{"responseHeader":{"status":0,"QTime":7,"params":{"q":"{!q.op=AND}id:\"108183\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"modified_tdt":"2016-11-18T00:00:00Z","thumb_s":"/f8/fa/f8fa875d10bb947241532401e32ca06c3d26254c.jpg","oldid_t":"compsci 16296","setname_s":"ir_computersa","file_s":"/3b/fc/3bfc72a48276724ab4120c16c08e8c8e6b439840.pdf","title_t":"Page 107","ocr_t":"The symbols Fx, Fy, and Fxy in Equation (4.1) are partial derivatives of F with respect to x , ?/, and xy. The partial derivative of F with respect to x is defined in [1, 81] as: Fx = F(x, y; x = 1) © F(x, y; x = 0). Function Fx is obtained by an Exclusive-OR operation between two functions which are formed from F by setting x once to 0 and once to 1. Similarly, the partial derivative of F with respect to y is defined as: Fy = F(x, y; y = 1) © F(x, y;y = 0). For example, partial derivatives Fx and Fy for logical AND are calculated in the following way: Fx = (x y) © (x y) = y © 0 = y, (4.2) Fy = (x y) © (x y) = x © 0 = x. (4.3) Value Fxy is obtained from F by taking a partial derivative of Fx with respect to y. Values of partial derivatives Fx, Fy, and Fxy for all sixteen possible Boolean operations are calculated in the same way and are shown in Table 4.4. Next, it is shown how the total differential leads to a novel algorithm for fast evaluation of arbitrary Boolean expressions. Evaluating Boolean Expressions In traditional methods, the evaluation of Boolean expressions is based on function values. This algorithm uses the total differentials of Boolean functions instead of function values. Let F(x,y) be a Boolean operation. Let x and y be dependent variables, represented by operations G and H: x = G(xi,yi), y = H(x2:y2)- 99","restricted_i":0,"id":108183,"created_tdt":"2016-11-18T00:00:00Z","format_t":"application/pdf","parent_i":108243,"_version_":1642982404934074368}]},"highlighting":{"108183":{"ocr_t":[]}}}