Axiomatizing Flat Iteration

Flat iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be a sum of atomic actions. It generalizes prefix iteration, in which the first argument is a single action. Complete finite equational axiomatizations are given for five notions of bisimulation congruence over basic CCS with flat iteration, viz. strong congruence, branching congruence, eta-congruence, delay congruence and weak congruence. Such axiomatizations were already known for prefix iteration and are known not to exist for general iteration. The use of flat iteration has two main advantages over prefix iteration: 1.The current axiomatizations generalize to full CCS, whereas the prefix iteration approach does not allow an elimination theorem for an asynchronous parallel composition operator. 2.The greater expressiveness of flat iteration allows for much shorter completeness proofs. In the setting of prefix iteration, the most convenient way to obtain the completeness theorems for eta-, delay, and weak congruence was by reduction to the completeness theorem for branching congruence. In the case of weak congruence this turned out to be much simpler than the only direct proof found. In the setting of flat iteration on the other hand, the completeness theorems for delay and weak (but not eta-) congruence can equally well be obtained by reduction to the one for strong congruence, without using branching congruence as an intermediate step. Moreover, the completeness results for prefix iteration can be retrieved from those for flat iteration, thus obtaining a second indirect approach for proving completeness for delay and weak congruence in the setting of prefix iteration.Comment: 15 pages. LaTeX 2.09. Filename: flat.tex.gz. On A4 paper print with: dvips -t a4 -O -2.15cm,-2.22cm -x 1225 flat. For US letter with: dvips -t letter -O -0.73in,-1.27in -x 1225 flat. More info at http://theory.stanford.edu/~rvg/abstracts.html#3

Axiomatizing Prefix Iteration with Silent Steps

Prefix iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz. branching congruence, eta-congruence, delay congruence and weak congruence. The completeness proofs for eta-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e. terms that may contain process variables. As a by-product, the omega-completeness of the axiomatizations is obtained as well as their completeness for closed terms. AMS Subject Classification (1991): 68Q10, 68Q40, 68Q55.CR Subject Classification (1991): D.3.1, F.1.2, F.3.2.Keywords and Phrases: Concurrency, process algebra, basic CCS, prefix iteration, branching bisimulation, eta-bisimulation, delay bisimulation, weak bisimulation, equational logic, complete axiomatizations

An Equational Axiomatization for Multi-Exit Iteration

This paper presents an equational axiomatization of bisimulation equivalence over the language of Basic Process Algebra (BPA) with multi-exit iteration. Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutionsof systems of recursion equations of the formX1 = P1 X2 + Q1...Xn = Pn X1 + Qnwhere n is a positive integer, and the Pi and the Qi are process terms. The additionof multi-exit iteration to BPA yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star (BPA). As aconsequence, the proof of completeness of the proposed equational axiomatizationfor this language, although standard in its general structure, is much more involvedthan that for BPA. An expressiveness hierarchy for the family of k-exit iteration operators proposed by Bergstra, Bethke and Ponse is also offered.

Towards a concurrency theory for supervisory control

In this paper we propose a process-theoretic concurrency model to express supervisory control properties. In light of the present importance of reliable control software, the current work ow of direct conversion from informal specication documents to control software implementations can be improved. A separate modeling step in terms of controllable and uncontrollable behavior of the device under control is desired. We consider the control loop as a feedback model for supervisory control, in terms of the three distinct components of plant, requirements and supervisor. With respect to the control ow, we consider event-based models as well as state-based ones. We study the process theory TCP as a convenient modeling formalism that includes parallelism, iteration, communication features and non-determinism. Via structural operational semantics, we relate the terms in TCP to labeled transition systems. We consider the partial bisimulation preorder to express controllability that is better suited to handle non-determinism, compared to bisimulation-based models. It is shown how precongruence of partial bisimulation can be derived from the format of the deduction rules. The theory of TCP is studied under nite axiomatization for which soundness and ground-completeness (modulo iteration) is proved with respect to partial bisimulation. Language-based controllability, as the neccesary condition for event-based supervisory control is expressed in terms of partial bisimulation and we discuss several drawbacks of the strict event-based approach. Statebased control is considered under partial bisimulation as a dependable solution to address non-determinism. An appropriate renaming operator is introduced to address an issue in parallel communication. A case for automated guided vehicles (AGV) is modeled using the theory TCP. The latter theory is henceforth extended to include state-based valuations for which partial bisimulation and an axiomatization are dened. We consider an extended case on industrial printers to show the modeling abilities of this extended theory. In our concluding remarks, we sketch a future research path in terms of a new formal language for concurrent control modeling

On bisimulations for the asynchronous π-calculus

AbstractThe asynchronous π-calculus is a variant of the π-calculus where message emission is non-blocking. Honda and Tokoro have studied a semantics for this calculus based on bisimulation. Their bisimulation relies on a modified transition system where, at any moment, a process can perform any input action.In this paper we propose a new notion of bisimulation for the asynchronous π-calculus, defined on top of the standard labelled transition system. We give several characterizations of this equivalence including one in terms of Honda and Tokoro's bisimulation, and one in terms of barbed equivalence. We show that this bisimulation is preserved by name substitutions, hence by input prefix. Finally, we give a complete axiomatization of the (strong) bisimulation for finite terms