ECCC-Report TR22-015https://eccc.weizmann.ac.il/report/2022/015Comments and Revisions published for TR22-015en-usSat, 12 Feb 2022 18:29:35 +0200
Paper TR22-015
| Lower Bounds for Unambiguous Automata via Communication Complexity |
Mika Göös,
Stefan Kiefer,
Weiqiang Yuan
https://eccc.weizmann.ac.il/report/2022/015We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results.
$\textbf{Complement:}$ There is a language $L$ recognised by an $n$-state UFA such that the complement language $\overline{L}$ requires NFAs with $n^{\tilde{\Omega}(\log n)}$ states. This improves on a lower bound by Raskin.
$\textbf{Union:}$ There are languages $L_1$, $L_2$ recognised by $n$-state UFAs such that the union $L_1\cup L_2$ requires UFAs with $n^{\tilde{\Omega}(\log n)}$ states.
$\textbf{Separation:}$ There is a language $L$ such that both $L$ and $\overline{L}$ are recognised by $n$-state NFAs but such that $L$ requires UFAs with $n^{\Omega(\log n)}$ states. This refutes a conjecture by Colcombet.Sat, 12 Feb 2022 18:29:35 +0200https://eccc.weizmann.ac.il/report/2022/015