Algebraic Verification Method for SEREs Properties via Groebner Bases Approaches

Algorithm 1

Assertion checking: 𝐴𝑠𝑠𝐶ℎ𝑘(𝐂,𝐺).

  Input: Circuit model 𝐂, an assertion 𝐺=[𝒜⇒𝒞];

  Output: Boolean: true or false;

  BEGIN

    /* Step 0: initialize input signals via testbench */

(0)𝐼𝑛𝑖𝑡𝑆𝑖𝑔𝑛𝑎𝑙𝑠(𝑋₀);

(1)   𝐒=∅;𝐌=∅;𝑃𝑆_𝐴=∅;𝐻=∅;𝑃𝑆_𝐶=∅;

   /* Step 1: build polynomial model */

(2)   𝐌=𝐵𝑢𝑖𝑙𝑑𝑃𝑆(𝐒);

   /* Step 3: build polynomial set for antecedent 𝒜 */

(3)   𝑃𝑆_𝒜=𝐵𝑢𝑖𝑙𝑑𝑃𝑆(𝒜);

   /* Step 3: build polynomial set for consequent 𝒞 */

(4)   𝑃𝑆_𝒞=𝐵𝑢𝑖𝑙𝑑𝑃𝑆(𝒞);

   /* Step 4: calculate the 𝑃𝑆_𝒜∪𝐌 */

(5)   𝐻=𝑃𝑆_𝒜∪𝐌;

   /* Step 5: calculate the Groebner base of ⟨𝐻⟩ */

(6)   𝐺𝐵_𝐻∶=𝑔𝑏𝑎𝑠𝑖𝑠(𝐻,≺);

   /* Step 6: calculate the Groebner base of ⟨𝐻⟩ */

(7)   if(1∈𝐺𝐵_𝐻){

(8)      return false; }

(9)   if(𝑟𝑒𝑚𝑑(𝑃𝑆_𝒞,𝐺𝐵_𝐻)≠0){

(10)     return false; }

(11) return 𝑡𝑟𝑢𝑒; /* Assertion does hold */

END ;