Recognizable Picture Languages: Separating UREC from coUREC via Communication Complexity

2026-09-22

AI Summary

通过引入通信复杂性提升技术，解决了Anselmo等人提出的关于可识别图像语言的UREC和coUREC分离问题。

Abstract

We introduce communication-complexity lifting techniques into the study of recognizable picture languages. As an application, we resolve a long-standing open problem of Anselmo et al. (2006) by constructing a language in UREC whose complement does not belong to REC. Our lower-bound argument is inspired by the communication-complexity approach to unambiguous automata of Göös et al. (2022), although its implementation in the setting of picture languages requires substantially different technical ingredients.

Problem

• UREC
• coUREC
• recognizable picture languages

Innovation

• communication-complexity lifting
• recognizable picture languages
• UREC
• coUREC