Understanding the mismatch combinator in chi calculus

AbstractThe theory of chi processes with the mismatch operator is studied. Four congruence relations are investigated. These are late open congruence, early open congruence, ground congruence and barbed congruence. The late and early open congruence relations are the chi calculus counterparts of the weak late and early congruence relations of pi calculus. Both turn out to be special cases of the ground congruence and the barbed congruence. The ground congruence is essentially the open congruence. Complete systems are given for all the four congruence relations. These systems use some interesting tau laws unknown from previous studies of the chi calculus without the mismatch combinator. The results of this paper point out that the mismatch operator changes the algebraic semantics of chi calculus dramatically. They also correct some common mistakes in literature