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

Duplication of constants in process algebra

The constant 0 (or !, nil ) has different roles in process algebra: on the one hand, it serves as the identity element of alternative composition, on the other hand, it stands for a blocked atomic action or for livelock. When extensions with timing are considered, these roles diverge. We argue that it is better to use two separate constants ¿0 and 0 for the different usages. With respect to the termination constant 1 (or ", skip), the situation is comparable: on the one hand, it serves as the identity element of sequential composition, on the other hand, it serves as the identity element of parallel composition, and stands for a skipped atomic action. We have separate constants ¿1 and 1 for the different usages

Syntax requirements of message sequence charts

A set of syntax requirements of MSC is discussed and formalized. The treatment is restricted to Basic MSCs without conditions. Syntax requirements of communication events in Basic MSCs are discussed and formalized. The formalization is syntax directed and based on functions and predicates

Action and predicate safety of hybrid processes

Abstract In this paper, we study two kinds of safety properties for hybrid processes, namely safety for actions and safety for predicates on model variables. We give an algebraic specification of these safety properties using the process algebra HyPA, and show how to reduce the question of safety of a linear process specification to the question of safety of its sub-processes. As an example, we study a variant of Fischer¿s protocol, in which there can be a relative error between the clocks that are used

Type checking mCRL2

In this paper we present a type system for the data language of mCRL2, a process algebra based language for formalising the behaviour of communicating system. Much of the type system is standard, and follows the line of, e.g., Pierce [Pie02]. The data language that is described is rich, and supports (infinite) sets and bags, universal and existential quantification, and lambda abstraction. Recursive types can be defined using equational definitions. Subtyping is included for the full data language, and a coercion is given to transform a well-typed expression into a strictly typed expression