Some Reducibilities on Regular Sets

Abstract. We discuss some known and introduce some new reducibilities on regular sets. We establish some facts on the corresponding degree structures and relate some reducibilities to natural hierarchies of regular sets. As an application, we characterize regular languages whose leaf-language classes (in the balanced model) are contained in the polynomial hierarchy. For any reducibility we try to give some motivation and interesting open questions, in a hope to convince the reader that study of these reducibilities is important for automata theory and computational complexity.

• Type: Conference
• Year: 2005
• Where: CIE
• Authors: Victor L. Selivanov
• Keywords: CIE 2005, Corresponding Degree Structures, Interesting Open Questions, Regular Sets