1,721,870 research outputs found
On Read-k Projections of the Determinant
Get PDFWe consider read-k determinantal representations of polynomials and prove some non-expressibility results. A square matrix M whose entries are variables or field elements will be called read-k, if every variable occurs at most k times in M. It will be called a determinantal representation of a polynomial f if f = det(M). We show that
- the n × n permanent polynomial does not have a read-k determinantal representation for k ∈ o(√n/log n) (over a field of characteristic different from two). We also obtain a quantitative strengthening of this result by giving a similar non-expressibility for k ∈ o(√n/log n) for an explicit n-variate multilinear polynomial (as opposed to the permanent which is n²-variate)
On Separating the Read-k-Times Branching Program Hierarchy
No full textWe obtain an exponential separation between consecutive levels in the hierarchy of classes of functions computable by polynomial-size syntactic read-k-times branching programs, for all k ? 0, as conjectured by various authors [Weg87, SS93, Pon95]. For every k, we exhibit two explicit functions that can be computed by linear-sized read-(k+1)-times branching programs but require size exp n\Omega i n 1=k+1 2 \Gamma2k k \Gamma4 jo to be computed by any read-k-times branching program. The result actually gives the strongest possible separation --- the exponential lower bound applies to both non-deterministic read-k-times branching programs and randomized read-k-times branching programs with 2-sided error ", for some " ? 0. The only previously known results are the separation between k = 1 and k = 2 [BRS93] and a separation of non-deterministic read-k from deterministic read-(k ln k= ln 2 +C), where C is some appropriate constant, for each k [Oko97]. A simple corollary of our result..
A Note on Read-k Times Branching Programs
Get PDF. A syntactic read-k times branching program has the restriction that no variable occurs more than k times on any path (whether or not consistent) . We exhibit an explicit Boolean function f; which cannot be computed by nondeterministic syntactic read-k times branching programs of size less than exp i \Omega ip n k 2k jj ; although its complement :f has a nondeterministic syntactic read-once branching program of polynomial size. This, in particular, means that the nonuniform analogue of NLOGSPACE = co \Gamma NLOGSPACE fails for syntactic read-k times networks with k = o(log n): We also show that (even for k = 1) the syntactic model is exponentially weaker then more realistic "nonsyntactic" one. Keywords: Branching programs, read-k times networks, lower bounds y To appear in: RAIRO J. Theoretical Informatics and Application z Universitat Trier, FB Informatik, 54286 Trier, GERMANY. E--mail: [email protected] Online access for ECCC: FTP: ftp.eccc.uni-trier.de:/pub/eccc/ W..
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Read, K G, H-728
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/412487Surname: READ. Given Name(s) or Initials: K G. Military Service Number or Last Known Location: H-728. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 376.229197
Item: [2016.0049.44749] "Read, K G, H-728
Comparing the sizes of nondeterministic branching read-k-times programs
No full textAbstractWe compare the complexities of Boolean functions for nondeterministic syntactic read-k-times branching and branching read-sk-times programs. It is shown that for each natural number k, k⩾2, there exists a sequence of Boolean functions such that the complexity of computation of each function of this sequence by nondeterministic syntactic branching read-k-times programs is exponentially larger (with respect to the number of variables of the Boolean function) than by nondeterministic branching read-(klnk/ln2+C)-times programs, where C is a constant independent of k. Besides, it is shown that for each natural numbers N and k(N), where 4⩽k(N)<C2lnN/lnlnN and C2<2 is a constant independent of k and N, there exists a Boolean function in N variables such that the complexity of this function for nondeterministic syntactic read-k-times branching programs is exponentially larger (with respect to N) than for nondeterministic syntactic read-(klnk/ln2+C)-times branching programs
A Note on Read-k Times Branching Programs
No full textA syntactic read-k times branching program has the restriction that no variable occurs more than k times on any path (whether or not consistent). We exhibit an explicit Boolean function f; which cannot be computed by nondeterministic syntactic read-k times branching programs of size less than exp i\Omega ip n k 2k jj ; although its complement :f has a nondeterministic syntactic read-once branching program of polynomial size. This, in particular, means that the nonuniform analogue of NLOGSPACE = co \Gamma NLOGSPACE fails for syntactic read-k times networks with k = o(log n): We also show that (even for k = 1) the syntactic model is exponentially weaker then more realistic "nonsyntactic" on
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