A process algebraic approach to hybrid systems

Many hybrid systems are safety critical systems, i.e. the incorrect functioning of the system can have severe consequences. Being able to model and analyse such systems prior to their implementation is viat. Usting thee process algebra µCRLt a case study on a conveyor belt system has been conducted (see[12]). The great complexity allowed for a thorough identification of gaps in the formalism for applications in the area of hybrid systems. The models in this paper are slightly simplified versions of the models in [12]

A process algebraic approach to hybrid systems

Many hybrid systems are safety critical systems, i.e. the incorrect functioning of the system can have severe consequences. Being able to model and analyse such systems prior to their implementation is viat. Usting thee process algebra µCRLt a case study on a conveyor belt system has been conducted (see[12]). The great complexity allowed for a thorough identification of gaps in the formalism for applications in the area of hybrid systems. The models in this paper are slightly simplified versions of the models in [12]

Verification of random behaviours

We introduce abstraction in a probabilistic process algebra. The process algebra can be employed for specifying processes that exhibit both probabilistic and non-deterministic choices in their behaviours. Several rules and axioms are identified, allowing us to rewrite processes to less complex processes by removing redundant internal activity. Using these rules, we have successfully conducted a verification of the Concurrent Alternating Bit Protocol. The verification shows that after abstraction of internal activity, the protocol behaves as a buffer

Bisimulation minimisations for Boolean equation systems

Boolean equation systems (BESs) have been used to encode several complex verification problems, including model checking and equivalence checking. We introduce the concepts of strong bisimulation and oblivious bisimulation for BESs, and we prove that these can be used for minimising BESs prior to solving these. Our results show that large reductions of the BESs may be obtained efficiently. Minimisation is rewarding for BESs with non-trivial alternations: the time required for solving the original BES exceeds the time required for quotienting plus the time for solving the quotient. Furthermore, we provide a verification example that demonstrates that bisimulation minimisation of a process prior to encoding the verification problem on that process as a BES can be arbitrarily less effective than minimising the BES that encodes the verification problem

Analysis of Boolean Equation Systems through Structure Graphs

We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyse a subclass of Boolean equation systems, viz., equation systems in standard recursive form. We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimisation of its structure graph

Decomposability in formal conformance testing

We study the problem of deriving a specification for a third-party component, based on the specification of the system and the environment in which the component is supposed to reside. Particularly, we are interested in using component specifications for conformance testing of black-box components, using the theory of input-output conformance (ioco) testing. We propose and prove sufficient criteria for decompositionality, i.e., that components conforming to the derived specification will always compose to produce a correct system with respect to the system specification. We also study the criteria for strong decomposability, by which we can ensure that only those components conforming to the derived specification can lead to a correct system

Message sequence charts in the software engineering process

The software development process benefits from the use of Message Sequence Charts (MSC), which is a graphical language for displyaing the interaction behaviour of a system. We describe canonical applications of MSC independent of any software development methodology. We illustrate the use of MSC with a case study: the Meeting Scheduler

Parity game reductions

Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain $10^9$ vertices or beyond. Equivalence relations can be used to reduce the size of a parity game, thereby potentially alleviating part of the computational burden. We reconsider (governed) bisimulation and (governed) stuttering bisimulation, and we give detailed proofs that these relations are equivalences, have unique quotients and they approximate the winning regions of parity games. Furthermore, we present game-based characterisations of these relations. Using these characterisations our equivalences are compared to relations for parity games that can be found in the literature, such as direct simulation equivalence and delayed simulation equivalence. To complete the overview we develop coinductive characterisations of direct- and delayed simulation equivalence and we establish a lattice of equivalences for parity games

Parity game reductions

Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain $10^9$ vertices or beyond. Equivalence relations can be used to reduce the size of a parity game, thereby potentially alleviating part of the computational burden. We reconsider (governed) bisimulation and (governed) stuttering bisimulation, and we give detailed proofs that these relations are equivalences, have unique quotients and they approximate the winning regions of parity games. Furthermore, we present game-based characterisations of these relations. Using these characterisations our equivalences are compared to relations for parity games that can be found in the literature, such as direct simulation equivalence and delayed simulation equivalence. To complete the overview we develop coinductive characterisations of direct- and delayed simulation equivalence and we establish a lattice of equivalences for parity games