Results 1  10
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18
TimeSpace Tradeoffs for Branching Programs
, 1999
"... We obtain the first nontrivial timespace tradeoff lower bound for functions f : {0, 1}^n → {0, 1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε)n, for some constant ε > 0 ..."
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Cited by 44 (2 self)
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We obtain the first nontrivial timespace tradeoff lower bound for functions f : {0, 1}^n → {0, 1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε)n, for some constant ε > 0. We also give the first separation result between the syntactic and semantic readk models [BRS93] for k > 1 by showing that polynomialsize semantic readtwice branching programs can compute functions that require exponential size on any syntactic readk branching program. We also show...
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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Cited by 33 (0 self)
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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...
TimeSpace Tradeoff Lower Bounds for Randomized Computation of Decision Problems
 In Proc. of 41st FOCS
, 2000
"... We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. ..."
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Cited by 28 (2 self)
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We prove the first timespace lower bound tradeoffs for randomized computation of decision problems.
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 circui ..."
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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.
XFA: Faster signature matching with extended automata
 In IEEE Symposium on Security and Privacy
, 2008
"... Automatabased representations and related algorithms have been applied to address several problems in information security, and often the automata had to be augmented with additional information. For example, extended finitestate automata (EFSA) augment finitestate automata (FSA) with variables to ..."
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Cited by 24 (7 self)
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Automatabased representations and related algorithms have been applied to address several problems in information security, and often the automata had to be augmented with additional information. For example, extended finitestate automata (EFSA) augment finitestate automata (FSA) with variables to track dependencies between arguments of system calls. In this paper, we introduce extended finite automata (XFAs) which augment FSAs with finite scratch memory and instructions to manipulate this memory. Our primary motivation for introducing XFAs is signature matching in Network Intrusion Detection Systems (NIDS). Representing NIDS signatures as deterministic finitestate automata (DFAs) results in very fast signature matching but for several classes of signatures DFAs can blowup in space. Using nondeterministic finitestate automata (NFA) to represent NIDS signatures results in a succinct representation but at the expense of higher time complexity for signature matching. In other words, DFAs are timeefficient but spaceinefficient, and NFAs are spaceefficient but timeinefficient. In our experiments we have noticed that for a large class of NIDS signatures XFAs have time complexity similar to DFAs and space complexity similar to NFAs. For our test set, XFAs use 10 times less memory than a DFAbased solution, yet achieve 20 times higher matching speeds. 1.
TimeSpace Tradeoffs for Nondeterministic Computation
 In Proceedings of the 15th IEEE Conference on Computational Complexity
, 2000
"... We show new tradeoffs for satisfiability and nondeterministic linear time. Satisfiability cannot be solved on general purpose randomaccess Turing machines in time n 1.618 and space n o(1) . This improves recent results of Fortnow and of Lipton and Viglas. In general, for any constant a less tha ..."
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Cited by 24 (2 self)
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We show new tradeoffs for satisfiability and nondeterministic linear time. Satisfiability cannot be solved on general purpose randomaccess Turing machines in time n 1.618 and space n o(1) . This improves recent results of Fortnow and of Lipton and Viglas. In general, for any constant a less than the golden ratio, we prove that satisfiability cannot be solved in time n a and space n b for some positive constant b. Our techniques allow us to establish this result for b < 1 2 ( a+2 a 2  a). We can do better for a close to the golden ratio, for example, satisfiability cannot be solved by a randomaccess Turing machine using n 1.46 time and n .11 space. We also show tradeoffs for nondeterministic linear time computations using sublinear space. For example, there exists a language computable in nondeterministic linear time and n .619 space that cannot be computed in deterministic n 1.618 time and n o(1) space. Higher up the polynomialtime hierarchy we can get be...
Inductive TimeSpace Lower Bounds for SAT and Related Problems
 Computational Complexity
, 2005
"... Abstract. We improve upon indirect diagonalization arguments for lower bounds on explicit problems within the polynomial hierarchy. Our contributions are summarized as follows. 1. We present a technique that uniformly improves upon most known nonlinear time lower bounds for nondeterminism andalterna ..."
