On some central problems in computational complexity:
In this thesis we examine some of the central problems in the theory of computational complexity, like the trade-offs between time and memory, the power of nondeterminism and parallelism, and the speed gained by adding new operations to random access machines. Our main result is the cahracterization...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Ithaca, New York
1975
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| Series: | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report
224 |
| Subjects: | |
| Summary: | In this thesis we examine some of the central problems in the theory of computational complexity, like the trade-offs between time and memory, the power of nondeterminism and parallelism, and the speed gained by adding new operations to random access machines. Our main result is the cahracterization of the power of multiplication in random access acceptors: we show, in Chapter 3, that for such models nondeterministic and deterministic computations are polynomially related and that there is a polynomial relationship between the amount of time required for acceptance by random access machines with multiplication, and the amount of tape required by Turing machines. Thus, the additional power gained by using multiplication is the same as that of memory over time (if any). We derive similar results for some other interesting instruction sets We also have some results for probabilistic and nondeterministic computations: we define threshold machines and show how probabilistic Turing machines may simulate them, and exhibit a set of complete problems for threshold machines. For nondeterministic computations, we present a hierarchy of the elementary recursive languages obtained by polynomially bounded quantification over objects of higher and higher type, which represent nondeterministic time bounded computations with larger and larger bounds. Finally, we discuss some deterministic computations, and conclude with a look at some open problems |
| Physical Description: | 139 Sp. |
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| 520 | 3 | |a In this thesis we examine some of the central problems in the theory of computational complexity, like the trade-offs between time and memory, the power of nondeterminism and parallelism, and the speed gained by adding new operations to random access machines. Our main result is the cahracterization of the power of multiplication in random access acceptors: we show, in Chapter 3, that for such models nondeterministic and deterministic computations are polynomially related and that there is a polynomial relationship between the amount of time required for acceptance by random access machines with multiplication, and the amount of tape required by Turing machines. Thus, the additional power gained by using multiplication is the same as that of memory over time (if any). We derive similar results for some other interesting instruction sets | |
| 520 | 3 | |a We also have some results for probabilistic and nondeterministic computations: we define threshold machines and show how probabilistic Turing machines may simulate them, and exhibit a set of complete problems for threshold machines. For nondeterministic computations, we present a hierarchy of the elementary recursive languages obtained by polynomially bounded quantification over objects of higher and higher type, which represent nondeterministic time bounded computations with larger and larger bounds. Finally, we discuss some deterministic computations, and conclude with a look at some open problems | |
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| series2 | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report |
| spelling | Simon, Janos Verfasser aut On some central problems in computational complexity Ithaca, New York 1975 139 Sp. txt rdacontent n rdamedia nc rdacarrier Cornell University <Ithaca, NY> / Department of Computer Science: Technical report 224 In this thesis we examine some of the central problems in the theory of computational complexity, like the trade-offs between time and memory, the power of nondeterminism and parallelism, and the speed gained by adding new operations to random access machines. Our main result is the cahracterization of the power of multiplication in random access acceptors: we show, in Chapter 3, that for such models nondeterministic and deterministic computations are polynomially related and that there is a polynomial relationship between the amount of time required for acceptance by random access machines with multiplication, and the amount of tape required by Turing machines. Thus, the additional power gained by using multiplication is the same as that of memory over time (if any). We derive similar results for some other interesting instruction sets We also have some results for probabilistic and nondeterministic computations: we define threshold machines and show how probabilistic Turing machines may simulate them, and exhibit a set of complete problems for threshold machines. For nondeterministic computations, we present a hierarchy of the elementary recursive languages obtained by polynomially bounded quantification over objects of higher and higher type, which represent nondeterministic time bounded computations with larger and larger bounds. Finally, we discuss some deterministic computations, and conclude with a look at some open problems Computers Numerical calculations Komplexes System (DE-588)4114261-5 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Theoretische Informatik (DE-588)4196735-5 s Algorithmus (DE-588)4001183-5 s Komplexes System (DE-588)4114261-5 s DE-604 Department of Computer Science: Technical report Cornell University <Ithaca, NY> 224 (DE-604)BV006185504 224 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Simon, Janos On some central problems in computational complexity Computers Numerical calculations Komplexes System (DE-588)4114261-5 gnd Theoretische Informatik (DE-588)4196735-5 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4196735-5 (DE-588)4001183-5 (DE-588)4113937-9 |
| title | On some central problems in computational complexity |
| title_auth | On some central problems in computational complexity |
| title_exact_search | On some central problems in computational complexity |
| title_full | On some central problems in computational complexity |
| title_fullStr | On some central problems in computational complexity |
| title_full_unstemmed | On some central problems in computational complexity |
| title_short | On some central problems in computational complexity |
| title_sort | on some central problems in computational complexity |
| topic | Computers Numerical calculations Komplexes System (DE-588)4114261-5 gnd Theoretische Informatik (DE-588)4196735-5 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Computers Numerical calculations Komplexes System Theoretische Informatik Algorithmus Hochschulschrift |
| volume_link | (DE-604)BV006185504 |
| work_keys_str_mv | AT simonjanos onsomecentralproblemsincomputationalcomplexity |