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76
New Collapse Consequences Of NP Having Small Circuits
, 1995
"... . We show that if a selfreducible set has polynomialsize circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomialtime hierarchy PH to ZPP(NP) under the assumption that NP has polynomialsize circuits. This improves on the wellknown ..."
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Cited by 56 (7 self)
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investigate the circuitsize complexity of several language classes. In particular, we show that for every fixed polynomial s, there is a set in ZPP(NP) which does not have O(s(n))size circuits. Key words. polynomialsize circuits, advice classes, lowness, randomized computation AMS subject
Lower Bounds for the Low Hierarchy
"... this paper. The low hierarchy, as defined in [Sc83], can only be used to classify the complexity of sets in NP. In order to talk about related sets that are not in NP, the extended low hierarchy was introduced in [BBS86]. (The levels of this hierarchy are labeled EL 2 ,EL 2 , A preliminary ver ..."
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Cited by 33 (4 self)
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this paper. The low hierarchy, as defined in [Sc83], can only be used to classify the complexity of sets in NP. In order to talk about related sets that are not in NP, the extended low hierarchy was introduced in [BBS86]. (The levels of this hierarchy are labeled EL 2 ,EL 2 , A preliminary
New Collapse Consequences of NP Having Small Circuits
"... We show that if a selfreducible set has polynomialsize circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomialtime hierarchy PH to ZPP(NP) under the assumption that NP has polynomialsize circuits. This improves on the wellknown r ..."
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We show that if a selfreducible set has polynomialsize circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomialtime hierarchy PH to ZPP(NP) under the assumption that NP has polynomialsize circuits. This improves on the well
SuperPolynomial versus HalfExponential Circuit Size in the Exponential Hierarchy
, 1999
"... . Circuit size lower bounds were previously established for functions in p 2 , ZPP NP , exp 2 , ZPEXP NP and MA exp . We ask the general question: Given a time bound t(n). What is the best circuit size lower bound that can be currently shown for the classes MATIME[t(n)], ZPTIME NP [t(n ..."
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Cited by 18 (4 self)
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. Circuit size lower bounds were previously established for functions in p 2 , ZPP NP , exp 2 , ZPEXP NP and MA exp . We ask the general question: Given a time bound t(n). What is the best circuit size lower bound that can be currently shown for the classes MATIME[t(n)], ZPTIME NP [t
On High and Low Sets for the Boolean Hierarchy
, 1998
"... The polynomialtime hierarchy (PH) is central for many considerations of complexity theory. We call a set A 2 NP high (low, resp.) for the class \Sigma p k of the polynomialtime hierarchy if \Sigma p k relativized to the oracle A yields \Sigma p k+1 (\Sigma p k , resp). These concept of hig ..."
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The polynomialtime hierarchy (PH) is central for many considerations of complexity theory. We call a set A 2 NP high (low, resp.) for the class \Sigma p k of the polynomialtime hierarchy if \Sigma p k relativized to the oracle A yields \Sigma p k+1 (\Sigma p k , resp). These concept
Tight lower bounds for certain parameterized NPhard problems
 Proc. 19th Annual IEEE Conference on Computational Complexity (CCC’04
, 2004
"... Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of wellknown NPhard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on deptht circuits cannot be solve ..."
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Cited by 62 (10 self)
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be solved in time no(k) poly(m), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t − 1)st level W [t − 1] of the Whierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NPhard problems, including weighted sat
Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy
 In Proceedings of the 12th Conference on the Foundations of Software Technology and Theoretical Computer Science
, 1992
"... Several problems concerning superpolynomial size circuits and superpolynomialtime advice classes are investigated. First we consider the implications of NP (and other fun damental complexity classes) having circuits slightly bigger than polynomial. We prove that if such circuits exist, for examp ..."
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Cited by 19 (6 self)
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Several problems concerning superpolynomial size circuits and superpolynomialtime advice classes are investigated. First we consider the implications of NP (and other fun damental complexity classes) having circuits slightly bigger than polynomial. We prove that if such circuits exist
Generalized Lowness and Highness and Probabilistic Complexity Classes
"... We introduce generalized notions of low and high complexity classes and study their relation to structural questions concerning bounded probabilistic polynomial time complexity classes. We show, for example, that for a bounded probabilistic polynomial time, LC = HC implies that the polynomial hierar ..."
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hierarchy collapses complexity class C = BP ΣP k to C. This extends Schöning’s result for C = ΣP k (LC and HC are the low and high sets defined by C.) We also show, with one exception, that containment relations between the bounded probabilistic classes and the polynomial hierarchy are preserved
Generating and Model Checking a Hierarchy of Abstract Models
, 1999
"... The use of automatic model checking algorithms to verify detailed gate or switch level designs of circuits is very attractive because the method is automatic and such models can accurately capture detailed functional, timing, and even subtle electrical behaviour of circuits. The use of binary decisi ..."
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Cited by 4 (1 self)
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decision diagrams has extended by orders of magnitude the size of circuits that can be so verified, but there are still very significant limitations due to the computational complexity of the problem. Verifying abstract versions of the model is attractive to reduce computational costs but this poses
Lowness and the Complexity of Sparse and Tally Descriptions
 IN PROC. 3RD INT'L SYMP. ON ALG. AND COMPUT
, 1992
"... We investigate the complexity of obtaining sparse descriptions for sets in various reduction classes to sparse sets. Let A be a set in a certain reduction class Rr(SPARSE). Then we are interested in finding upper bounds for the complexity (relative to A) of sparse sets S such that A 2 Rr (S). By est ..."
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Cited by 6 (2 self)
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). By establishing such upper bounds we are able to derive the lowness of A. In particular, we show that if a set A is in the class R p hd (R p c (SPARSE)) then A is in R p hd (R p c (S)) for a sparse set S 2 NP(A). As a consequence we can locate R p hd (R p c (SPARSE)) in the EL \Theta 3 level
Results 1  10
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