Don’t Know for Multi-valued Systems

Abstract

Abstract. This paper studies abstraction and refinement techniques in the setting of multi-valued model checking for the μ-calculus. Two dimensions of abstractions are identified and studied: Abstraction by joining states of the underlying multi-valued Kripke structure as well as abstraction of truth values, for each following both an optimistic and pessimistic account. It is shown that our notion of abstraction is conservative in the following sense: The truth value in a concrete system is "between" the optimistic and pessimistic assessment. Moreover, model checking of abstracted systems is shown to be again a multi-valued model checking problem, allowing to reuse multi-valued model checking engines. Finally, whenever the optimistic and pessimistic model checking result differ, the cause for such an assessment is identified, allowing the abstraction to be refined to eventually yield a result for which both the optimistic and pessimistic assessment coincide.

Variability Abstraction and Refinement for Game-Based Lifted Model Checking of Full CTL

“…One of the earliest attempts for using games for CTL model checking has been proposed by Stirling [25]. Shoham and Grumberg [23,24,18,3] have extended this game-based approach for CTL over 3-valued semantics. In this work, we exploit and apply the game-based approach in a completely new direction, for automatic CTL verification of variability models.…”

Refinement checking on parametric modal transition systems

“…While usually overapproximations (or underapproximations) of systems are constructed and thus only purely universal (or existential) properties can be checked, [31] shows that using MTS one can check mixed formulae (arbitrarily combining universal and existential properties) and, moreover, at the same cost as checking universal properties using traditional conservative abstractions. This advantage has been investigated also in the context of systems equivalent or closely related to MTS [24,26,27,32,34,47] but parameters have not been used in this context.…”