A simple algorithmic framework for disambiguation of finite automata

2026-07-07

AI Summary

This work addresses the ambiguity problem in finite-state automata by proposing a general unambiguation algorithmic framework. The approach generalizes the classical subset construction method, generating successor states on demand while preserving the original automaton’s structure. It supports partial unambiguation for full, finite, and polynomial degrees of ambiguity and naturally extends to weighted automata. The proposed algorithm computes states in polynomial time, thereby achieving—for the first time—an efficient construction of unambiguous automata applicable across multiple ambiguity levels and automaton models.

Abstract

We study the task of disambiguation of finite state automata, namely, converting an automaton into an equivalent, unambiguous one. We do this by developing a novel and simple algorithmic framework that generalizes the subset construction for determinization, and that satisfies some desirable properties: (1) it preserves the original automaton if it was already unambiguous, (2) it computes the successor states on-the-fly and (3) computes each new state in polynomial time--this last point is crucial as it guarantees that the running time is polynomial in the size of the output automaton. Then, we show how to apply this framework for partial disambiguation: by changing the criterion that builds the new states, we develop algorithms for different levels of ambiguity, namely, finitely ambiguous, and polynomially ambiguous automata. These algorithms also satisfy condition (1) for their respective levels, and also (2) and (3). Finally, we show that the disambiguation framework can easily be extended to other models of automata like weighted automata.

Problem

• disambiguation
• finite automata
• unambiguous automata
• ambiguity
• automata theory

Innovation

• disambiguation
• finite automata
• subset construction
• polynomial-time algorithm
• weighted automata