Random sparse unary predicates

Details Random sparse unary predicates Random sparse unary predicates

1994-01-15

arxiv.org/abs/math/9401214v1

Random Structures Algorithms 5 (1994), 375--394

Mathematics

Logic

Scientific paper

The main result is the following Theorem: Let p=p(n) be such that p(n) in [0,1] for all n and either p(n)<< n^{-1} or for some positive integer k, n^{-1/k}<< p(n)<< n^{-1/(k+1)} or for all epsilon >0, n^{- epsilon}<< p(n) and n^{- epsilon}<< 1-p(n) or for some positive integer k, n^{-1/k}<< 1-p(n)<< n^{-1/(k+1)} or 1-p(n)<< n^{-1}. Then p(n) satisfies the Zero-One Law for circular unary predicates. Inversely, if p(n) falls into none of the above categories then it does not satisfy the Zero-One Law for circular unary predicates.

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