Understanding CFG Nodes and Information Loss in Program Semantics
Explore the concept of Control Flow Graph (CFG) nodes and information loss in program semantics. Learn how nodes store constant values and how imprecise information at one point can lead to the loss of other crucial data, impacting program understanding.
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m1 l(m1, n) ESSSD[s, m1] m2 l(m2, n) n ESSSD[s, m2] s . . . l(mk, n) ESSSD[s, mk] mk
1: start .(???) 2: a=1 . [a 1] 3: b=1 . [b 1] . [c (a)+ (b)] F 4: a<3 6: c=a+b 7: exit . (a)>=3? : . (a)<3? : T 5: a=a+b
node 1 2 3 4 5 6 7 iteration 0 {(???)} 1 Store {(???)} {(1??)} 2 Store {(???)} {(1??)} {(11?)} 3 Store {(???)} {(1??)} {(11?)} (11?) (21?) (11?) (21?) {(11?)} 4 Store {(???)} {(1??)} {(11?)} 5 Store (11?) (21?) {(???)} {(1??)} 6 Store (11?) (21?) (31?) (11?) (21?) {(???)} {(1??)} 7 Store (11?) (21?) (31?) (11?) (21?) {(31?)} {(???)} {(1??)} 8 Store (11?) (21?) (31?) (11?) (21?) {(31?)} {(???)} {(1??)} {(314)} 9 Store (11?) (21?) (31?) (11?) (21?) {(31?)} {(???)} {(1??)} {(314)} 10 Store means that the indicated variable has a constant value at a node in the CFG. For example, variable b has the constant value 1 at node 4. (Note that we also treat ? as a constant.)
node 1 2 3 4 5 6 7 iteration 0 1 Store [ ] {(???)} [???] 2 Store [ ] {(???)} [???] {(1??)} [1??] 3 Store [ ] {(???)} [???] {(1??)} [1??] {(11?)} [11?] 4 Store [ ] {(???)} [???] {(1??)} [1??] {(11?)} [11?] {(11?)} [11?] (11?) (21?) [ 1?] (11?) (21?) [ 1?] 5 Store [ ] {(???)} [???] {(1??)} [1??] {(11?)} [11?] (11?) (21?) [ 1?] 6 Store [ ] {(???)} [???] {(1??)} [1??] (11?) (21?) (31?) [ 1?] (11?) (21?) [ 1?] 7 Store [ ] {(???)} [???] {(1??)} [1??] (11?) (21?) (31?) [ 1?] (11?) (21?) [ 1?] 8 Store [ ] {(???)} [???] {(1??)} [1??] {(31?)} [ 1?] (11?) (21?) (31?) [ 1?] (11?) (21?) [ 1?] 9 Store [ ] {(???)} [???] {(1??)} [1??] {(31?)} [ 1?] {(314)} [ 1 ] (11?) (21?) (31?) [ 1?] (11?) (21?) [ 1?] 10 Store [ ] {(???)} [???] {(1??)} [1??] {(31?)} [ 1?] {(314)} [ 1 ] shows places where we obtain worse information than what the collecting semantics indicates. The loss of information at one point can cause other information to be lost (e.g., variable c at point 7, due to imprecise information for variable a at point 6).
