Simple parallel algorithms for the maximal independent set (MIS) problem are presented. The first algorithm is a Monte Carlo algorithm with a very local property. The local property of this algorithm may make it a useful protocol design tool in distributed computing environments and artificial intelligence. One of the main contributions of this paper is the development of powerful and general techniques for converting Monte Carlo algorithms into deterministic algorithms. These techniques are used to convert the Monte Carlo algorithm for the MIS problem into a simple deterministic algorithm with the same parallel running time.