Left is Better than Right for Reducing Nondeterminism of NFAs

We study the NFA reductions by invariant equivalences. It is well-known that the NFA minimization problem is PSPACE-complete. Therefore, there have been approaches to reduce the size of NFAs in low polynomial time by computing invariant equivalence and merging the states within same equivalence class. Here we consider the nondeterminism reduction of NFAs by invariant equivalences. We, in particular, show that the left-invariant equivalence is more useful than the right-invariant equivalence for reducing NFA nondeterminism. We also present experimental evidence for showing that NFA reduction by leftinvariant equivalence achieves the better reduction of nondeterminism than right-invariant equivalence.