L. Cai, J. Chen, and J. H astad. Circuit bottom fan-in and computational power. SIAM Journal on Computing, 27(2):341--355, March 1998. Home/Search Document Details and Download
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A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
.... who showed that for all d there exist #, # 0 so that there are functions on n variables, computable with polynomial size, depth d circuits of bottom fan in n but which require exponential size to compute with depth d circuits of bottom fan in n , and later results of Cai, Chen and Hastad [13], who showed that for each constant d, there exist functions computable with polynomial size, depth d, bottom fan in 2 circuits that require exponential size to compute with depth d circuits with bottom fan in 1, and that for each constant k, there exists a function of n variables computable by ....
L. Cai, J. Chen, and J. Hastad. Circuit bottom fan-in and computational power. SIAM Journal on Computing, 27(2):341--355, March 1998.
Programs Over Semigroups of Dot-Depth One - Alexis Maciel Department (1996) (3 citations) (Correct)
.... Along the way, we will give a simple direct argument that the hierarchy de ned by k interleaves strictly with the one de ned by AC k , i.e. 1 1 AC 2 thus re ning a result of [16] This result can also be derived from a special case of a more general theorem in [7]. The fact that semigroups of dot depth one form a p variety allows us to generalize a result of Straubing [19] and P eladeau [13] on regular languages expressible by 1 formulas with arbitrary numerical predicates. They showed that one may restrict to regular predicates without losing any ....
....resulting in a BC that simulates the original k 1 circuit. This contradicts Theorem 1. 2 Note that the separation between BC k , as well as that between k , is superpolynomial. An exponential separation between BC k has been obtained recently by Cai, Chen and H astad [7] by using random restriction techniques as in [9] This implies an exponential separation between AC k , by the same argument as in the proof of Corollary 2. 4 The p variety corresponding to 1 4.1 Algebraic characterizations of d 1 A subset of A is a locally testable language i ....
L. Cai, J. Chen and J. Hastad, Circuit Bottom Fan-in and Computational Power, SIAM J. on Computing 27 (1998) 341-355.
Gap-Languages and Log-Time Complexity Classes - Regan, Vollmer (1997) (2 citations) (Correct)
....the same computation by M as on x 0 . But then changing the target bit of x 0 to 1 yields a member of L bs that M rejects, giving the desired contradiction. In fact, this argument shows that a machine accepting L bs under proviso B must take time Omega Gammaime 2 n) Cai, Chen, and Hastad [CCH95] show that for all k 1, Sigma R k ae Sigma S k ae Sigma B k Sigma U k ae Sigma R k 1 ; 2) thereby refuting Sipser s claim [Sip83, BS90] that Sigma R k = Sigma S k . That Sigma S k ae Sigma B k falls out of their stated proof of Pi S k ae Pi U k ; we suspect ....
....d = 1; also, F n d is identically 0 if n is not a power of d. We identify F d with the language f x : F d (x) 1 g. For instance, the language F 1 equals 0 1(0 1) and belongs to Sigma R 1 (hence also to NLOGTIME) but not to Pi U 1 (hence not to DLOGTIME) Lemma 2. 3 (cf. [CC95, CCH95]) For all d 1, a) F d belongs to Sigma R d but not to Pi U d . b) F d is complete for Sigma U d under U m , complete for Sigma dlt d under dlt m , complete for Sigma S d under S m , and complete for Sigma R d under dlt proj . c) For all languages A, if A ....
[Article contains additional citation context not shown here]
L. Cai, J. Chen, and J. Hastad. Circuit bottom fan-in and computational power, 1995.
Gap-Languages and Log-Time Complexity Classes - Regan, Vollmer (1997) (2 citations) (Correct)
....BS90] that all addresses are encoded by binary strings of length dlog ne, and after each query, the index tape is indeed erased. Proviso (R) was defined by Ruzzo [Ruz81] for alternating machines. A fourth proviso, intermediate in power between U and S, has also been defined by Cai and Chen et al. [CCDF94, CC95, CCH95], taking an idea from the Block Transfer model of [ACS87] B) for block read write ) M writes two addresses i; j with i j on its index tape, and receives the string x i : x j on that tape, at a cost of dlog ne (j Gamma i) time units. This is equivalent to the B c formalism in ....
....the same computation by M as on x 0 . But then changing the target bit of x 0 to 1 yields a member of L bs that M rejects, giving the desired contradiction. In fact, this argument shows that a machine accepting L bs under proviso B must take time Omega Gammaime 2 n) Cai, Chen, and Hastad [CCH95] show that for all k 1, Sigma R k ae Sigma S k ae Sigma B k Sigma U k ae Sigma R k 1 ; 2) thereby refuting Sipser s claim [Sip83, BS90] that Sigma R k = Sigma S k . That Sigma S k ae Sigma B k falls out of their stated proof of Pi S k ae Pi U k ; we suspect ....
[Article contains additional citation context not shown here]
L. Cai, J. Chen, and J. Hastad. Circuit bottom fan-in and computational power, 1995. Accepted to SIAM J. Comput.
A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
No context found.
L. Cai, J. Chen, and J. H astad. Circuit bottom fan-in and computational power. SIAM Journal on Computing, 27(2):341--355, March 1998.
A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
No context found.
L. Cai, J. Chen, and J. Hastad. Circuit bottom fan-in and computational power. SIAM Journal on Computing, 27(2):341--355, March 1998.
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