We identify a new restriction on Boolean circuits called bijectivity and prove that bijective Boolean circuits require exponential size to compute the Boolean permanent function. As consequences of this lower bound, we show exponential size lower bounds for: (a) computing the Boolean permanent using monotone multilinear circuits ; (b) computing the 0-1 permanent function using monotone arithmet...

In this paper we investigate an extended version of modal dependence logic by allowing arbitrary Boolean connectives. Modal dependence logic was recently introduced by Jouko Väänänen by extending modal logic by a the dependence atom dep(·). In this paper we study the computational complexity of the model checking problem. For a complete classification of arbitrary Boolean functions we are using...

The latest results of benchmarking research are presented for a variety of beyond-CMOS charge- and spin-based devices. In addition to improving the device-level models, several new device proposals and a few majorly modified devices are investigated. Deep pipelining circuits are employed to boost the throughput of low-power devices. Furthermore, the benchmarking methodology is extended to inter...

The input-state incidence matrix of control Boolean network is proposed. It is shown that this matrix contains complete information of the input-state mapping. Using it, an easily verifiable necessary and sufficient condition for the controllability of Boolean control network is obtained. The corresponding control which drives a point to a given reachable point is designed. Moreover, certain to...

We study the length of polynomials over nite simple non-Abelian groups needed to realize Boolean functions. We apply the results for bounding the length of 5-permutation branching programs recognizing a Boolean set. Moreover, for Boolean and general functions on these groups, we present upper bounds on the length of shortest polynomials computing an arbitrary nary Boolean or general function, o...

The conceptions of χ-value and K-rotation symmetric Boolean functions are introduced by Cusick. K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the k − th power of ρ. In this paper, we discuss cubic 2-value 2-rotation symmetric Boolean function with 2n variables, which denoted by F2n(x2n). We give the recursive formula of weight of F2...

We present a new propositional proof system based on a somewhat recent characterization of polynomial space (PSPACE) called Boolean programs, due to Cook and Soltys. The Boolean programs are like generalized extension atoms, providing a parallel to extended Frege. We show that this new system, BPLK, is polynomially equivalent to the system G, which is based on the familiar but very different qu...