R. Beigel, J. Tarui, and S. Toda. On probabilistic ACC circuits with an exactthreshold output gate. In 3rd Annual International Symposium on Algorithms and Computation, pp. 420--429, 1992. LNCS 650. Home/Search Document Details and Download
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Lower Bounds For Uniform Constant Depth Circuits - Gore (1993) (Correct)
....of AC 0 and other circuit complexity classes. In addition to observing that there are sets in 1 In [BT91] the class SYM was called SYMMC. The name SYM has been suggested by Barrington in his recent survey [Bar92] Beigel, Tarui and Toda have used the name SYM in their recent paper [BTT92] as well. 87 superlogarithmic deterministic space classes and superpolynomial deterministic time classes, we have also shown that there are sets in P PP that are immune to AC 0 . In fact, we have shown that P PP contains sets that are immune to ACC(subexp) Theorem 4.3) Corollary 8.1 ....
....deterministic time classes, we have also shown that there are sets in P PP that are immune to AC 0 . In fact, we have shown that P PP contains sets that are immune to ACC(subexp) Theorem 4.3) Corollary 8.1 trivially implies that P PP contains sets that are immune to uniform SYM . In [BTT92] Beigel, Tarui and Toda have considered augmented ACC circuit families where the circuits are allowed to have probabilistic inputs and are also allowed to have an exact threshold gate as the output gate (an exact threshold gate outputs 1 if exactly k of its inputs are 1, where k is a parameter; ....
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R. Beigel, J. Tarui, and S. Toda. On probabilistic ACC circuits with an exact-threshold output gate. In Proc. 3rd Annual International Symposium on Algorithms and Computation, Lecture Notes in Computer Science 650, pages 420--429. Springer-Verlag, 1992.
Circuit Complexity before the Dawn of the New Millennium - Allender (1996) (18 citations) (Correct)
....with n log O(1) n AND gates at the input level, and a single symmetric gate at the root. Circuits of this sort, called SYM circuits because they are in some sense only a bit more powerful than a single symmetric gate, were shown to be able to simulate an even larger class of circuits in [BTT92] Later work by [GKR 95] shows that the symmetric gate can be chosen to be the middle bit function (that outputs the middle bit of the number r, where r is the number of inputs to the gate that evaluate to 1) Unfortunately, no analog to the second part of Smolensky s argument is known to ....
R. Beigel, J. Tarui, and S. Toda. On probabilistic ACC circuits with an exact-threshold output gate. In Proceedings of the 3rd ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation (ISAAC), volume 650 of Lecture Notes in Computer Science, pages 420--429. SpringerVerlag, 1992.
The Polynomial Method in Circuit Complexity - Beigel (1995) (26 citations) Self-citation (Beigel) (Correct)
....lower bounds on the size of threshold circuits. Toda [53] used polynomials to prove upper bounds on the power of the polynomial hierarchy. This led to a series of upper bounds on the power of the polynomial hierarchy [54, 52] AC [2, 3, 52, 18] and ACC [58, 20, 30, 37] and related classes [21, 42]. Beigel and Gill [15] pushed the use of polynomials in order to prove closure properties of counting classes. This was extended by Hertrampf [34] see also [16] Beigel, Reingold, and Spielman [19] discovered that rational functions could be used as well for closure properties of PP. This work ....
R. Beigel, J. Tarui, and S. Toda. On probabilistic ACC circuits with an exactthreshold output gate. In 3rd Annual International Symposium on Algorithms and Computation, pp. 420--429, 1992. LNCS 650.
On Closure Properties of P in the Context of PF - Ogihara, Thierauf, Toda Self-citation (Toda) (Correct)
....in the lemma. Define u = T 1. Then we have: ffl u 0 (i; x; j; k) j 0 (mod m j ) u(i; x; j; k) j 0 (mod m p(n) j ) and 4 Preceding to this work, essentially the same result was proven in a quite different form in a manuscript by Beigel, Tarui, and Toda. But, in the conference version [BTT92], the result is stated in a weaker form. Though the result will appear in their journal version, since its style is quite different and does not fit in our paper, we include the full proof of the theorem. 8 ffl u 0 (i; x; j; k) j 1 (mod m j ) u(i; x; j; k) j 1 (mod m p(n) j ) Define a ....
R. Beigel, J. Tarui, and S. Toda, On probabilistic ACC circuits with an exactthreshold output gate, In Proc. 3rd Int. Symp. on Algorithms and Computation, Lecture Notes in Computer Science #650 (1992), pp. 420--429.
On Closure Properties of #P in the Context of PF o #P - Ogihara, Thierauf, Toda, al. Self-citation (Toda) (Correct)
....not have to worry about detecting the nonexistence of the majority, we may de ne the function : N N as the output of M 0 . 4 Preceding to this work, essentially the same result was proven in a quite di erent form in a manuscript by Beigel, Tarui, and Toda. But, in the conference version [BTT92], the result is stated in a weaker form. Though the result will appear in their journal version, since its style is quite di erent and does not t in our paper, we include the full proof of the theorem. 6 Let x 2 n and p be a polynomial such that for all i e(x) f(i; x) 2 p(n) and e(x) ....
R. Beigel, J. Tarui, and S. Toda, On probabilistic ACC circuits with an exact-threshold output gate, In Proc. 3rd Int. Symp. on Algorithms and Computation, Lecture Notes in Computer Science #650 (1992), pp. 420-429.
The Polynomial Method in Circuit Complexity - Beigel (1995) (26 citations) Self-citation (Beigel) (Correct)
....lower bounds on the size of threshold circuits. Toda [53] used polynomials to prove upper bounds on the power of the polynomial hierarchy. This led to a series of upper bounds on the power of the polynomial hierarchy [54, 52] AC 0 [2, 3, 52, 18] and ACC [58, 20, 30, 37] and related classes [21, 42]. Beigel and Gill [15] pushed the use of polynomials in order to prove closure properties of counting classes. This was extended by Hertrampf [34] see also [16] Beigel, Reingold, and Spielman [19] discovered that rational functions could be used as well for closure properties of PP. This work ....
R. Beigel, J. Tarui, and S. Toda. On probabilistic ACC circuits with an exactthreshold output gate. In 3rd Annual International Symposium on Algorithms and Computation, pp. 420--429, 1992. LNCS 650.
On the Power of Generalized MOD-Classes - Köbler, Toda Self-citation (Toda) (Correct)
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R. Beigel, J. Tarui and S. Toda. On probabilistic ACC circuits with an exact-threshold output gate. In Proceedings 3rd Symposium on Algorithms and Computation, 420-429, 1992.
Extension of Toda's Theorem to Middle Bit Classes - Köbler (Correct)
No context found.
R. Beigel, J. Tarui and S. Toda, On probabilistic ACC circuits with an exact-threshold output gate. In Proceedings 3rd Symposium on Algorithms and Computation, (1992), 420-429.
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