## The Ground Congruence for Chi Calculus

### Yuxi Fu, Zhenrong Yang

To appear at Foundations of Software Technology and Theoretical Computer Science (FSTTCS2000), New Delhi, India, December 13-15 2000

## Abstract

The definition of open bisimilarity on $\chi$-processes does not give rise to a sensible relation on the $\chi$-processes with the mismatch operator. The paper proposes ground open bisimilarity as a principal open bisimilarity on the $\chi$-processes with the mismatch operator. This equivalence is equivalent to the relation derived from a simple bisimulation by closing under certain contexts. The algebraic properties of the ground open congruence is studied. The paper also takes a close look at barbed congruence. This relation is similar to the ground congruence. The precise relationship between the two is worked out. It is shown that the sound and complete system for the ground congruence can be obtained by removing one tau law from the complete system for the barbed congruence.

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