Compatible sequences and a slow Winkler percolation

Authors:
Peter Gács
Affiliations:
Boston University, Computer Science Department, 111 Cummington Street, Boston, MA
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

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Abstract

Two infinite 0-1 sequences are called compatible when it is possible to cast out 0's from both in such a way that they become complementary to each other. Answering a question of Peter Winkler, we show that if the two 0-1-sequences are random i.i.d. and independent from each other, with probability p of 1's, then if p is sufficiently small they are compatible with positive probability. The question is equivalent to a certain dependent percolation with a power-law behavior: the probability that the origin is blocked at distance n but not closer decreases only polynomially fast and not, as usual, exponentially.