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

Folk Theorems on the Correspondence between State-Based and Event-Based Systems

Kripke Structures and Labelled Transition Systems are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find many ad-hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in Kripke Structures and divergence-sensitive branching bisimulation in Labelled Transition Systems. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimisation techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences.Comment: Full version of SOFSEM 2011 pape

On the Executability of Interactive Computation

The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are reactively executable. In this article we provide a comparison of the two models. We show, on the one hand, that the behaviour exhibited by ITMs is reactively executable, and, on the other hand, that the stream translations naturally associated with RTMs are interactively computable. We conclude from these results that the theory of reactive executability subsumes the theory of interactive computability. Inspired by the existing model of ITMs with advice, which provides a model of evolving computation, we also consider RTMs with advice and we establish that a facility of advice considerably upgrades the behavioural expressiveness of RTMs: every countable transition system can be simulated by some RTM with advice up to a fine notion of behavioural equivalence.Comment: 15 pages, 0 figure

On the axiomatizability of impossible futures

A general method is established to derive a ground-complete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves omega-completeness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, ground- and omega-complete axiomatizations are derived for weak failures, completed trace and trace semantics. We then present a finite, sound, ground-complete axiomatization for the concrete impossible futures preorder, which implies a finite, sound, ground-complete axiomatization for the weak impossible futures preorder. In contrast, we prove that no finite, sound axiomatization for BCCS modulo concrete and weak impossible futures equivalence is ground-complete. If the alphabet of actions is infinite, then the aforementioned ground-complete axiomatizations are shown to be omega-complete. If the alphabet is finite, we prove that the inequational theories of BCCS modulo the concrete and weak impossible futures preorder lack such a finite basis

An Event Structure Model for Probabilistic Concurrent Kleene Algebra

We give a new true-concurrent model for probabilistic concurrent Kleene algebra. The model is based on probabilistic event structures, which combines ideas from Katoen's work on probabilistic concurrency and Varacca's probabilistic prime event structures. The event structures are compared with a true-concurrent version of Segala's probabilistic simulation. Finally, the algebraic properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules.Comment: Submitted and accepted for LPAR19 (2013

On infinite guarded recursive specifications in process algebra

In most presentations of ACP with guarded recursion, recursive specifications are finite or infinite sets of recursion equations of which the right-hand sides are guarded terms. The completeness with respect to bisimulation equivalence of the axioms of ACP with guarded recursion has only been proved for the special case where recursive specifications are finite sets of recursion equations of which the right-hand sides are guarded terms of a restricted form known as linear terms. In this note, we widen this completeness result to the general case.Comment: 9 pages, there is text overlap with earlier papers (arXiv:1703.06822, arXiv:1912.10041, arXiv:2003.00473

Tree morphisms and bisimulations

A category of (action labelled) trees is defined that can be used to model unfolding of labelled transition systems and to study behavioural relations over them. In this paper we study five different equivalences based on bisimulation for our model. One, that we called resource bisimulation, amounts essentially to three isomorphism. Another, its weak counterpart, permits abstracting from silent actions while preserving the tree structure. The other three are the well known strong, branching and weak bisimulation equivalence. For all bisimulations, but weak, canonical representatives are constructed and it is shown that they can be obtained via enriched functors over our categories of trees, with and without silent actions. Weak equivalence is more problematic; a canonical minimal representative for it cannot be denned by quotienting our trees. The common framework helps in understanding the relationships between the various equivalences and the results provide support to the claim that branching bisimulation is the natural generalization of strong bisimulation to systems with silent moves and that resource and weak resource have an interest of their own

Change Mining in Adaptive Process Management Systems

The wide-spread adoption of process-aware information systems has resulted in a bulk of computerized information about real-world processes. This data can be utilized for process performance analysis as well as for process improvement. In this context process mining offers promising perspectives. So far, existing mining techniques have been applied to operational processes, i.e., knowledge is extracted from execution logs (process discovery), or execution logs are compared with some a-priori process model (conformance checking). However, execution logs only constitute one kind of data gathered during process enactment. In particular, adaptive processes provide additional information about process changes (e.g., ad-hoc changes of single process instances) which can be used to enable organizational learning. In this paper we present an approach for mining change logs in adaptive process management systems. The change process discovered through process mining provides an aggregated overview of all changes that happened so far. This, in turn, can serve as basis for all kinds of process improvement actions, e.g., it may trigger process redesign or better control mechanisms

A Branching Time Model of CSP

I present a branching time model of CSP that is finer than all other models of CSP proposed thus far. It is obtained by taking a semantic equivalence from the linear time - branching time spectrum, namely divergence-preserving coupled similarity, and showing that it is a congruence for the operators of CSP. This equivalence belongs to the bisimulation family of semantic equivalences, in the sense that on transition systems without internal actions it coincides with strong bisimilarity. Nevertheless, enough of the equational laws of CSP remain to obtain a complete axiomatisation for closed, recursion-free terms.Comment: Dedicated to Bill Roscoe, on the occasion of his 60th birthda