The theory of chi processes with the mismatch operator is studied. Two open congruence relations are investigated. These are
weak early open congruence and weaklate open congruence. Complete systems are given for both congruence relations. These systems
use some new tau laws. The results of this paper correct some popular mistakes in literature.
The author is funded by NNSFC (69873032) and the 863 Hi-Tech Project (863-306-ZT06-02-2). He is also supported by BASICS,
Center of Basic Studies in Computing Science, sponsored by Shanghai Education Committee. BASICS is affiliated to the Department
of Computer Science at Shanghai Jiaotong University.