can single work items kernels run in parallel on same device

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However, this got me tinkering though. I did try changing the CL_MEM_READ_WRITE to CL_MEM_WRITE_ONLY.

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That sounds like the host compiler/runtime was assuming a false dependency between the answer[] buffers, either because the buffers are defined as an array, or because you are using host pointers. I always use CL_MEM_READ_WRITE for the buffers being accessed by parallel kernels, and never had such problem. However, I do not use host pointers.