- (2i:0^ in .NET Integrated 2d Data Matrix barcode in .NET - (2i:0^ 5 - (2i:0^Gs1 Datamatrix Barcode barcode library with .netgenerate, create data matrix none with .net projects1 88.net Framework data matrix reader on .netUsing Barcode decoder for .NET Control to read, scan read, scan image in .NET applications. 1 3: Iteration This is clearly true (since k ^ N and k ^ N together imply that k = N). The requirement (13.11) checks the initialization. We have to verify that { (KAf } fe,5 := 0,0 { O^k^N A s = Using the assignment axiom, this follows from A 0= ( Z i : 0 ^ i < which is true by the empty-range rule for summations. The requirement (13.12) checks the loop body. We have to verify that A 5 = ( Z i : 0 < i < f e : a [ i ] ) A k A N~k A N-(k+l) 0 k,s := k-I,S od Control pdf 417 data for .net barcode pdf417 data with .net{ 5 = (Zi:Q^ where S, the value to be assigned to 5 in the body of the loop, is the only missing element. We calculate the appropriate value of S using the assignment axiom. The specification of the assignment in the body of the loop is given by the Hoare triple:RDLC barcode integrated in .netgenerate, create barcode none with .net projectsA sxXk = ( I . i : k ^ i < N : a [ i ] x X i )rCj3 . ~~ fC _L j ij A k>0 } . A k>0 { O^k^N A sxXk = (Zi:k^i 0 => (Kk- 1 3: Iteration So, it is indeed only the appropriate value of 5 that needs to be determined. We now use the summation rules to calculate the appropriate value of the unknowns: SxXk~l = (Zi:k-l^ = { SxXk~l { SxX ~ <=splitting the range on i = k- 1 , assuming 0 < k ^ N } = (Zi:k^i 0 k,s := k-l ,{ s = (Zi:0^ Note that this derivation of the algorithm constitutes a formal proof of Homer's rule. Note also how the calculation of S (as opposed to guessing what it should be) avoids making a 'one-off error. With problems like this one, it is very easy for array indices to be 'one-off. For example, we might have guessed the value sxX + a[k] for S. The consequences are often noticed immediately, but not always. And, in the digital world, a small error of this nature can be disastrous! Exercise 13.13. Verify the correctness of the initialization and the termination condition. D