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SuperLinear TimeSpace Tradeoff Lower Bounds for Randomized Computation
, 2000
"... We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by Ajtai [Ajt99a, ..."
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We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by Ajtai [Ajt99a, Ajt99b] in his timespace tradeoffs for deterministic RAM algorithms computing element distinctness and for Boolean branching programs computing a natural quadratic form. Ajtai's bounds were of the following form...
A time lower bound for satisfiability
 In Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP
, 2004
"... Abstract. We show that a deterministic Turing machine with one ddimensional work tape and random access to the input cannot solve satisfiability in time na for a < p(d + 2)/(d + 1). For conondeterministic machines, we obtain a similar lower bound for any a such that a3 < 1 + a/(d + 1). The same boun ..."
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Cited by 6 (1 self)
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Abstract. We show that a deterministic Turing machine with one ddimensional work tape and random access to the input cannot solve satisfiability in time na for a < p(d + 2)/(d + 1). For conondeterministic machines, we obtain a similar lower bound for any a such that a3 < 1 + a/(d + 1). The same bounds apply to almost all natural NPcomplete problems known. 1 Introduction Proving time lower bounds for natural problems remains the most difficultchallenge in computational complexity. We know exponential lower bounds on severely restricted models of computation (e.g., for parity on constant depthcircuits) and polynomial lower bounds on somewhat restricted models (e.g., for palindromes on single tape Turing machines) but no nontrivial lower bounds ongeneral randomaccess machines. In this paper, we exploit the recent timespace lower bounds for satisfiability on general randomaccess machines to establishnew lower bounds of the second type, namely a time lower bound for satisfiability on Turing machines with one multidimensional work tape and random accessto the input.
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
TimeSpace Lower Bounds for Satisfiability
 In Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP
, 2001
"... We survey the recent lower bounds on the running time of generalpurpose randomaccess machines that solve satisfiability in a small amount of work space, and related lower bounds for satisfiability in nonuniform models. ..."
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Cited by 1 (1 self)
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We survey the recent lower bounds on the running time of generalpurpose randomaccess machines that solve satisfiability in a small amount of work space, and related lower bounds for satisfiability in nonuniform models.
Diagonalization
, 2000
"... We give a modern historical and philosophical discussion of diagonalization as a tool to prove lower bounds in computational complexity. We will give several examples and discuss four possible approaches to use diagonalization for separating logarithmicspace from nondeterministic polynomialtime ..."
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We give a modern historical and philosophical discussion of diagonalization as a tool to prove lower bounds in computational complexity. We will give several examples and discuss four possible approaches to use diagonalization for separating logarithmicspace from nondeterministic polynomialtime. 1 Introduction The greatest embarrassment in computational complexity theory comes from our inability to achieve signicant complexity class separations. In recent years we have seen many interesting results come from an old techniquediagonalization. Deceptively simple, diagonalization, combined with techniques for collapsing classes, can yield quite interesting lower bounds on computation. In 1874, Cantor [Can74] rst used diagonalization for showing the set of reals is not countable. The proof worked by assuming an enumeration of the reals and designing a set that onebyone is dierent from every set in the enumeration. Drawn as a table this process considers the diagonal set and re...