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QR-Code for C#.net The main idea. As in the illustrating paragraph, the basic idea is pushing the in .NET Insert barcode code39 in .NET The main idea. As in the illustrating paragraph, the basic idea is pushing the

The main idea. As in the illustrating paragraph, the basic idea is pushing the using none toadd none in asp.net web,windows applicationc# encoding qr code error probability on yes none for none -instances (of ) to the reduction, while pushing the error probability on no-instances to the coRP-problem. Focusing on the case that (x) = 1, this is achieved by augmenting the input x with a random sequence of modi ers that act on the random-input of algorithm A such that for a good choice of modi ers it holds that for every r {0, 1} p(. .NET x. ) there exists a modi er none none in this sequence that when applied to r yields r that satis es A (x, r ) = 1. Indeed, not all sequences of modi ers are good, but a random sequence will be good with high probability and bad sequences will be accounted for in the error probability of the reduction. On the other hand, using only modi ers that are permutations guarantees that the error probability on no-instances only increase by a factor that equals the number of modi ers that we use, and this error probability will be accounted for by the error probability of the coRP-problem.

Details follow. The aforementioned modi ers are implemented by shifts (of the set of all strings by xed offsets). Thus, we augment the input x with a random sequence of shifts, denoted s1 , .

. . , sm {0, 1} p(.

x. ) , such that for a good none none choice of (s1 , . . .

, sm ) it holds that for every r {0, 1} p(. x. ) there exists an i [m none for none ] such that A (x, r si ) = 1. We will show that, for any yes-instance x and a suitable choice of m, with very high probability, a random sequence of shifts is good. Thus, for def m A ( x, s1 , .

. . , sm , r ) = i=1 A (x, r si ), it holds that, with very high probability over the choice of s1 , .

. . , sm , a yes-instance x is mapped to an augmented input x, s1 , .

. . , sm that is accepted by A with probability 1.

On the other hand, the acceptance probability of augmented no-instances (for any choice of shifts) only increases by a factor of m. In further detailing the foregoing idea, we start by explicitly stating the simple randomized mapping (to be used as a randomized Karp-reduction), and next de ne the target promise problem. s1 , .

. . , sm {0, 1}m , and output the pair (x, s), where s = (s1 , .

. . , sm ).

Note that this mapping, denoted M, is easily computable by a probabilistic polynomial-time algorithm.. The promise problem. We de ne the following promise problem, denoted yes ,. The randomized mapping. On input x {0, 1}n , we set m = p(. x. ), uniformly select no ),. having instances of the form (x, s) such that s. = p(. x. )2 .. The yes-instances are none none pairs (x, s), where s = (s1 , . . .

, sm ) and m = p(. x. ), such that for every r none none {0, 1}m there exists an i satisfying A (x, r si ) = 1. The no-instances are pairs (x, s), where again s = (s1 , . .

. , sm ) and m = p(. x. ), such that for at leas none for none t half of the possible r {0, 1}m , for every i it holds that A (x, r si ) = 0. To see that is indeed a coRP promise problem, we consider the following randomized algorithm. On input (x, (s1 , .

. . , sm )), where m = p(.

x. ) = . s1 . = = . sm ,. RANDOMNESS AND COUNTING the algorithm uniformly none for none selects r {0, 1}m , and accepts if and only if A (x, r si ) = 1 for some i {1, . . .

, m}. Indeed, yes-instances of are accepted with probability 1, whereas no-instances of are rejected with probability at least 1/2..

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