Algebraic Verification Method for SEREs Properties via Groebner Bases Approaches

Algorithm 2

Assertion checking: 𝑇𝑒𝑚𝑝𝑜𝑟𝑎𝑙𝐴𝑠𝑠𝐶ℎ𝑘(𝐂,𝑠,𝑐𝑦𝑐𝑙𝑒𝑠).

  Input: Circuit model 𝐂, a temporal assertion 𝑠, running cycles 𝑐𝑦𝑐𝑙𝑒𝑠;

  Output: Boolean: true or false;

  BEGIN

(1)  𝑖=0;

(2)  𝑠𝑤𝑖𝑡𝑐ℎ(𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟(𝑠)){

(3)   case 𝐚𝐥𝐰𝐚𝐲𝐬:{

(4)    𝑤ℎ𝑖𝑙𝑒(𝑖<𝑐𝑦𝑐𝑙𝑒𝑠){

(5)     𝑖𝑓(!𝐴𝑠𝑠𝐶ℎ𝑘(𝐶,𝑠,𝑖)){;

(6)       return false;}

(7)     𝑖+=𝑑𝑒𝑝(𝑠)}

(8)    } /* end while */

(9)   case eventually:{

(10)   𝑤ℎ𝑖𝑙𝑒(𝑖<𝑐𝑦𝑐𝑙𝑒𝑠){

(11)    𝑖𝑓(𝐴𝑠𝑠𝐶ℎ𝑘(𝐶,𝑠,𝑖)){;

(12)      return true;}

(13)    𝑖+=𝑑𝑒𝑝(𝑠)}

(14)   } /* end while */

(15)  }/* end case */

(16)  case never :{

(17)   𝑤ℎ𝑖𝑙𝑒(𝑖<𝑐𝑦𝑐𝑙𝑒𝑠){

(18)    𝑖𝑓(𝐴𝑠𝑠𝐶ℎ𝑘(𝐶,𝑠,𝑖)){;

(19)      return false;}

(20)    𝑖+=𝑑𝑒𝑝(𝑠)}

(21)   } /* end while */

(22)  }/* end case */

(23)   𝐝𝐞𝐚𝐟𝐮𝐥𝐭:{

(24)   𝑟𝑒𝑡𝑢𝑟𝑛𝐴𝑠𝑠𝐶ℎ𝑘(𝐶,𝑠,𝑖);

(25)   }/* end switch */

(26)  }

END ;