) The average sensitivity of a function # can be defined equivalently as the sum of the influences of all variables on #, where the influence of u i on #, denoted I i (#) is the probability that flipping the i th variable of a random Boolean input will flip the output. In other words, I i ....
M. Dietzfelbinger, M. Kutylowski and R. Reischuk, `Feasible timeoptimal algorithms for Boolean functions on exclusive-write parallel random access machine', SIAM J. Comp., 25 (1996), 1196--1230.
On Polynomial Representations of Boolean Functions Related to.. - Shparlinski (1998) (3 citations) (Correct)
.... the maximum, over all binary vectors x = x 1 , x r ) # 0, 1 r , of the number of points y # 0, 1 r on the unit Hamming sphere around x with B(y) #= B(x) This parameter is of interest because it can be used to obtain lower bounds for the CREW PRAM complexity of B , see [7, 8, 9, 21, 27]. That is. the complexity on a parallel random access machine with an unlimited number of all powerful processors such that simultaneous reads of a single memory cell by several processors are permitted, but simultaneous writes are not. Now, let us select an r bit square free integer x with x # ....
M. Dietzfelbinger, M. Kuty#lowski and R. Reischuk, `Feasible timeoptimal algorithms for Boolean functions on exclusive-write parallel random access machine', SIAM J. Comp., 25 (1996), 1196--1230.
Circuit and Decision Tree Complexity of Some Number.. - Bernasconi, Damm.. (1998) (1 citation) (Correct)
....integer x = x 1 : x n is square free. Thus g 0 is very similar to the function g given by (1) It has been shown in [25] that the bound oe(g 0 ) bn=60c holds. This parameter is of interest because it can be used to obtain lower bounds for the CREW PRAM complexity of Boolean functions (see [10, 11, 21, 26]) that is the complexity on a parallel random access machine with an unlimited number of all powerful processors, such that simultaneous reads of a single memory cell by several processors are permitted, but simultaneous writes are not. In particular, from the above bound on oe(g 0 ) one ....
M. Dietzfelbinger, M. Kuty/lowski and R. Reischuk, `Feasible timeoptimal algorithms for Boolean functions on exclusive-write parallel random access machine', SIAM J. Comp., 25 (1996), 1196--1230.
Circuit Complexity of Testing Square-Free Numbers - Bernasconi, Shparlinski (1999) (1 citation) (Correct)
....f(x (i) fi fi fi : In [27] it has been shown that for the function g(x) deciding if an n bit integer x is square free, the bound oe(g) bn=60c holds. This sensitivity is of interest because it can be used to obtain lower bounds for the CREW PRAM complexity of a Boolean function f (see [11, 12, 23, 28]) that is the complexity on a parallel random access machine with an unlimited number of all powerful processors, such that simultaneous reads of a single memory cell by several processors are permitted, but simultaneous writes are not. In particular, from the above bound on oe(g) one immediately ....
M. Dietzfelbinger, M. Kuty/lowski and R. Reischuk, `Feasible time-optimal algorithms for Boolean functions on exclusive-write parallel random access machine', SIAM J. Comp., 25 (1996), 1196--1230.
On the Average Sensitivity of Testing Square-Free Numbers - Bernasconi, Damm, al. (1998) (1 citation) (Correct)
....average (taken with respect to the uniform distribution) of the sensitivity of f on input w over all w of a given length. These definitions are made precise below. The sensitivity is of interest because it can be used to obtain lower bounds for the CREW PRAM complexity of Boolean functions (see [9, 10, 16, 19]) that is the complexity on a parallel random access machine with an unlimited number of allpowerful processors, such that simultaneous reads of a single memory cell by several processors are permitted, but simultaneous writes are not. The average sensitivity is a finer characteristic of Boolean ....
M. Dietzfelbinger, M. Kuty/lowski and R. Reischuk, `Feasible time-optimal algorithms for Boolean functions on exclusive-write parallel random access machine', SIAM J. Comp., 25 (1996), 1196--1230.
Approximate compaction and padded-sorting on CREW PRAMs - Kutylowski, Wierzbicki (Correct)
....b n steps, where b = 1 2 (3 p 5) 22, 9] The runtime blog b n 2:34c can be achieved, if the number of processors is exponential in n [8, 22] An improvement over a number of processors is possible. For instance, n bits can be sorted by an n processor CREW PRAM in log b n o(log n) steps [10]. Obviously, there is a trade off between time complexity and the padding factor. For a very small padding factor we get a problem very close to regular sorting (and therefore with large time complexity) while very large padding factors help to reduce the runtime of padded sorting on CRCW PRAMs. ....
....CREW PRAM is able to padded sort n bits leaving as many as n= log n gaps, while the deterministic one requires at least n Gammalog n gaps. The algorithm of Theorem 6 is not feasible in the sense that we use a huge number of processors, however this can be easily improved by using results from [10] and allowing a slight increase of the runtime. 1.2 Applications for approximate compaction and compression Padded sorting, approximate compaction and compression have similar time complexities: Proposition7. i) If an n processor CREW PRAM padded sorts n bits with padding factor in time T , ....
M. Dietzfelbinger, M. Kuty/lowski, and R. Reischuk, Feasible time-optimal algorithms for Boolean functions on exclusive-write PRAMs, SIAM J. Comput., to appear.
Timings for Associative Operations on the MASC Model - Jin, Baker, Batcher (2001) (Correct)
No context found.
M. Dietzfelbinger, M. Mkutylowski, and R. Reischuk, Feasible Time-optimal Algorithms for Boolean Functions on Exclusive-write Parallel Random-access Machines, SIAM J. Computing, Vol. 25, No. 6, Dec. 1996.
Timings for Associative Operations on the MASC Model - Jin, Baker, Batcher (2001) (Correct)
No context found.
M. Dietzfelbinger, M. Mkutylowski, and R. Reischuk, Feasible Time-optimal Algorithms for Boolean Functions on Exclusive-write Parallel Random-access Machines, SIAM J. Computing, Vol. 25, No. 6, Dec. 1996.
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