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

On well-foundedness and expressiveness of promoted tyft : being promoted makes a difference

In this paper, we solve two open problems posed by Karen L. Bernstein regarding her promoted tyft format for structured operational semantics. We show that, unlike formats with closed terms as labels, such as the tyft format, the well-foundedness assumption cannot be dropped for the promoted tyft format while preserving the congruence result. We also show that the well-founded promoted tyft format is incomparable to the tyft format with closed terms as labels, i.e., there are transition relations that can be specified by the promoted tyft format but not by the tyft format, and vice versa

Tree rules in probabilistic transition system specifications with negative and quantitative premises

Probabilistic transition system specifications (PTSSs) in the ntmufnu/ntmuxnu format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that isimilarity is a congruence.Similar to the nondeterministic case of rule format tyft/tyxt, we show that the well-foundedness requirement is unnecessary in the probabilistic setting. To achieve this, we first define an extended version of the ntmufnu/ntmuxnu format in which quantitative premises and conclusions include nested convex combinations of distributions. This format also guarantees that bisimilarity is a congruence. Then, for a given (possibly non-well-founded) PTSS in the new format, we construct an equivalent well-founded transition system consisting of only rules of the simpler (well-founded) probabilistic ntree format. Furthermore, we develop a proof-theoretic notion for these PTSSs that coincides with the existing stratification-based meaning in case the PTSS is stratifiable. This continues the line of research lifting structural operational semantic results from the nondeterministic setting to systems with both probabilistic and nondeterministic behavior.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Hybrid transition systems

The theory of hybrid systems studies the combination of continuous and discrete behaviour. "V hell discrete software IS combined with mechanical and electrical components, or IS interacting with, for example, chemical processes, an embed-ded system aris(1s in which the interaction between the continuous behaviou