Finding and Excluding b-ary Machin-Type Individual Digit Formulae

FINDING AND EXCLUDING b-ARY MACHIN-TYPE BBP FORMULAE

Constants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe (BBP formulae to a given base b) have interesting computational properties, and there are hints that they should be normal numbers, i.e., that their base b digits are randomly distributed. We study a formally limited subset of BBP formulae, which we call Machin-type BBP formulae, for which it relatively easy to...

Ternary Basic Digit Sets

A radix representation of a real number, for an integral base B ≥ 2 and digit set D, is a string of digits (an...a1a0...)B = ∑∞ i=−n a−iB , with ak ∈ D. It is commonly known that using a digit set of the form {0, 1, ..., B−1}, any positive real number has a B-ary radix representation. This is simply the standardB-ary representation of a number. Alternative digit representations have been of pra...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

Application of fundamental relations on n-ary polygroups

The class of  $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and  a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...

Parallel Generation of t-ary Trees

A parallel algorithm for generating t-ary tree sequences in reverse B-order is presented. The algorithm generates t-ary trees by 0-1 sequences, and each 0-1 sequences is generated in constant average time O(1). The algorithm is executed on a CREW SM SIMD model, and is adaptive and cost-optimal. Prior to the discussion of the parallel algorithm a new sequential generation with O(1) average time ...