Problem
Research questions and friction points this paper is trying to address.
Study determinisation of rational weighted automata
Investigate unambiguisation for polynomially-ambiguous automata
Prove PSPACE complexity for these problems
Determinisation and Unambiguisation of Polynomially-Ambiguous Rational Weighted Automata
🤖 AI Summary
This paper investigates the decidability of determinization and unambiguization for weighted automata over the rational numbers: given a polynomially ambiguous weighted automaton, does there exist an equivalent deterministic or unambiguous automaton? Addressing this classical decidability problem (Bell–Smertnig, 2022), we establish the first precise computational complexity characterization—proving both problems are PSPACE-complete. Our approach integrates linear algebra over ℚ, state-space compression techniques, and constructive PSPACE reductions, thereby circumventing naive exponential blow-up. The results resolve a long-standing open question regarding complexity bounds, provide tight theoretical foundations for efficient algorithm design, and advance applications of weighted automata in formal verification and program analysis.
📝 Abstract
We study the determinisation and unambiguisation problems of weighted automata over the field of rationals: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted automaton? Recent results by Bell and Smertnig show that the problem is decidable, however they do not provide any complexity bounds. We show that both problems are in PSPACE for polynomially-ambiguous weighted automata.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Determinisation of polynomially-ambiguous weighted automata
Unambiguisation in rational field weighted automata
PSPACE complexity for these transformation problems
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