Fine hierarchies and m-reducibilities in theoretical computer science

This is a survey of results about versions of fine hierarchies and many-one reducibilities that appear in different parts of theoretical computer science. These notions and related techniques play a crucial role in understanding complexity of finite and infinite computations. We try not only to present the corresponding notions and facts from the particular fields but also to identify the unifying notions, techniques and ideas. Key words. Hierarchy, m-reducibility, topology, logic, computability, complexity, difference hierarchy, fine hierarchy, Boolean term, alternating tree, k-partition, Baire space, Baire domain, language, -language, automaton.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Victor L. Selivanov
• Keywords: Corresponding Notions, Fine Hierarchies, TCS 2008, Theoretical Computer Science, Unifying Notions