The multiplicative complexity of a Boolean function f is defined as the minimum number of binary conjunction (AND) gates required to construct a circuit representing f , when only exclusive-or, conjunction and negation gates may be used. This article explores in detail the multiplicative complexity of symmetric Boolean functions. New techniques that allow such exploration are introduced. They a...

Secure Evaluation of Private Functions (PF-SFE) allows two parties to compute a private function which is known by one party only on private data of both. It is known that PF-SFE can be reduced to Secure Function Evaluation (SFE) of a Universal Circuit (UC). Previous UC constructions only simulated circuits with gates of d = 2 inputs while gates with d > 2 inputs were decomposed into many gates...

A recent work of Chen, Kabanets, Kolokolova, Shaltiel and Zuckerman (CCC 2014, Computational Complexity 2015) introduced the Compression problem for a class C of circuits, defined as follows. Given as input the truth table of a Boolean function f : {0, 1} → {0, 1} that has a small (say size s) circuit from C, find in time 2 any Boolean circuit for f of size less than trivial, i.e. much smaller ...

The effective gauge field actions generated by charged fermions in QED3 and QCD3 can be made invariant under both small and large gauge transformations at any temperature by suitable regularization of the Dirac operator determinant, at the price of parity anomalies. We resolve the paradox that the perturbative expansion is not invariant, as manifested by the temperature dependence of the induce...

A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The wellknown physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by exami...

Design of parity preserving logic based on emerging nanotechnology is very limited due to present technological limitation in tackling its high error rate. In this work, Quantum-dot cellular automata (QCA), a potential alternative to CMOS, is investigated for designing easily testable logic circuit. A novel self-testable logic structure referred to as the testable-QCA (t-QCA), using parity pres...

The Nambu-Goto string in a three-dimensional (3D) Minkowski spacetime is quantized preserving Lorentz invariance and parity. The spectrum of massive states contains anyons. An ambiguity in the ground state energy is resolved by the 3D N=1 Green-Schwarz superstring, which has massless ground states describing a dilaton and dilatino, and first-excited states of spin 1/4.