L. Adleman. Two theorems on random polynomial time. FOCS 78.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....some finite level. Thus, if the polynomial hierarchy is strict, then each of these statements is false. Parts 1) 2) 3) and 5) of this corollary are immediate from Theorems 2.3, 3.1, 3.2, 3.3, and 3.4, and Propositions 2.5 and 2.6. Part 4) is an implication of part 3) using methods of Adleman [37] and Karp and Lipton [38] Part 6) is proved from part 4) as follows. The decision version of circuit minimization has instances where is a circuit and , and the question is whether there is a circuit equivalent to with . This problem has a form: there exists a such that and, for all inputs ....

....words over the alphabet . In particular, we are interested in bit codewords (where ) that contain exactly one occurrence of the symbol ; denote this set of words containing One Two by For those readers familiar with complexity theory, the argument follows. Using that 6 MBE D, it follows as in [37] that if MBE D2 P 6 P poly. Hemaspaandra et al. 39, Theorem 11] have observed that a result of Karp and Lipton [38] relativizes; in particular, if 6 P poly then 6 =6 for all k 3. As will become clear shortly, the symbol serves as a synchronization symbol ; for example, the DIFs we ....

L. Adleman, "Two theorems on random polynomial time," in Proc. 19th IEEE Symp. Foundations of Computer Science, 1978, pp. 75--83.

....Turing machines that take polynomial length advice, or alternatively by polynomial sized circuits. If A is not weakly coherent then A is called strongly incoherent. Recall that BPP=poly = P=poly, because randomness can be incorporated into nonuniform advice using standard techniques [2]. Hence, there is no need to consider weak probabilistic examiners, because, for a fixed oracle, they are equivalent to weak deterministic examiners. In particular, for a fixed oracle, every BPP examiner is a P=poly examiner, and so every coherent set is weakly coherent. A tally set is a subset ....

L. Adleman, Two Theorems on Random Polynomial Time, in Proc. of the 19th Symposium on Foundations of Computer Science (1978), IEEE, 75--83.

....so the algorithm correctly outputs 1. If F has no solutions then the algorithm cannot find one, so the algorithm correctly outputs 0. ii. If UniqueSAT and UnSAT are p separable, then obviously P = UP. iii. If UniqueSAT and UnSAT are p separable, then R = NP [56] iv. If R = NP then NP P=poly [1], so the polynomial time hierarchy collapses [61] Corollary 10. All NP hard sets (under tt reductions) are p superterse relative to almost all oracles B. Proof: The preceding results relativize. R relative to almost all oracles [20] It is also known that P 6= UP for ....

L. Adleman. Two theorems on random polynomial time. In Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science, pages 75-- 83, 1978.

....; ffl 2 : Z FPCP c;s [r; f; l] 1 Gamma (1 ffl 1 ) Delta (1 Gamma c) c Gamma ffl 1 , s = 1 ffl 2 ) Delta s and r = fl maxf Gamma log 2 (ffl 1 (1 Gamma c) log 2 (l) Gamma log 2 (ffl 2 s)g. Proof: The proof is reminiscent of Adleman s proof that RP P=poly [Ad]. Suppose we are given a pcp system for which we want to reduce the randomness complexity. The idea is that it suffices to choose the random pad for the verifier out of a relatively small set of possibilities (instead than from all possibilities) Furthermore, most small sets (i.e. sets of size ....

L. Adleman. Two theorems on random polynomial time. Proceedings of the 19th Symposium on Foundations of Computer Science, IEEE, 1978, pp. 75--83.

....= I #Q) 1 is finite. Furthermore Q # v is equal to the limit as # tends to 1 of (I #Q) 1 v. The two functions above map matrices to matrices, and by specifying a particular entry [i, j] of the output, we may view them as mapping matrices to real numbers (and in our case the range will be [0, 1]) For any real valued function f on some domain D, we define the threshold language L f associated to f to be the set of inputs x D such that f(x) 1 2. We will consider three versions of the membership problem for this language, the exact, approximate and onesided versions. In each we ....

