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Tautological Constraints in .NET Integration QR Code in .NET Tautological Constraints




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Tautological Constraints generate, create qr code jis x 0510 none in .net projects Visual Studio 2005 x := 1; /\x = 1 VS .NET QR Code ; while x = 10 do x := x + 2; /\(x 1 odd(x) x = 10) x := 1/\x = 1; while x = 10 do x := x + 2; /\F, indicating that the loop will not terminate because it is postconstrained by F. To illustrate further, consider the following program: q := 0; r := x; while r y do begin r := r y; q := q + 1 end First, we observe that q := 0; r := x q := 0; r := x; /\q = 0 r = x and for the loop construct /\q = 0 r = x; while r y do begin r := r y; q := q + 1 end the loop body clearly indicates that the loop intrinsic set is a set of pairs of the form (r, q) recursively de ned as follows: 1.

(x, 0) L. 2. If (r, q) L then (r y, q+1) L.

In general, we can translate a recursive de nition of this sort by generating a number of elements in the set until we can see the pattern clear enough to guess its de nition in the standard subset notation. We can then prove the correctness of the guess by using mathematical induction. In this case, L can be described in the standard subset notation as L = {(r, q).

P(r, q)} = {(r, q). r = x q y q qr codes for .NET 0}. Hence, we have /\q = 0 r = x; while r y do begin r := r y; q := q + 1 end /\q = 0 r = x; while r y do begin r := r y; q := q + 1 end; /\r = x q y q 0 /\q = 0 r = x; while r y do begin r := r y; q := q + 1 end; /\r = x q y q 0 r < y.

(by 6.1). (by 6.5). (by 6.3). Path-Oriented Program Analysis As explained prev QR Code ISO/IEC18004 for .NET iously, the preceding constitutes a proof that T{q := 0 r := x; while r y do begin r := r y; q := q + 1 end}r = x q y q 0 r < y, i.e.

, the program will perform the integer division x y to produce the quotient q and remainder r. A few more substantial examples follow. Example: The function GCD (greatest common divisor) has the following properties: GCD(a, b) = GCD(a b, b) if a> b, GCD(a, b) = GCD(a, b a) if a < b, GCD(a, b) = a = b if a = b.

(1) (2) (3). Now, consider the following program for computing GCD(x, y) for any pair of positive integers x and y: /\x > 0 y > 0; a := x; b := y; while a = b do begin if a > b then a := a b else b := b a end; The active variables of the while loop are a and b. L, the intrinsic set of this loop, is a set of pairs recursively de ned as follows: 1. (x, y) L.

2. If (a, b) L a = b, and if a > b then (a b, b) L, else if a b then (a, b a) L. L can be described in the standard subset notation: L = {(a, b) .

GCD(a, b) = GCD( qr codes for .NET x, y)}. For example, if x = 21 and y = 6, GCD(21, 6) = GCD(15, 6) = GCD(9, 6) = GCD(3, 6) = GCD(3, 3).

Thus the intrinsic set L is {(21, 6), (15, 6), (9, 6), (3, 6), (3, 3)}. Obviously, according to Corollary 6.1, we have /\ x > 0 y > 0; a:= x; b := y; /\ x > 0 y > 0; a := x; b := y; /\ a > 0 b > 0; For the loop construct, we have.

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