Size Matters: Logarithmic Space is Real Time

We show that all the problems solvable by a nondeterministic machine with logarithmic work space (NL) can be solved in real time by a parallel machine, no matter how tight the real-time constraints are. We also show that several other real-time problems are in effect solvable in nondeterministic log...

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Published in:International journal of computers & applications Vol. 29; no. 4; pp. 327 - 336
Main Authors: Bruda, S.D., Akl, S.G.
Format: Journal Article
Language:English
Published: Calgary Taylor & Francis 2007
Taylor & Francis Ltd
Subjects:
Algorithms
Buses
Conflict resolution
independence system
Languages
matroid
Optimization
parallel complexity
Power
Real time
Real-time computation
reconfigurable multiple bus machine
Studies
timed ω-language
ISSN:1206-212X, 1925-7074
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Abstract We show that all the problems solvable by a nondeterministic machine with logarithmic work space (NL) can be solved in real time by a parallel machine, no matter how tight the real-time constraints are. We also show that several other real-time problems are in effect solvable in nondeterministic logarithmic space once their real-time constraints are dropped and they become non-realtime. We thus conjecture that NL contains exactly all the problems that admit feasible real-time parallel algorithms. The issue of real-time optimization problems is also investigated. We identify the class of such problems that are solvable in real time. In the process, we determine the computational power of directed reconfigurable multiple bus machines (DRMBMs) with polynomially bounded resources and running in constant time, which is found to be the same as the power of directed reconfigurable networks with the same properties. We also show that write conflict resolution rules such as Priority or even Combining do not add computational power over the Collision rule, and that a bus of width 1 (a wire) suffices for any constant time computation on DRMBM.
AbstractList We show that all the problems solvable by a nondeterministic machine with logarithmic work space (NL) can be solved in real time by a parallel machine, no matter how tight the real-time constraints are. We also show that several other real-time problems are in effect solvable in nondeterministic logarithmic space once their real-time constraints are dropped and they become non-real-time. We thus conjecture that NL contains exactly all the problems that admit feasible real-time parallel algorithms. The issue of real-time optimization problems is also investigated. We identify the class of such problems that are solvable in real time. In the process, we determine the computational power of directed reconfigurable multiple bus machines (DRMBMs) with polynomially bounded resources and running in constant time, which is found to be the same as the power of directed reconfigurable networks with the same properties. We also show that write conflict resolution rules such as Priority or even Combining do not add computational power over the Collision rule, and that a bus of width 1 (a wire) suffices for any constant time computation on DRMBM. [PUBLICATION ABSTRACT]
We show that all the problems solvable by a nondeterministic machine with logarithmic work space (NL) can be solved in real time by a parallel machine, no matter how tight the real-time constraints are. We also show that several other real-time problems are in effect solvable in nondeterministic logarithmic space once their real-time constraints are dropped and they become non-realtime. We thus conjecture that NL contains exactly all the problems that admit feasible real-time parallel algorithms. The issue of real-time optimization problems is also investigated. We identify the class of such problems that are solvable in real time. In the process, we determine the computational power of directed reconfigurable multiple bus machines (DRMBMs) with polynomially bounded resources and running in constant time, which is found to be the same as the power of directed reconfigurable networks with the same properties. We also show that write conflict resolution rules such as Priority or even Combining do not add computational power over the Collision rule, and that a bus of width 1 (a wire) suffices for any constant time computation on DRMBM.
Author Akl, S.G.
Bruda, S.D.
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  surname: Akl
  fullname: Akl, S.G.
  organization: School of Computing, Queen's University
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Cites_doi 10.1109/TEC.1962.5219459
10.1145/22145.22197
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10.1201/9781420049503-c28
10.1006/jpdc.1997.1385
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SubjectTerms Algorithms
Buses
Conflict resolution
independence system
Languages
matroid
Optimization
parallel complexity
Power
Real time
Real-time computation
reconfigurable multiple bus machine
Studies
timed ω-language
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Title Size Matters: Logarithmic Space is Real Time
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