Results 1  10
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1,910,210
Exponential Lower Bounds for the Pigeonhole Principle
, 1992
"... In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact ..."
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Cited by 121 (27 self)
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In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact
Microlocal Exponential Lower Bounds
 In preparation
"... In this paper we investigate microlocal lower bounds, as expressed by local lower bounds for the Bargmann transform, using only the most rudimentary techniques from complex analysis. The Bargmann transform is defined for u ∈ S ′ (R n), z ∈ C n, ..."
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Cited by 3 (3 self)
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In this paper we investigate microlocal lower bounds, as expressed by local lower bounds for the Bargmann transform, using only the most rudimentary techniques from complex analysis. The Bargmann transform is defined for u ∈ S ′ (R n), z ∈ C n,
Exponential lower bounds for policy iteration
 In Automata, Languages and Programming
, 2010
"... ar ..."
Exponential lower bounds for the Treelike Hajós Calculus
 INF. PROCESS. LETT
, 1997
"... The Hajós Calculus is a simple, nondeterministic procedure which generates precisely the class of non3colorable graphs. In this note, we prove exponential lower bounds on the size of treelike Hajós constructions. ..."
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Cited by 7 (1 self)
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The Hajós Calculus is a simple, nondeterministic procedure which generates precisely the class of non3colorable graphs. In this note, we prove exponential lower bounds on the size of treelike Hajós constructions.
Exponential lower bounds for the Bargmann transform
"... Abstract. We study local lower bounds for the Bargmann transform and give applications to quasimodes of elliptic semiclassical pseudodifferential operators and to functions with limited smoothness. 1. ..."
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Cited by 1 (1 self)
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Abstract. We study local lower bounds for the Bargmann transform and give applications to quasimodes of elliptic semiclassical pseudodifferential operators and to functions with limited smoothness. 1.
An Exponential Lower Bound for Depth 3 Arithmetic Circuits
, 1998
"... We prove the first exponential lower bound on the size of any depth 3 arithmetic circuit with unbounded fanin computing an explicit function (the determinant) over an arbitrary finite field. This answers an open problem of [N91] and [NW95] for the case of finite fields. We intepret here arithmetic c ..."
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Cited by 55 (1 self)
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We prove the first exponential lower bound on the size of any depth 3 arithmetic circuit with unbounded fanin computing an explicit function (the determinant) over an arbitrary finite field. This answers an open problem of [N91] and [NW95] for the case of finite fields. We intepret here arithmetic
An Exponential Lower Bound for the Size of Monotone Real Circuits
 J. COMP. SYSTEM SCIENCES
, 1995
"... We prove a lower bound, exponential in the eighth root of the input length, on the size of monotone arithmetic circuits that solve an NP problem related to clique detection. The result is more general than the famous lower bound of Razborov and Andreev, because the gates of the circuit are allow ..."
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Cited by 26 (0 self)
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We prove a lower bound, exponential in the eighth root of the input length, on the size of monotone arithmetic circuits that solve an NP problem related to clique detection. The result is more general than the famous lower bound of Razborov and Andreev, because the gates of the circuit
Some exponential lower bounds on formulasize
 in modal logic. Advances in Modal Logic
, 2014
"... We present two families of exponential lower bounds on the size of modal formulae and use them to establish the following succinctness results. We show that the logic of contingency (ConML) is exponentially more succinct than basic modal logic (ML). We strengthen the known proofs that the socalled ..."
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Cited by 1 (1 self)
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We present two families of exponential lower bounds on the size of modal formulae and use them to establish the following succinctness results. We show that the logic of contingency (ConML) is exponentially more succinct than basic modal logic (ML). We strengthen the known proofs that the so
An Exponential Lower Bound to the Size of Bounded Depth Frege . . .
, 1994
"... We prove lower bounds of the form exp (n ffl d ) ; ffl d ? 0; on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d; for any constant d: This is the largest lower bound for the strongest proof system, for whic ..."
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Cited by 67 (10 self)
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We prove lower bounds of the form exp (n ffl d ) ; ffl d ? 0; on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d; for any constant d: This is the largest lower bound for the strongest proof system
Exponential Lower Bounds and Separation for Query Rewriting
"... We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of firstorder and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower bounds and separation results from circuit complexity to prove ..."
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Cited by 16 (11 self)
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We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of firstorder and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower bounds and separation results from circuit complexity to prove
Results 1  10
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1,910,210