Improved MHP analyses

May-Happen-in-Parallel (MHP) analysis is becoming the backbone of many of the parallel analyses and optimizations. In this paper, we present new approaches to do MHP analysis for X10-like languages that support async-finish-atomic parallelism. We present a fast incremental MHP algorithm to derive all the statements that may run in parallel with a given statement. We also extend the MHP algorithm of Agarwal et al. (answers if two given X10 statements may run in parallel, and under what condition) to improve the computational complexity, without compromising on the precision.