We introduce a new criterion to discern the relative expressiveness of process calculi. Intuitively, a calculus is replacement free if replacing a sub-process that cannot perform any visible action by an arbitrary one never affects the capability of the resulting process to perform a visible action. By relying on two slightly different formulations of our criterion we partition the set of process calculi into three classes. Then, we prove that no suitable encodings between any two of such classes exist; hence calculi belonging to different classes have different relative expressiveness. Finally, we classify many well-known variants of the mainstream calculi CCS and the π-calculus, thus demonstrating their expressiveness gaps.

我们引入了一个新的判据来辨别过程计算的相对表达。凭直觉，演算是无替换的，如果用任意一个替换不能执行任何可见动作的子流程从不影响所得流程执行可见动作的能力。依靠我们准则的两种略有不同的公式，我们将过程计算集划分为三类。然后，我们证明在此类中的任何两个类之间不存在合适的编码。因此，属于不同类别的结石具有相对的表现力。最后，我们对主流结石CCS和π演算的许多著名变体进行分类，从而证明了它们在表达能力上的差距。