Vince Grolmusz

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We consider the relative power of concurrentwrite PRAMs when the number of processors (and input variables) is fixed at n, and infinite shared memory is allowed. Several different models (COMMON, ARBITRARY, PRIORITY) have been used for algorithm design in the literature; these models differ in their method of write-conflict resolution. Recent work in(More)
We prove a version of the Ray-Chaudhuri–Wilson and Frankl–Wilson theorems for k-wise intersections and also generalize a classical code-theoretic result of Delsarte for k-wise Hamming distances. A set of code-words a; a; . . . ; ak of length n have k-wise Hamming-distance ‘; if there are exactly ‘ such coordinates, where not all of their coordinates(More)
Modular gates are known to be immune for the random restriction techniques of Ajtai Ajt83], Furst, Saxe, Sipser FSS84], Yao Yao85] and H astad H as86]. We demonstrate here a random clustering technique which overcomes this diiculty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Th erien(More)
We give a generalization for the Deza-Frankl-Singhi Theorem in case of multiple intersections. More exactly, we prove, that if H is a set-system, which satisfies that for some k, the k-wise intersections occupy only ` residue-classes modulo a p prime, while the sizes of the members of H are not in these residue classes, then the size of H is at most (k − 1)(More)
MOTIVATION Enormous and constantly increasing quantity of biological information is represented in metabolic and in protein interaction network databases. Most of these data are freely accessible through large public depositories. The robust analysis of these resources needs novel technologies, being developed today. RESULTS Here we demonstrate a(More)
We examine n×nmatrices over Zm, with 0’s in the diagonal and nonzeros elsewhere. If m is a prime, then such matrices have large rank (i.e., n1/(p−1) − O(1) ). If m is a non-prime-power integer, then we show that their rank can be much smaller. For m = 6 we construct a matrix of rank exp(c √ log n log log n). We also show, that explicit constructions of such(More)
We examine the power of Boolean functions with low L 1 norms in several settings. In large part of the recent literature, the degree of a polynomial which represents a Boolean function in some way was chosen to be the measure of the complexity of the Boolean function (see, e. have high degree, but small L 1 norms. So, in conjunction with communication(More)