An empirical complexity study for a 2CPA solver

The computational decision problem CPA [ 1 ; 2 ; 3  ; 4 ] is a variant of the probabilitistic satisfiability problem PSAT [ 5 , 11 , 15 ]. In this paper we investigate the behavior of an algorithm which decides CPA applied to the still NP-complete subproblem 2CPA , instances have at most two literals per clause . We locate , as it is done for some satisfiability problems [ 10 , 12 ; 13  ; 14 , 17 ], a critical value for the ratio a = m/n, m is the number of binary clauses present in the instance and n is the number of events . point divides “ almost all coherent ” instances from “ almost all not coherent ”: the most difficult instances lies near this point .