....method to show that if we omit the requirement that the generator be computable, and take, for each S,2 to be a random function mapping c 1 S bits, then the result would fool all probabilistic computations running in space S. This fact can be viewed as a rough analog to Adleman s result ([1]) that BPP can be computed by non uniform polynomial circuits. Of course, we do not now know how to construct e#ciently computable generators that achieve the optimal simulation (otherwise, this would be quite a different paper ) The crux of the problem, then, is to find a PRGE whose seed length ....

L. Adleman. Two theorems on random polynomial time. In 19th IEEE Symposium on Foundations of Computer Science, pages 75--83, 1978.

....direct construction of an O(log n) pebble, n state deterministic JAG for directed st connectivity. More interestingly, they also prove a lower bound of Omega# log n= log log n) on the space required by JAGs solving this problem, nearly matching the upper bound. Standard techniques (Adleman [1], Aleliunas et al. 2] extend this result to any randomized JAG whose time bound is at most exponential in its space bound. Berman and Simon [11] extend this space lower bound to probabilistic JAGs with even larger time bounds, namely exponential in log n. In this paper we use a variant of ....

L. M. Adleman. Two theorems on random polynomial time. In 19th Annual Symposium on Foundations of Computer Science, pages 75--83, Ann Arbor, MI, Oct. 1978. IEEE.

....1 Gamma fl with an O(log(1=fl) slowdown in efficiency. As a consequence, in a nonuniform model of computation (e.g. circuits) we can set fl = 1=jXj and then fix the coin tosses of A to obtain a deterministic procedure solving the same problem with only a O(log jXj) slowdown in efficiency (as in [Adl78] We are now ready to define codes that are nice for our purpose. These codes are parameterizd by two parameters: an integer k that counts (roughly) the length of the message to be encoded; and a positive real number that is related to the fraction of error from which we expect to be able ....

Leonard Adleman. Two theorems on random polynomial time. In 19th Annual Symposium on Foundations of Computer Science, pages 75--83, Ann Arbor, Michigan, 16--18 October 1978. IEEE.

.... a polynomially sized advice that depends only on the input size 7 : Corollary 17 For every finite field F q the following holds: 7 Since our reduction achieves exponentially small error probability, hardness under non uniform reductions also follows from general results about derandomization [1]. However, the ad hoc derandomization method we just described is more efficient and intuitive. ffl For any ae 1=2, and fl 1 GAPRNC (ae) fl;q is hard for NP under non uniform deterministic polynomial reductions. ffl For every real fl 1, GAPDIST fl;q is hard for NP under non uniform ....

L. Adleman, "Two Theorems on Random Polynomial Time", in Proc. 19th Symposium on Foundations of Computer Science 1978, pp. 75--83.

....# (0, 1 3) we have: # # (#) # C#(#)log 1 # , where C is a constant independent of # and #. 6 Proof. Let P (U 1 , U n ) be a polynomial that 1 3 approximates #. Defining Q 0 (U 1 , U n ) 1 5 (3P (U 1 , U n ) 1) wehave Q 0 (u) # [0, 2 5 ]for u # # 1 (0) and Q 1 (u) # [ 3 5 , 1] for u # # 1 (1) Let w(z) denote the univariate polynomial w(z) 3z 2 2z 3 . This is the unique cubic polynomial having no constant or linear term that satisfies w(1 z) 1 w(z) It is routine to show that for any z # [0, 2 5 ]wehave w(z) # [0,z 1.1 )andw(1 z) # (1 ....

