In this paper a novel all-optical logic NAND, NOR and XOR gate based on nonlinear directional coupler theory is demonstrated. We use the identical structure which contains three waveguides, for designing these gates; the only difference however, is the power of inputs light beam. In other words, while a beam with 4 W/μm in power considered as logical one, the output is NAND gate and if a beam w...

Let C be a threshold logic circuit computing a Boolean function MODm : {0, 1}n → {0, 1}, where n ≥ 1 and m ≥ 2. Then C outputs “0” if the number of “1”s in an input x ∈ {0, 1}n to C is a multiple of m and, otherwise, C outputs “1.” The function MOD2 is the so-called PARITY function, and MODn+1 is the OR function. Let s be the size of the circuit C, that is, C consists of s threshold gates, and ...

Today we show that PARITY is not in AC0. AC0 is a family of circuits with constant depth, polynomial size, and unbounded fan-in for the AND and OR gates. We establish this result through an application of the Switching Lemma. This result is the first use of randomization in its full power in complexity. Circuits were defined in previous lectures. In this lecture, we always assume that the circu...

In this paper we rst give a uniform AC 0 algorithm which uses partial sums to compute multiple addition. Then we use it to show that multiple addition is computable in uniform TC 0 by using count only once sequentially. By constructing bit matrix for multiple addition, we prove that multiple product with poly-logarithmic size is computable in uniform TC 0 (by using count k + 1 times sequentiall...

We investigate the self-correcting properties of a network of Majorana wires, in the form of a trijunction, in contact with a parity-preserving thermal environment. As opposed to the case where Majorana bound states are immobile, braiding Majorana bound states within a trijunction introduces dangerous error processes that we identify. Such errors prevent the lifetime of the memory from increasi...

We show that an intermediate scale supersymmetric left-right seesaw scenario with automatic R-parity conservation can cure the problem of tachyonic slepton masses that arises when supersymmetry is broken by anomaly mediation, while preserving ultraviolet insensitivity. The reason for this is the existence of light B − L = 2 higgses with yukawa couplings to the charged leptons. We find these the...

Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain and loss mechanisms break the Hermiticity while preserving parity-time PT symmetry. For a value γPT of the gain and loss strength parameter the eigenfrequencies undergo a spontaneous phase ...

We show that Shuffle(x, y, w), the problem of determining whether a string w can be composed from an order preserving shuffle of strings x and y, is not in AC, but it is in AC. The fact that shuffle is not in AC is shown by a reduction of parity to shuffle and invoking the seminal result [FSS84], while the fact that it is in AC is implicit in the results of [Man82a]. Together, the two results p...

The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with an inverse mass parameter, in addition to a possible topological mass term. The novelty is that the modified YM equation is not the Euler-Lagrange equation of any gauge-invariant local action for the YM gauge potential alone. Instead, consistency is achieve...