Non-regular complexity theory

• Project/Area Number: 23K10976
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: Akita University
• Principal Investigator: Fazekas Szilard 秋田大学, 理工学研究科, 准教授 (70725382)
• Project Period (FY): 2023-04-01 – 2026-03-31
• Project Status: Granted (Fiscal Year 2023)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2025: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2024: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2023: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: automata / complexity / regularity / rewriting

Outline of Research at the Start

Complexity of non-classical automata can be expressed quantitatively by the number of non-regular transitions they perform while processing inputs. I aim to generalize the concept of non-regular steps to Turing machine computations, which allows treating several stronger-than-regular models in the same framework. The key question is how much of the non-regular resources allows qualitative changes, i.e., larger classes of accepted languages. The goal is a non-regular complexity theory, where languages are classified based on the number of non-regular transitions made by their minimal machines.