Axiomatization without Prefix Combinator

The chi calculus proposed several years ago enjoys some properties unknown from the experience with pi calculus, one of which is the ability to model concurrent computation without the use of prefix combinator. The atomic chi calculus studied in this paper is obtained from polyadic chi calculus by leaving out the prefix operator. This omission is impossible in the pi framework because it would render the input actions of pi useless. This paper focuses on complete systems of strong equivalence relations on finite atomic chi processes. The two equivalence relations investigated in this paper are strong bisimilarity and strong asynchronous bisimilarity. These bisimilarities are required to be closed under substitution on each bisimulation step. By exploring some properties enjoyed by the atomic chi calculus, it is shown that they coincide respectively with their ground counterparts. In the definitions of strong ground bisimilarity and strong asynchronous ground bisimilarity closure under substitution is not explicitly required. Based upon this fact complete systems are given for both relations. The axiomatic systems are novel in that they use none of the prefix, choice and match combinators.