Counterexample-Preserving Reduction for Symbolic Model Checking

Algorithm 1

The “max-match” rule-selection strategy.

  Input: The original specification 𝜑.

  Output: The reduced specification.

    (1) let  Γ∶=∅; /*  Γ memorizes the sub-formulae with infeasible condition */

   (2) let  Δ∶={𝜓∈ (sub(𝜑)∖Γ) such that ψ matches some reduction rule(s)};

   (3) foreach  𝜓₁,𝜓₂∈Δ s.t. 𝜓₁≠𝜓₂  do

   (4)  if  𝜓₁∈  sub(𝜓₂ )  then

   (5)    Δ∶=Δ∖ 𝜓₁;  /∗ that is, we only proceed “max” subformulae */

   (6)  end

   (7) end

   (8) if  Δ=∅  then

   (9)  return  𝜑;

 (10) end

  (11) foreach  𝜓∈Δ  do

 (12)  let  Θ∶= the set of rules that can be applied to 𝜓;

 (13)     /* note that we have |Θ|≤5 for each  𝜓  */

 (14)  while  Θ≠∅  do

 (15)     choose 𝑅∶=(Cond⊳𝜓≈𝜂) in  Θ;

 (16)     if Cond is stated then

 (17)     𝜑∶=𝜑^𝜓_𝜂; /*  𝜑^𝜓_𝜂 is obtained from 𝜑 by replacing 𝜓 with 𝜂  */

 (18)     break;

 (19)     end

(20)     Θ∶=Θ∖ {𝑅};

 (21)  end

(22)  Δ∶=Δ∖ {𝜓};

(23)  if  Θ=∅  then

(24)     Γ∶=Γ∪{𝜓}; /*  𝜓 would be excluded in the next iteration */

(25)  end

(26) end

(27) goto 2;