Fine hierarchies and m-reducibilities in theoretical computer science☆

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Abstract

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.

Keywords

Hierarchy
m-reducibility
Topology
Logic
Computability
Complexity
Difference hierarchy
Fine hierarchy
Boolean term
Alternating tree
k-partition
Baire space
Baire domain
Language
ω-language
Automaton

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Supported by a DAAD project within the program “Ostpartnerschaften”, by DFG Mercator program, by DFG-RFBR Grant 06-01-04002 and by RFBR Grant 07-01-00543a.

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