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In this paper we establish an abstraction of on-the-fly determinization offinite-state automata using transition monoids and demonstrate how it can beapplied to bound the asymptotics. We present algebraic and combinatorialproperties that are sufficient for a polynomial state complexity of thedeterministic automaton constructed on-the-fly. A special case of our findingsis that automata with many non-deterministic transitions almost always admit adeterminization of polynomial complexity. Furthermore, we extend our ideas toweighted finite-state automata.

An Analysis of On-the-fly Determinization of Finite-state Automata