Some Ideas on Random Generation of K-sat Instances

In our previous research work, we have studied the detection and the use of symmetries to improve the eeciency of satissability algorithms. We have believed that the most hard SAT problems present strucural properties such as symmetries. However, recently several authors have exhibited a threshold phenomena on randomly generated K-SAT instances. It is shown that hard instances can be generated randomly using the xed clause-length model. The experiments we have performed on such instances show that they don't contain symmetries. This fact renews our interest in random generation of SAT instances. More precisely, we focus our research on the two following questions : is it possible to use conditions based on symmetry in random generation in order to generate even harder instances ? we have observed that the instances generated by the xed clause-length model contains about 50% of horn clauses. What happens if we tend the probability of negating the variables from 0.5 to 1 ? What lies between polynomial and NP-Complete instances ?