Structural complexity theory
Open-knowledge reference entry
In computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather than computational complexity of individual problems and algorithms. It involves the research of both internal structures of various complexity classes and the relations between different complexity classes.
History
The theory has emerged as a result of (still failing) attempts to resolve the first and still the most important question of this kind, the P = NP problem. Most of the research is done basing on the assumption of P not being equal to NP and on a more far-reaching conjecture that the polynomial time hierarchy of complexity classes is infinite.
Important results
The compression theorem
The compression theorem is an important theorem about the complexity of computable functions.
The theorem states that there exists no largest complexity class, with computable boundary, which contains all computable functions.
Space hierarchy theorems
The space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions. For example, a deterministic Turing machine can solve more decision problems in space n log n than in space n. The somewhat weaker analogous theorems for time are the time hierarchy theorems.
Time hierarchy theorems
The time hierarchy theorems are important statements about time-bounded computation on Turing machines.
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