Descriptive and Computational Complexity (1989)
| Venue: | COMPUTATIONAL COMPLEXITY THEORY, PROC. SYMP. APPLIED MATH |
| Citations: | 48 - 0 self |
BibTeX
@INPROCEEDINGS{Immerman89descriptiveand,
author = {Neil Immerman},
title = {Descriptive and Computational Complexity},
booktitle = {COMPUTATIONAL COMPLEXITY THEORY, PROC. SYMP. APPLIED MATH},
year = {1989},
pages = {75--91},
publisher = {American Mathematical Society}
}
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Abstract
Computational complexity began with the natural physical notions of time and space. Given a property, S, an important issue is the computational complexity of checking whether or not an input satisfies S. For a long time, the notion of complexity referred to the time or space used in the computation. A mathematician might ask, "What is the complexity of expressing the property S?" It should not be surprising that these two questions -- that of checking and that of expressing -- are related. However it is startling how closely tied they are when the second question refers to expressing the property in first-order logic. Many complexity classes originally defined in terms of time or space resources have precise definitions as classes in first-order logic. In 1974 Fagin gave a characterization of nondeterministic polynomial time (NP) as the set of properties expressible in second-order existential logic
