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...

We consider the procedures for automatic derivation of axiom systems and term rewrite systems for process language in the GSOS format. We show that, for a decidable subclass of GSOS process languages, namely syntactically well-founded and linear GSOS process languages, the generated term rewrite systems are strongly normalising, confluent, and sound and complete for bisimulation modulo the associativity and commutativity of the choice operator on closed terms.