A Constraint Oriented Proof Methodology based on Modal Transition Systems

In this paper, we present a constraint-oriented state-based proof methodology for concurrent software systems which exploits compositionality and abstraction for the reduction of the verification problem under investigation. Formal basis for this methodology are Modal Transition Systems allowing loose state-based specifications, which can be refined by successively adding constraints. Key concepts of our method are projective views, separation of proof obligations, Skolemization and abstraction. The method is even applicable to real time system

Automata games for multiple-model checking

3-valued models have been advocated as a means of system abstraction such that verifications and refutations of temporal-logic properties transfer from abstract models to the systems they represent. Some application domains, however, require multiple models of a concrete or virtual system. We build the mathematical foundations for 3-valued property verification and refutation applied to sets of common concretizations of finitely many models. We show that validity checking for the modal mu-calculus has the same cost (EXPTIME-complete) on such sets as on all 2-valued models, provide an efficient algorithm for checking whether common concretizations exist for a fixed number of models, and propose using parity games on variants of tree automata to efficiently approximate validity checks of multiple models. We prove that the universal topological model in [M. Huth, R. Jagadeesan, and D. A. Schmidt. A domain equation for refinement of partial systems. Mathematical Structures in Computer Science, 14(4):469-505, 5 August 2004] is not bounded complete. This confirms that the approximations aforementioned are reasonably precise only for tree-automata-like models, unless all models are assumed to be deterministic. © 2006 Elsevier B.V. All rights reserved

Modal Interface Automata

De Alfaro and Henzinger's Interface Automata (IA) and Nyman et al.'s recent combination IOMTS of IA and Larsen's Modal Transition Systems (MTS) are established frameworks for specifying interfaces of system components. However, neither IA nor IOMTS consider conjunction that is needed in practice when a component shall satisfy multiple interfaces, while Larsen's MTS-conjunction is not closed and Bene\v{s} et al.'s conjunction on disjunctive MTS does not treat internal transitions. In addition, IOMTS-parallel composition exhibits a compositionality defect. This article defines conjunction (and also disjunction) on IA and disjunctive MTS and proves the operators to be 'correct', i.e., the greatest lower bounds (least upper bounds) wrt. IA- and resp. MTS-refinement. As its main contribution, a novel interface theory called Modal Interface Automata (MIA) is introduced: MIA is a rich subset of IOMTS featuring explicit output-must-transitions while input-transitions are always allowed implicitly, is equipped with compositional parallel, conjunction and disjunction operators, and allows a simpler embedding of IA than Nyman's. Thus, it fixes the shortcomings of related work, without restricting designers to deterministic interfaces as Raclet et al.'s modal interface theory does.Comment: 28 page