Multi-valued Model Checking Games

Abstract

This work extends the game-based framework of µ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. We define a new game for this problem and derive from it a direct model checking algorithm that handles the multi-valued structure without any reduction. We investigate the properties of the new game, both independently, and in comparison to the automata-based approach. We show that the usual resemblance between the two approaches does not hold in the multivalued setting and show how it can be regained by changing the nature of the game.

Modeling and Model Checking Software Product Lines

“…Multi-valued modal µ-calculus combines Kozen's modal µ-calculus [Koz83] and multi-valued µ-calculus as defined by Grumberg and Shoham [SG05] in a way suitable for specifying and checking properties of PL-CCS programs. More specifically, we extend the work of [SG05], which only supports unlabeled diamond and box operators, by providing also action-labeled versions of these operators, which is essential to formulate properties of PL-CCS programs.…”

“…More specifically, we extend the work of [SG05], which only supports unlabeled diamond and box operators, by providing also action-labeled versions of these operators, which is essential to formulate properties of PL-CCS programs.…”

“…We introduce the multi-valued modal µ-calculus as combination of Kozen's modal µ-calculus [Koz83] and multi-valued µ-calculus as defined by Grumberg and Shoham [SG05], yielding a property specification language suitable for specifying and checking properties of PL-CCS programs. More specifically, the result of model checking a property for a PL-CCS program is the set of configurations satisfying the property at hand and not only the answer if the property holds or not.…”

Don’t Know for Multi-valued Systems

“…In the following we introduce a multi-valued modal version of the μ-calculus along the lines of [7]. Let V be a set of propositional variables.…”

“…Then, the semantics of a formula with respect to a mv-KS is one element of the lattice, denoting either the extent to which the formula holds, the trust value of some person performing actions, or the set of all products satisfying the formula. Model Checking multi-valued versions of the classical logics LTL, CTL, CTL * , and the μ-calculus has the been extensively studied already, for example in [6,4,5,7].…”