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Cited by 14 (5 self)
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Abstract. We improve upon indirect diagonalization arguments for lower bounds on explicit problems within the polynomial hierarchy. Our contributions are summarized as follows. 1. We present a technique that uniformly improves upon most known nonlinear time lower bounds for nondeterminism andalternating computation, on both subpolynomial (n o(1) ) space RAMs and sequential onetape machines with random access to the input. We obtain improved lower bounds for Boolean satisfiability (SAT), as well as all NPcomplete problems that have efficient reductions from SAT, and ΣkSAT, for constant k ≥ 2. For example, SAT cannot be solved by random access machines using n √ 3 time and subpolynomial space. 2. We show how indirect diagonalization leads to timespace lower bounds for computation with bounded nondeterminism. For both the random access and multitape Turing machine models, we prove that for all k ≥ 1, there is a constant ck> 1 such that linear time with n 1/k nondeterministic bits is not contained in deterministic n ck time with subpolynomial space. This is used to prove that satisfiability of Boolean circuits with n inputs and n k size cannot be solved by deterministic multitape Turing machines running in n k·ck time and subpolynomial space.
TimeSpace Tradeoffs for Counting NP Solutions Modulo Integers
 In Proceedings of the 22nd IEEE Conference on Computational Complexity
, 2007
"... We prove the first timespace tradeoffs for counting the number of solutions to an NP problem modulo small integers, and also improve upon known timespace tradeoffs for Sat. Let m> 0 be an integer, and define MODmSat to be the problem of determining if a given Boolean formula has exactly km satisf ..."
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Cited by 11 (5 self)
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We prove the first timespace tradeoffs for counting the number of solutions to an NP problem modulo small integers, and also improve upon known timespace tradeoffs for Sat. Let m> 0 be an integer, and define MODmSat to be the problem of determining if a given Boolean formula has exactly km satisfying assignments, for some integer k. We show for all primes p except for possibly one of them, and for all c < 2cos(π/7) ≈ 1.801, there is a d> 0 such that MODpSat is not solvable in n c time and n d space by general algorithms. That is, there is at most one prime p that does not satisfy the tradeoff. We prove that the same limitation holds for Sat and MOD6Sat, as well as MODmSat for any composite m that is not a prime power. Our main tool is a general method for rapidly simulating deterministic computations with restricted space, by counting the number of solutions to NP predicates modulo integers. The simulation converts an ordinary algorithm into a “canonical ” one that consumes roughly the same amount of time and space, yet canonical algorithms have nice properties suitable for counting.
Algorithms and Resource Requirements for Fundamental Problems
, 2007
"... no. DGE0234630. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. ..."
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Cited by 10 (7 self)
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no. DGE0234630. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.
MAking Hard Problems Harder
, 2005
"... We present a general approach to the hoary problem of (im)proving circuit lower bounds. We define notions of hardness condensing and hardness extraction, in analogy to the corresponding notions from the computational theory of randomness. A hardness condenser is a procedure that takes in a Boolean f ..."
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Cited by 7 (0 self)
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We present a general approach to the hoary problem of (im)proving circuit lower bounds. We define notions of hardness condensing and hardness extraction, in analogy to the corresponding notions from the computational theory of randomness. A hardness condenser is a procedure that takes in a Boolean function as input, as well as an advice string, and outputs a Boolean function on a smaller number of bits which has greater hardness when measured in terms of input length. A hardness extractor takes in a Boolean function as input, as well as an advice string, and outputs a Boolean function defined on a smaller number of bits which has close to maximum hardness. We prove several positive and negative results about these objects. First, we observe that hardnessbased pseudorandom generators can be used to extract deterministic hardness from nondeterministic hardness. We derive several consequences of this observation. Among other results, we show that if E has exponential nondeterministic hardness, then E with linear advice has close to maximum deterministic hardness. We demonstrate a rare downward closure result: there is δ> 0 such that E with subexponential advice is contained in nonuniform space 2 δn if and only if there is k> 0 such that P with quadratic advice can be approximated in nonuniform space n k. Next, we consider limitations on natural models of hardness condensing and extraction. We show lower bounds on the length of the advice required for hardness condensing in a very general model of “relativizing ” condensers. We show that nontrivial blackbox extraction of deterministic hardness from deterministic hardness is essentially impossible. Finally, we prove positive results on hardness condensing in certain special cases. We show how to condense hardness from a biased function without any advice, using a hashing technique. We also give a hardness condenser without advice from averagecase hardness to worstcase hardness. Our technique involves a connection between hardness condensing and certain kinds of explicit constructions of covering codes.