We show that for any coprime m, r there is a circuit of the form MODm ◦ ANDd(n) whose correlation with MODr is at least 2 −O( n d(n) ). This is the first correlation lower bound for arbitrary m, r, whereas previously lower bounds were known for prime m. Our motivation is the question posed by Green et al. [11] to which the 2( n d(n) ) bound is a partial negative answer. We first show a 2−Ω(n) c...

We consider constant depth circuits augmented with few modular, or more generally, arbitrary symmetric gates. We prove that circuits augmented with o(log n) symmetric gates must have size n n) to compute a certain (complicated) function in ACC. This function is also hard on the average for circuits of size n logn augmented with o(log n) symmetric gates, and as a consequence we can get a pseudor...

ACC is the class of all problems computable by constant depth, unbounded fan-in circuits with ∧,∨,¬ and MODm gates for any constant m. A related class to ACC is P/poly, which contains all problems computable by polynomial-size circuits with ∧,∨, and ¬ gates. IfC is a circuit with n inputs, then we use tt(C) to denote the string of length 2 obtained by evaluating C on all 2 possible inputs in le...

DEA Classic models cannot be used for inaccurate and indeterminate data, and it is supposed that the data for all inputs and outputs are accurate and determinate. However, in real life situations uncertainty is more common. This article attempts to get the common weights for Decision-Making Units by developing DEA multi-objective models in the grey environment. First, we compute the privilege o...

Decision making is an important task for entrepreneurs, and proper performance of purchasing has a direct effect on decreasing costs, increasing profitability, and survival of an entrepreneur. Also, entrepreneurs must follow formal rational decision processes as much as possible with fewer costs. To do so, they can use Design of Experiment techniques in combination with decision-aids. In this p...

Organizations need to evaluate project proposals and select the ones that are the most effective in reaching the strategic goals by considering sustainability issue. In order to enhance the effectiveness and the efficiency of project oriented organizations, in this paper a new multi-objective decision making (MODM) approach of sustainable project portfolio selection is proposed which applies in...

The performance of a product is often evaluated by several quality characteristics.  ptimizing the manufacturing process with respect to only one quality characteristic will not always lead to the optimum values for other characteristics. Hence, it would be desirable to improve the overall quality of a product by improving quality characteristics, which are considered to be important. The probl...

one of the main principles of the passive defense is the principle of site selection. in this paper, we propose a multiple objective nonlinear programming model that considers the principle of the site selection in terms of two qualitative and quantitative aspects. the purpose of the proposed model is selection of the place of facilities of a system in which not only it observes the dispersion ...