) Frits W. Vaandrager MIT Laboratory for Computer Science Cambridge, MA 02139, USA frits@theory.lcs.mit.edu Abstract The relation between process algebra and I/O automata models is investigated in a general setting of structured operational semantics (SOS). For a series of (approximations of) key properties of I/O automata, syntactic constraints on inference rules are proposed which guarantee these properties. A first result is that, in a setting without assumptions about actions, the well-known trace and failure preorders are substitutive for any set of rules in a format due to De Simone. Next additional constraints are imposed which capture the notion of internal actions and guarantee substitutivity of the testing preorders of De Nicola and Hennessy, and also of a preorder related to the failure semantics with fair abstraction of unstable divergence of Bergstra, Klop and Olderog. Subsequent constraints guarantee that input actions are always enabled and output actions cannot be bl...

The aim of this paper is to nd the nest `observable ' and `implementable' equivalence on concurrent processes. This is a part of a larger programme to develop a theory of observable processes where semantics of processes are based on locally and nitely observable process behaviour, and all process constructs are allowed, provided their operational meaning is de ned by realistically implementable transition rules.

The expressive power of process algebras is investigated in a general setting of structural operational semantics. The notion of an effective operational semantics is introduced and it is observed that no effective operational semantics for an enumerable language can specify all effective process graphs up to trace equivalence. A natural class of Plotkin style SOS specifications is identified, containing the guarded versions of calculi like CCS, SCCS, Meije and ACP, and it is proved that any specification in this class induces an effective operational semantics. Using techniques introduced by Bloom, it is shown that for the guarded versions of CCS-like calculi, there is a double exponential bound on the speed with which the number of outgoing transitions in a state can grow. As a corollary of this result it follows that two expressiveness results of De Simone for Meije and SCCS depend in a fundamental way on the use of unguarded recursion. A final result of this paper is that all operators definable via a finite number of rules in a format due to De Simone, are derived operators in the simple process calculus PC. 1991 Mathematics Subject Classification: 68Q05, 68Q10, 68Q55, 68Q75, 03D20. 1991 CR Categories: D.3.1, D.3.3, F.1.1, F.1.2, F.3.2, F.4.1. Keywords & Phrases: process algebra, PC, labeled transition systems, process graphs, effective process graphs, effective operational semantics, structural operational semantics, expressiveness, bisimulation equivalence, trace equivalence, action transducers. Notes: Most of this work was carried out while the author was at the MIT Laboratory for Computer Science, supported by ONR contract N00014-85-K-0168. Part of this work took place in the context of the ESPRIT Basic Research Action 7166, CONCUR2. This p...

We present a general and uniform method for defining structural operational semantics (SOS) of process algebra operators by traditional Plotkin-style rules equipped with an ordering, the new feature which states the order of application of rules when deriving transitions of process terms. Our method allows to represent negative premises and copying in the presence of silent actions. We identify a number of general formats of unordered and ordered rules with silent actions and show that divergence sensitive branching and weak bisimulation relations are preserved by all operators in the relevant formats. A comparison with the existing formats for branching and weak bisimulations shows that our formats are more general.

We prove that testing preorder of De Nicola and Hennessy is preserved by all operators of De Simone process languages. Building upon this result we propose an algorithm for generating axiomatisations of testing preorder for arbitrary De Simone process languages. The axiom systems produced by our algorithm are finite and complete for processes with nite behaviour. In order to achieve completeness for a subclass of processes with infiite behaviour we use one infinitary induction rule. The usefulness of our results is illustrated in specification and verification of small concurrent systems, where suspension, resumption and alternation of execution of component systems occur. We argue that better speci cations can be written in customised De Simone process languages, which contain both the standard operators as well as new De Simone operators that are specifically tailored for the task in hand. Moreover, the automatically generated axiom systems for such specification languages make the verification more straightforward.

. Aceto, Bloom and Vaandrager proposed in [ABV92] a procedure for generating a complete axiomatisation of strong bisimulation for process languages in the GSOS format. However, the choice operator +, which the procedure uses, as well as other auxiliary GSOS operators, which it introduces to obtain a finite axiomatisation, do not preserve many of weak equivalences. We propose a modification of this procedure, which works for a subclass of process languages in the De Simone format with a special treatment of silent actions. A choice of such a subclass of process languages guarantees that all the considered and auxiliary operators preserve many of weak equivalences. Our procedure generates a complete axiomatisation of refusal simulation preorder and it can be easily adapted to coarser preorders. The completeness result depends on the completeness result for the basic process language, which we prove. This language does not use prefixing with ø and the choice operator +. Instead, we employ...

this paper we will only consider those formats of rules which treat silent actions as invisible; for example the formats in [8, 10, 11, 9, 12]. A number of important results were established for these formats. Firstly, certain weak equivalences were shown to be preserved by all process operators in these formats [10, 9, 12]. Secondly, (completed) trace congruences with respect to these formats were discovered [10, 11]. Thirdly, algorithms for generating complete axiomatisations of some weak equivalences were developed [13, 14, 15]. The main conceptual contribution of the paper is a new method for defining process operators, including the sequential composition and priority operators, by transition rules with no negative antecedents. Our method is based on a simple idea of ordering the transition rules for each operator. The behaviour of a process can then be determined by examining the rules of its main operator, starting with the rules highest in the ordering and then considering the rules lower in the ordering. As a result, a rule lower in the ordering can only be applied if none of the rules above it can. Intuitively, this has the effect of applying a rule with negative antecedents. A simple example is given to illustrate our method. Consider a priority operator `, which gives a a priority over b, defined by the following rules.

We present a general and uniform method for defining structural operational semantics (SOS) of process operators by traditional Plotkin-style transition rules equipped with orderings. This new feature allows one to control the order of application of rules when deriving transitions of process terms. Our method is powerful enough to deal with rules with negative premises and copying. We show that rules with orderings, called ordered SOS rules, have the same expressive power as GSOS rules. We identify several classes of process languages with operators defined by rules with and without orderings in the setting with silent actions and divergence. We prove that branching bisimulation and eager bisimulation relations are preserved by all operators in process languages in the relevant classes.

We propose a format of transition rules (stable format) for processes which extends De Simone's in that it admits process operators which recognise stability, that is, the inability to perform autonomous actions. The format uses negative premises, but differently from previously proposed formats. We show that refusal testing is the trace congruence generated by the format. We identify a subformat (timed format) which serves as a format for discretetimed process algebra in the style of Hennessy and Regan's TPL. 1. Introduction It is well-known how to use syntax-directed rules to associate labelled transition systems with terms in process algebra. This is often called structured operational semantics (SOS) [Plo81], and was pioneered by Milner for CCS [Mil80, Mil89]. The meaning of each operator on processes is given by transition rules. We can classify operators according to the form these may take. We say that an operator is in a certain format if its rules belong to that format. Forma...