Conditional transition systems with upgrades

Abstract

• We define two equivalent variants of transition systems having guards. • We define equivalent notions of bisimilarity for both variants and characterise them via a bisimulation game. • We show how to compute bisimilarity symbolically via BDDs. • We provide an extension of the formalism in presence of action precedence. We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we show that such transition systems can be modelled in two ways: as conditional transition systems (CTS) with a partial order on conditions, or as lattice transition systems (LaTS), where transitions are labelled with the elements from a distributive lattice. We define equivalent notions of bisimilarity for both variants and characterise them via a bisimulation game. We explain how conditional transition systems are related to featured transition systems for the modelling of software product lines. Furthermore, we show how to compute bisimilarity symbolically via BDDs by defining an operation on BDDs that approximates an element of a Boolean algebra into a lattice. We have implemented our procedure and provide runtime results. This is an extended version of the TASE 2017 paper [1] , including all proofs, additional examples, an extension of the formalism to account for deactivation of updates and detailed runtime results.