On Determinism and Unambiguity of Weighted Two-way Automata

TL;DR

This paper investigates the relationships between weighted two-way automata and one-way automata, showing how unambiguity and determinism are preserved or transformed during conversions, especially in the context of commutative semirings.

Contribution

It establishes that unambiguous weighted two-way automata are equivalent to deterministic ones in commutative semirings, clarifying the conditions under which determinism is preserved.

Findings

Conversion preserves unambiguity but not determinism

Unambiguous one-way automata convert to deterministic two-way automata

Unambiguous two-way automata are equivalent to deterministic two-way automata in commutative semirings

Abstract

In this paper, we first study the conversion of weighted two-way automata to one-way automata. We show that this conversion preserves the unambiguity but does not preserve the determinism. Yet, we prove that the conversion of an unambiguous weighted one-way automaton into a two-way automaton leads to a deterministic two-way automaton. As a consequence, we prove that unambiguous weighted two-way automata are equivalent to deterministic weighted two-way automata in commutative semirings.