Jeroen Ketema

Towards Model Checking Executable UML Specifications in mCRL2

We describe a translation of a subset of executable UML (xUML) into the process algebraic specification language mCRL2. This subset includes class diagrams with class generalisations, and state machines with signal and change events. The choice of these xUML constructs is dictated by their use in the modelling of railway interlocking systems. The long-term goal is to verify safety properties of interlockings modelled in xUML using the mCRL2 and LTSmin toolsets. Initial verification of an interlocking toy example demonstrates that the safety properties of model instances depend crucially on the run-to-completion assumptions.

A distributed scheduling algorithm for real-time (D-SAR) industrial wireless sensor and actuator networks

Current wireless standards and protocols for industrial applications, such as WirelessHART and ISA100.11a, typically use centralized network management for communication scheduling and route establishment. However, due to their centralized nature, these protocols have difficulty coping with dynamic large-scale networks. To address this problem, we propose D-SAR, a distributed resource reservation algorithm that allows source nodes to meet the Quality-of-Service requirements for peer-to-peer communication. D-SAR uses concepts derived from circuit switching and Asynchronous Transfer Mode (ATM) networks and applies them to wireless sensor and actuator networks. Simulations show that latency in connection setup is 93% less in D-SAR compared to WirelessHART and that 89% fewer messages are sent during connection setup in case the distance from source to destination is 12 hops.

Automated verification of executable UML models

We present a fully automated approach to verifying safety properties of Executable UML models (xUML). Our tool chain consists of a model transformation program which translates xUML models to the process algebra mCRL2, followed by symbolic model checking using LTSmin. If a safety violation is found, an error trace is visualised as a UML sequence diagram. As a novel feature, our approach allows safety properties to be specified as UML state machines.

On confluence of infinitary combinatory reduction systems

We prove that fully-extended, orthogonal infinitary combinatory reduction systems with finite right-hand sides are confluent modulo identification of hypercollapsing subterms. This provides the first general confluence result for infinitary higher-order rewriting.

INFINITARY COMBINATORY REDUCTION SYSTEMS: CONFLUENCE

We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fully-extended, orthogonal iCRSs are confluent modulo identification of hypercollapsing subterms. As a corollary, we obtain that fully-extended, orthogonal iCRSs have the normal form property and the unique normal form property (with respect to reduction). We also show that, unlike the case in first-order infinitary rewriting, almost non-collapsing iCRSs are not necessarily confluent.

Infinitary Combinatory Reduction Systems

We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting. The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary @l-calculus are special cases. Furthermore, we generalise a number of known results from first-order infinitary rewriting and infinitary @l-calculus to iCRSs. In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all complete developments of U end in the same term and that (2) any tiling diagram involving strongly convergent reductions S and T can be completed iff at least one of S/T and T/S is strongly convergent. We also prove an ancillary result of independent interest: a set of redexes in an orthogonal iCRS has a complete development iff the set has the so-called finite jumps property.

Infinitary Combinatory Reduction Systems: Normalising Reduction Strategies

We study normalising reduction strategies for infinitary Combinatory Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and needed-fair strategies are normalising for orthogonal, fully-extended iCRSs. These facts properly generalise a number of results on normalising strategies in first-order infinitary rewriting and provide the first examples of normalising strategies for infinitary lambda-calculus.

On Normalisation of Infinitary Combinatory Reduction Systems

For fully-extended, orthogonal infinitary Combinatory Reduction Systems, we prove that terms with perpetual reductions starting from them do not have (head) normal forms. Using this, we show that 1 needed reduction strategies are normalising for fully-extended, orthogonal infinitary Combinatory Reduction Systems, and that n 1 weak and strong normalisation coincide for such systems as a whole and, in case reductions are non-erasing, also for terms.

Reinterpreting Compression in Infinitary Rewriting

Departing from a computational interpretation of compression in infinitary rewriting, we view compression as a degenerate case of standardisation. The change in perspective comes about via two observations: (a) no compression property can be recovered for non-left-linear systems and (b) some standardisation procedures, as a ‘side-effect’, yield compressed reductions.

Comparing Böhm-Like Trees

Extending the infinitary rewriting definition of Bohm-like trees to infinitary Combinatory Reduction Systems (iCRSs), we show that each Bohm-like tree defined by means of infinitary rewriting can also be defined by means of a direct approximant function. In addition, we show that counterexamples exists to the reverse implication.