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TimeSpace Tradeoffs for Satisfiability
 Journal of Computer and System Sciences
, 1997
"... We give the first nontrivial modelindependent timespace tradeoffs for satisfiability. Namely, we show that SAT cannot be solved simultaneously in n 1+o(1) time and n 1\Gammaffl space for any ffl ? 0 on general randomaccess nondeterministic Turing machines. In particular, SAT cannot be solved ..."
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Cited by 29 (1 self)
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We give the first nontrivial modelindependent timespace tradeoffs for satisfiability. Namely, we show that SAT cannot be solved simultaneously in n 1+o(1) time and n 1\Gammaffl space for any ffl ? 0 on general randomaccess nondeterministic Turing machines. In particular, SAT cannot be solved deterministically by a Turing machine using quasilinear time and p n space. We also give lower bounds for logspace uniform NC 1 circuits and branching programs. Our proof uses two basic ideas. First we show that if SAT can be solved nondeterministically with a small amount of time then we can collapse a nonconstant number of levels of the polynomialtime hierarchy. We combine this work with a result of Nepomnjascii that shows that a nondeterministic computation of super linear time and sublinear space can be simulated in alternating linear time. A simple diagonalization yields our main result. We discuss how these bounds lead to a new approach to separating the complexity classes NL a...
On the Complexity of SAT
, 1999
"... We show that nondeterministic time NT IME(n) is not contained in deterministic time n # 2# and polylogarithmic space, for any # > 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n # 2# ) and polylogarithmic space. A similar result is presented for uniform cir ..."
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Cited by 25 (1 self)
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We show that nondeterministic time NT IME(n) is not contained in deterministic time n # 2# and polylogarithmic space, for any # > 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n # 2# ) and polylogarithmic space. A similar result is presented for uniform circuits.
Tight lower bounds for stconnectivity on the NNJAG model
 SIAM J. on Computing
, 1999
"... Abstract. Directed stconnectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Compu ..."
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Cited by 6 (1 self)
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Abstract. Directed stconnectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218–227]. Let n be the number of nodes in the input graph and S and T be the space and time used by the NNJAG, respectively. We show that, for any δ>0, if an NNJAG uses space S ∈ O(n1−δ), then T ∈ 2Ω(log2 (n/S)) ; otherwise n log n) / log log n) S
Some Pointed Questions Concerning Asymptotic Lower Bounds, And News From The Isomorphism Front
 Current Trends in Theoretical Computer Science
, 2001
"... this article, we now know that such problems are all isomorphic to the standard complete set for the complexity class, under depththree AC ..."
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Cited by 5 (1 self)
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this article, we now know that such problems are all isomorphic to the standard complete set for the complexity class, under depththree AC
On the Complexity of SAT (Revised)
"... We show 1 that nondeterministic time NT IME(n) is not contained in deterministic time n √ 2−ɛ and polylogarithmic space, for any ɛ> 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n √ 2−ɛ) and polylogarithmic space. A similar result is presented for uniform cir ..."
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We show 1 that nondeterministic time NT IME(n) is not contained in deterministic time n √ 2−ɛ and polylogarithmic space, for any ɛ> 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n √ 2−ɛ) and polylogarithmic space. A similar result is presented for uniform circuits. 1
STCON in Directed UniquePath Graphs
"... ABSTRACT. We study the problem of spaceefficient polynomialtime algorithms for directed stconnectivity (STCON). Given a directed graph G, and a pair of vertices s,t, the STCON problem is to decide if thereexistsapathfrom s to t in G. For general graphs, thebestpolynomialtime algorithm forSTCONuse ..."
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ABSTRACT. We study the problem of spaceefficient polynomialtime algorithms for directed stconnectivity (STCON). Given a directed graph G, and a pair of vertices s,t, the STCON problem is to decide if thereexistsapathfrom s to t in G. For general graphs, thebestpolynomialtime algorithm forSTCONusesspacethatisonlyslightlysublinear. However,forspecialclassesofdirectedgraphs, polynomialtime polylogarithmicspace algorithms are known for STCON. In this paper, we continuethisthreadofresearchandstudyaclassofgraphscalleduniquepathgraphswithrespecttosource s, where there is at most one simple path from s to any vertex in the graph. For these graphs, we give a polynomialtime algorithm that uses Õ(n ε) space for any constant ε ∈ (0,1]. We also give a polynomialtime, Õ(n ε)space algorithm to recognize uniquepath graphs. Uniquepath graphs are related to configuration graphs of unambiguous logspace computations, but they can have some directed cycles. Our results may be viewed along the continuum of sublinearspace polynomialtime algorithms for STCON in different classes of directed graphs from slightly sublinearspace algorithms forgeneral graphs toO(logn) space algorithms fortrees. 1
The Computational Complexity Column
, 1998
"... Introduction Investigation of the measuretheoretic structure of complexity classes began with the development of resourcebounded measure in 1991 [56]. Since that time, a growing body of research by more than forty scientists around the world has shown resourcebounded measure to be a powerful too ..."
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Introduction Investigation of the measuretheoretic structure of complexity classes began with the development of resourcebounded measure in 1991 [56]. Since that time, a growing body of research by more than forty scientists around the world has shown resourcebounded measure to be a powerful tool that sheds new light on many aspects of computational complexity. Recent survey papers by Lutz [60], AmbosSpies and Mayordomo [3], and Buhrman and Torenvliet [22] describe many of the achievements of this line of inquiry. In this column, we give a more recent snapshot of resourcebounded measure, focusing not so much on what has been achieved to date as on what we hope will be achieved in the near future. Section 2 below gives a brief, nontechnical overview of resourcebounded measure in terms of its motivation and principal ideas. Sections 3, 4, and 5 describe twelve specific open problems in the area. We have used the following three criteria in choosing these problems. 1. Their