Algorithm 2. Pseudocode of PROPAGATE_FORWARD for MCMC-LTMS.

PROPAGATE_FORWARD (clause_set)

Inputs: clause_set, the clauses describe system Outputs: a 3-bit flag, bit0 ~ unit propagate, bit1 ~ conflict, bit2 ~ true clause  clause_set, clause_set is replaced by the clauses remain the same

bit<3> flag = 0 for clause in clause_set   CLAUSE_SCAN(clause, false_assign, true_assign, unknown_literal))   if(true_assign is not empty)     reason = (unknown_literal is empty)? true: false //rule 2     PROPAGATE_TRUE_CLAUSE(clause, true_assign, false_assign, reason)//rule 3     flag = flag | (1<<2)   else if(unknown_literal.size > 1)     remain_clause.insert(clause)   else if(unknown_literal.size == 1) //rule 1     store clause, false_assign, unknown_literal in fringe   else     PROPAGATE_FALSE_CLAUSE(clause, false_assign)     flag = flag | (1<<1) for clause, false_assign, literal in fringe   flag = flag | PROPAGATE_FRINGE_CLAUSE(clause, false_assign, literal)?: (1<<0): (1<<1) clause_set = remain_clause return flag