Lower Bounds for Unambiguous Automata via Communication Complexity
Kaspars Balodis, Shalev Ben-David, Mika Göös, Siddhartha Jain, Robin Kothari · arXiv (Cornell University) · 2021
We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. 1) Complement: There is a language L recognised by an n-state UFA such that the complement language ̅L requires NFAs with n^Ω̃(log n) states. This improves on a lower bound by Raskin. 2) Union: There are languages L₁, L₂ recognised by n-state UFAs such that the union L₁∪L₂ requires UFAs with n^Ω̃(log n) states. 3) Separation: There is a language L such that both L and ̅L are recognised by n-state NFAs but such that L requires UFAs with n^Ω(log n) states. This refutes a conjecture by Colcombet.