Finite State Machine (FSM) is the key kernel behind ma popular applications, including regular expression matc ing, text tokenization, and Huffman decoding. Parallelizi FSMs is extremely difficult because of the strong depende cies and unpredictable memory accesses. Previous effo have largely focused on multi-core parallelization, and us different approaches, including speculative and enumerati execution, both of which have been effective but also ha limitations. With increasing width and improving flexibil in SIMD instruction sets, this paper focuses on combini SIMD and multi/many-core parallelism for FSMs. We ha developed a novel strategy, called enumerative speculatio Instead of speculating on a single state as in speculative e ecution or enumerating all possible states as in enumerati execution, our strategy speculates transitions from seve possible states, reducing the prediction overheads of speculation approach and the large amount of redundant work in the enumerative approach. A simple lookback approach produces a set of guessed states to achieve high speculation success rates in our enumerative speculation. We evaluate our method with four popular FSM applications: Huffman decoding, regular expression matching, HTML tokenization, and Div7. We obtain up to 2.5x speedup using SIMD on one core and up to 95x combining SIMD with 60 cores of an Intel Xeon Phi. On a single core, we outperform the best single-state speculative execution version by an average of 1.6x, and in combining SIMD and many-core parallelism, outperform enumerative execution by an average of 2x.