....no constant or linear term that satisfies w(1 z) 1 w(z) It is routine to show that for any z # [0, 2 5 ]wehave w(z) # [0,z 1.1 )andw(1 z) # (1 z 1. 1 , 1] For i # 0, define the polynomial Q i 1 = w(Q i ) Then it follows by induction that Q i (u 1 , u n ) # [0, 1] for all (u 1 , u n ) # B n and also Q i # i approximates # with # i = 2 5) 1.1 i , and that deg(Q i ) 3 i deg(P ) We can then choose m of size O(log log # 1 ) so that #m # # , and deg(Q i ) # C deg(P)log 1 # , for some absolute constant C . ## Formu l ae are defined in the ....

[Article contains additional citation context not shown here]

L. Adleman, `Two theorems on random polynomial time', Proc. 19th IEEE Symposium on Foundations of Computer Science, 1978, 75--83.

....Min Max Theorem that shows that each player has a near optimal mixed strategy that plays uniformly from a multiset of size logarithmic in the number of pure strategies available to the opponent. The proof is a surprisingly simple probabilistic argument similar to circuit derandomization techniques [1, 15]. However, the central nature of games in theory suggests that this simple result may have far reaching consequences. This result was obtained independently by Althofer [3] Strengthening the connection between randomized and distributional complexities. This connection was first established by ....

....have linear size encodings. Thus, the stronger direction holds (approximately) for complexity measures that allow program size to grow linearly with input size. This includes most measures of circuit complexity. Note that this application is similar to known circuit derandomization techniques [1, 15]. However, the theorem has many other applications. For instance, by applying it to the program input game for the input player we show that there are hard distributions that can be generated by small circuits. Anti checkers and circuits that generate hard random instances. We give applications ....

Leonard M. Adleman. Two theorems on random polynomial time. In Proc. of the 19th IEEE Annual Symp. on Foundation of Computer Science, pages 75--83, 1978.

No context found.

L. Adleman. Two theorems on random polynomial time. FOCS 78.

No context found.

Leonard M. Adleman. Two theorems on random polynomial time. In proceedings of FOCS '78, pages 75--83, 1978.

No context found.

L. Adleman. Two theorems on random polynomial time. FOCS 78.

No context found.

L. Adleman. Two theorems on random polynomial time. In Proceedings of the Nineteenth Annual IEEE Symposium on Foundations of Computer Science, pages 75-83, 1978.

No context found.

L. Adleman. Two theorems on random polynomial time. Proceedings of the Nineteenth Annual Symposium on the Foundations of Computer Science, IEEE, 1978.

No context found.

L. Adleman, Two theorems on random polynomial time,in"Proc. 19th IEEE Symposium on Foundations of Computer Science", 1978, 75--83.

No context found.

L. Adleman, Two theorems on random polynomial time, in Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science, 1978, pp. 75--83.

No context found.

L. Adleman. Two theorems on random polynomial time. Proceedings of the Nineteenth Annual Symposium on the Foundations of Computer Science, IEEE, 1978.

No context found.

L. Adleman. Two theorems on random polynomial time. In 10th FOCS, pages 75--83, 1978.

No context found.

L. Adleman, "Two theorems on random polynomial time," in: Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Angeles, 1978, pp. 75--83.

No context found.

L. Adleman. Two theorems on random polynomial time. Proceedings of the Nineteenth Annual Symposium on the Foundations of Computer Science, IEEE, 1978.

No context found.

Leonard Adleman. Two theorems on random polynomial time. In Proceedings of the 19th IEEE Symposium on Foundations of Computer Science, pages 75-- 83, 1978.

No context found.

L. Adleman. Two theorems on random polynomial time. Proceedings of the Nineteenth Annual Symposium on the Foundations of Computer Science, IEEE, 1978.

No context found.

Adleman, L. (1978). Two theorems on random polynomial time. Proc. of 19th Symposium on Foundations of Computer Science (FOCS), 75--83. 27

No context found.

L. Adleman, \Two Theorems on Random Polynomial Time", in Proc. 19th Symposium on Foundations of Computer Science 1978, pp. 75-83.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC