An algorithm is proposed to decide whether a function of n variables is a quadratic Boolean function. If so, how can we obtain the quadratic terms? Different from the Qnine-McCluskey method; my algorithm is based on the counting of value 0 and 1, and allows a high level of parallelism.

Keywords: quadratic Boolean functions, decision, Q-M Algorithm, prime implicant, miniterm.

For any given orthonormal base function g, it is proved that generalized Boolean functions retain properties of a quotient group. Here I proposed a construction of the homomorphic kernel, with which a method of generating GBF's is obtained.

Key words generalized Boolean function; coset; homomorphic kernel; quotient group; generation.

In this paper some examples of decomposition of Boolean functions, in the sense of T. Sasa, are presented. Also, PLA implementations for an arbitrary function, a symmetric function and parity function are investigated.

Keywords: Boolean function; multiple-valued decomposition; programmable logic array; decoder.

Just like the consistent condition on Boolean equations, I have proved the similar condition on generalized Boolean equations of n variables. Also I use the successive elimination method to determine orthonormal base functions g and solutions of x1,···,xn.

Key words: Boolean equation; generalized Boolean function; consistent conditions; orthonormal solution; successive elimination method.

This paper, based on the concept of generalized Boolean function introduced by N.Tandareanu, has answered the following questions: for {0,1} is a subset of A and A is a pure subset of a Boolean algebra B, whether an n-variable function fn is an A-generalized Boolean function, and if it is, the problem is how to obtain all the functions g such that f belongs to GBFn(g). By proposing the decision conditions and the concept of g-generating matrix, we give a method for deciding one-variable functions, and indicate the problem of n-variable function fn can be reduced to that of its one-variable sub functions.

Key words: Boolean algebra; generalized Boolean function; g-generating matrix; second-order Stirling number; one-variable sub function.

The program complexities of for-do repetition structure typically given by MeCabe, Prather, and Z-W, are recalculated and analyzed. Also, the unclear formulary in the Z-W expression is corrected.

Keywords: program complexity; for-do structure; MeCabe metric; Prather metric; Z-W metric.

This paper deals with unstructuredness resulted from conversion of mutiple conditions in selection and repetition structures. Unlike the traditional methods, a new cascade approach is presented. The cascade programs can be obtained by decomposing multiple conditions and adding logic variables. The results are compared with those transformed by some other methods, based on the software complexity measure proposed by Prather.

Keywords: cascade; nest; software complexity measure; structured transformation; unstructuredness.

Generally in practice, as the production cost consists of the fixed inventory and the product expense, the cost function is often expressed as linear function. Under this condition, an improved algorithm is presented for dynamic programming of production and inventory, greatly reducing the complexity of the original problem. A sample comparison between two methods is given to predict a plan in 19-stage periods by the implemented PASCAL program.

In this paper a decomposition method for arbitrary Boolean functions on B2 is proposed and the relations between two classes of function fi(X) and fj(X) are also presented, We obtain that any Boolean function can be decomposed to a monotone function and another function using product and sum operations, This method is known, with example, to be very intuitive, which is significant both in the research and in the application of Boolean functions.

Keyword: Boolean function; Hasse diagram; monotone function; partition.