Compatible sequences and a slow Winkler percolation

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.

• Type: Conference
• Year: 2001
• Where: STOC
• Authors: Péter Gács
• Keywords: Algorithms, Certain Dependent Percolation, Infinite 0-1 Sequences, Positive Probability, STOC 2001