Difficulty: Hard · Puzzle 4 of 6 · Topic: Constraint Solving Order Puzzles
How many legal tuples exist, and what is P(c==1)? Explain why c can still be 1 when b==0.
class chain_imp;
rand bit a;
rand bit b;
rand bit c;
constraint rel {
(a == 1) -> (b == 1);
(b == 1) -> (c == 1);
}
endclassSplit on b first; implication only constrains when antecedent is true.
1) If b=0: second implication imposes no requirement on c; first implication forces a=0. Tuples: (0,0,0),(0,0,1).
2) If b=1: second implication forces c=1; first implication allows a=0 or 1. Tuples: (0,1,1),(1,1,1).
3) Total legal tuples=4.
4) c==1 appears in 3 tuples -> P(c==1)=3/4.Answer: There are 4 legal tuples and P(c==1)=3/4 (75%).
A common wrong claim is that b==0 implies c==0; implication does not force the consequent when antecedent is false.
Add one constraint that makes P(c==1)=1/2 without changing legality too much.