S. All local authors can be reached viae-mail at theaddress last-name@cs.unibo.it. Written requests and comments should be addressed to tr-admin@cs.unibo.it. UBLCS Technical Report Series 93-20 An Information Flow Security Property for CCS, R. Focardi, R. Gorrieri, October 1993. 93-21 A Classification of Security Properties, R. Focardi, R. Gorrieri, October 1993. 93-22 Real Time Systems: A Tutorial, F. Panzieri, R. Davoli, October 1993. 93-23 A Scalable Architecture for Reliable Distributed Multimedia Applications, F. Panzieri, M. Roccetti, October 1993. 93-24 Wide-Area Distribution Issues in Hypertext Systems, C. Maioli, S. Sola, F. Vitali, October 1993. 93-25 On Relating Some Models for Concurrency, P. Degano, R. Gorrieri, S. Vigna, October 1993. 93-26 Axiomatising ST Bisimulation Equivalence, N. Busi, R. van Glabbeek, R. Gorrieri, December 1993. 93-27 A Theory of Processeswith Durational Actions, R. Gorrieri, M. Roccetti, E. Stancampiano, December1993. 94-1 Further Modifications t...

A Partial Combinatory Algebra is completable if it can be extended to a total one. Klop [11, 12] gave a sufficient condition for completability of a PCA M = (M,·,K,S) in the form of ten axioms (inequalities) on terms of M. We prove that Klop’s sufficient condition is equivalent to the existence of an injective s-m-n function over M (that in turns is equivalent to the Padding Lemma). This is proved by working with an alternative characterization of PCA’s, recently introduced by the authors (Effective Applicative Structures). As a corollary, we show that nine of Klop’s ten axioms are actually redundant (the so called Barendregt’s axiom is enough to guarantee completability). Moreover, we prove that any Uniformly Reflexive Structure [17, 18, 16] is completable. 1