Groebner Bases Based Verification Solution for SystemVerilog Concurrent Assertions

Algorithm 1

“𝐴𝑠𝑠𝐶ℎ𝑘𝑃𝑜𝑙𝑦𝐵𝑢𝑖𝑙𝑑(𝑀,𝑇,𝐴)”.

Input:

(1) circuit model 𝑀;

(2) initial condition 𝑇;

(3) an assertion 𝐴;

Output: Boolean: 𝑡𝑟𝑢𝑒 or 𝑓𝑎𝑙𝑠𝑒;

BEGIN

 /*Step  1: initialize input signals via testbench */

(00) 𝐼𝑛𝑖𝑡𝑆𝑖𝑔𝑛𝑎𝑙𝑠(𝑇);

(01) 𝕸=0/;PS_𝐴=0/;𝐻=0/;PS_𝑇=0/;

 /*Step  2: build polynomial model */

(02) 𝕸=⟦𝑀⟧=𝐵𝑢𝑖𝑙𝑑PS(𝑀);

 /*Step  3: build polynomial set for initial condition 𝑇*/

(03) 𝑃𝑆_𝑇=⟦𝑇⟧=𝐵𝑢𝑖𝑙𝑑PS(𝑇);

 /*Step  4: build polynomial set for consequent 𝒜 */

(04) 𝑃𝑆_𝐴=⟦𝐴⟧=𝐵𝑢𝑖𝑙𝑑PS(𝐴);

 /*Step  5: calculate the PS_𝑇∪𝕸*/

(05) 𝐻=PS_𝒯∪𝕸;

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

(06) GB_𝐻∶=𝑔basis(𝐻,≺);

 /*Step  7: determine the basis is {1} or not */

(07) if(1∈GB_𝐻)  {

(08)   return 𝑓𝑎𝑙𝑠𝑒; }

 /*Step  8: check every polynomial */

 /*𝐴={𝑎₁,𝑎₂,…,𝑎_|𝐴|}*/

(09) 𝑖=1;

(10) 𝑤ℎ𝑖𝑙𝑒(𝑖≤|𝐴|){

(11)  if(𝑟𝑒𝑚𝑑(𝑎_𝑖,GB_𝐻)≠0) {

(12)    return 𝑓𝑎𝑙𝑠𝑒; }

(13)   i++;

(14)  } /* endwhile */

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

END;