A Latent Implementation Error Detection Method for Software Validation

Algorithm 1

Counterexample-Guided Synchronous Simulation (CGSS).

Given MS for a system model and ct for a counterexample trace, where:

(1) ∃𝜎_𝑆 ∈ Traces (MS), that is, ∃𝑞−→₀^𝑡0𝑞−→₁^𝑡1⋯−→^𝑡𝑛𝑞_𝑛∶𝑞_𝑖 ∈𝑄 (MS) and 𝑡_𝑖 ∈𝐿 (MS), (0≤𝑖≤𝑛);

(2) ct could be specified as: ∃𝑐−−→₀^𝑎0𝑐−−→₁^𝑎1⋯−−→^𝑎𝑚𝑐_𝑚∶𝑐_𝑗 ∈𝑄 (ct) and 𝑎_𝑗 ∈𝐿 (ct), (0≤𝑗≤𝑚);

(3) 𝑄 (MS) ∩  𝑄 (ct) = Φ and 𝐿 (MS) ⊇ 𝐿 (ct) and 𝑞₀=𝑐₀;

Procedure  CGSS {

  /* omit all internal actions in the counterexample trace */

 ct_new = Trim  (ct), where 𝐿 (ct_new) ⊆ LI (ct) ∪ LU (ct)

 /* based on ct _new trace to perform synchronous simulation with MS model */

 for each pair  𝑎_𝑗 ∈𝐿 (ct_new) starting from 𝑎₀  and  𝑡_𝑖 ∈𝐿 (MS) starting from 𝑡₀{

  /* the external trace of counterexample acts the same as the trace in MS, exit to report non-empty set */

  if  𝑎_𝑗 is the last action of ct_new  and  𝑎_𝑗=𝑡_𝑖 then return non-empty set; exit;

  /* omit considering internal actions and go for the next iteration */

  if  𝑡_𝑖∈ LE (MS)  then  𝑡_𝑖=𝑡_𝑖+1; continue;

  /* the same external action leads to one synchronous simulation step, and go for the next iteration */

  if  𝑎_𝑗=𝑡_𝑖  then  𝑎_𝑗=𝑎_𝑗+1, 𝑡_𝑖=𝑡_𝑖+1; continue;

  /* the different external action leads to failure simulation, and exit to report empty set */

  if  𝑎_𝑗≠𝑡_𝑖  then  return empty set; exit;

 } // end of for each pair

} // end of procedure