Study Of Computational Theory On Complete Interactive Model

It has been about 30 years from the start of Process Calculi. During the time, hun-dreds of models and equivalences have been proposed and research have delved intoplenty of branches. Nevertheless, much less research have been done in computationaltheory on complete interactive models. In this branch, the first problem faced is to de-fine suitable complete models. Absolute equality is an important concept in completemodels and whether it coincides with traditional external equality is also an interestingand important problem. The answer of this problem could increase the understandingof bisimulation, and more importantly, it assists in proving the completeness. Thereare some results about coincidence issue. It is relatively easy to prove the coincidenceif the summation operator is in the language, otherwise it is harder. In fact it is an openproblem whether the two equality coincide in some languages without summation.Summation operator has powerful observational capability and absolute equalityis defined from the observational point of view, so we can use it to force interactantsto do some specific action sequences. Without summation operator the model will besimple. The simpler the model is, the less observational capability it has, and the moredifficult the proof of coincidence. But when the model is simple enough, in particularwhen it is finite, we can resort to the finite properties of interactants to enforce theproof tools. In a finite model without summation operator, after an interactant do anexternal action the other interactive capabilities are all reserved. With this property weproved the coincidence results in Finite CCS andπCalculus without Summation.