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The Role of Relativization in Complexity Theory
 Bulletin of the European Association for Theoretical Computer Science
, 1994
"... Several recent nonrelativizing results in the area of interactive proofs have caused many people to review the importance of relativization. In this paper we take a look at how complexity theorists use and misuse oracle results. We pay special attention to the new interactive proof systems and progr ..."
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Cited by 43 (10 self)
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Several recent nonrelativizing results in the area of interactive proofs have caused many people to review the importance of relativization. In this paper we take a look at how complexity theorists use and misuse oracle results. We pay special attention to the new interactive proof systems and program checking results and try to understand why they do not relativize. We give some new results that may help us to understand these questions better.
On Separators, Segregators and Time versus Space
"... We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that N T IM E(n ..."
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Cited by 6 (0 self)
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We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that N T IM E(n
Relationships among Time and Space Complexity Classes
, 2001
"... Abstract Multitape Turing machines are the canonical mathematical model for studying the time and space requirements of problems. Most computational problems that are efficient in practice have efficient algorithms on multitape Turing machines, and vice versa. We survey the literature on relationshi ..."
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Abstract Multitape Turing machines are the canonical mathematical model for studying the time and space requirements of problems. Most computational problems that are efficient in practice have efficient algorithms on multitape Turing machines, and vice versa. We survey the literature on relationships among time and space classes defined using multitape Turing machines. We discuss the result of Paul, Hopcroft and Valiant that deterministic space T is more powerful than deterministic time T and the result of Paul, Pippenger, Szemeredi and Trotter that nondeterministic linear time is more powerful than deterministic linear time. We also discuss techniques to simulate Turing machines by Turing machines with different sets of resources, and techniques to diagonalize against complexity classes, with specific reference to the recent research by Fortnow et al. on timespace tradeoffs for the Satisfiability problem. Finally, we mention a few results on models other than Turing machines and resources other than time and space, and list the major open problems in this area. Contents 1 Introduction 1 2 The Valiant Paradigm 5