2 research outputs found
Probabilistic communication complexity over the reals
Deterministic and probabilistic communication protocols are introduced in
which parties can exchange the values of polynomials (rather than bits in the
usual setting). It is established a sharp lower bound on the communication
complexity of recognizing the -dimensional orthant, on the other hand the
probabilistic communication complexity of its recognizing does not exceed 4. A
polyhedron and a union of hyperplanes are constructed in \RR^{2n} for which a
lower bound on the probabilistic communication complexity of recognizing
each is proved. As a consequence this bound holds also for the EMPTINESS and
the KNAPSACK problems
Simulating probabilistic by deterministic algebraic computation trees
AbstractA probabilistic algebraic computation tree (probabilistic ACT) which recognizes L ⊂ Rn in expected time T, and which gives the wrong answer with probability ⩽ ϵ < 12, can be simulated by a deterministic ACT in O(T2n) steps. The same result holds for linear search algorithms (LSAs). The result for ACTs establishes a weaker version of results previously shown by the author for LSAs, namely that LSAs can only be slightly sped up by their nondeterministic versions. This paper shows that ACTs can only be slightly sped up by their probabilistic versions. The result for LSAs solves a problem posed by Snir (1983). He found an example where probabilistic LSAs are faster than deterministic ones and asked how large this gap can be