ENGLISH

Feasible Computations and Provable Complexity Properties

By Juris Hartmanis

Book information

Publisher
Society for Industrial Mathematics
Year
1987
ISBN
9780898710274, 0898710278
Open Library ID
OL8271696M
Language
english
Format
DJVU
Filesize
425 kB (435311 bytes)
Series
CBMS-NSF Regional Conference Series in Applied Mathematics
Pages
73\73
Library
Kolxo3
DPI
300
Time added
2010-11-11 16:01:50

Description

An overview of current developments in research on feasible computations; and a consideration of this area of research in relation to provable properties of complexity of computations. The author begins by defining and discussing efficient reductions between problems and considers the families and corresponding complete languages of NL, DCSL, CSL, P, NP, PTAPE, EXPTIME, and EXPTAPE. Definitions and results are uniformly extended to computationally simpler natural families of languages such as NL, P, and CSL by using Log n-tape bounded reductions. The problem of determining what can and cannot be formally proven about running times of algorithms is discussed and related to the problem of establishing sharp time bounds for one-tape Turing machine computations, and the inability to formally prove running times for algorithms is then related to the presence of gaps in the hierarchy of complexity classes. The concluding discussion is on the possibility that the famous P=NP? problem is independent of the axioms of formal mathematical systems such as set theory.

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