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

TL;DR

This paper introduces an algebraic framework for on-the-fly determinization of finite-state automata, showing it often results in polynomial complexity, especially for automata with many non-deterministic transitions, and extends to weighted automata.

Contribution

It provides a novel algebraic and combinatorial analysis of on-the-fly determinization, establishing conditions for polynomial state complexity and extending results to weighted automata.

Findings

Automata with many non-deterministic transitions often admit polynomial determinization.

Algebraic and combinatorial properties can bound the asymptotic complexity.

Extension of determinization techniques to weighted finite-state automata.

Abstract

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