Multi-valued symbolic model-checking

Abstract

This article introduces the concept of multi-valued model-checking and describes a multi-valued symbolic model-checker, χ Chek. Multi-valued model-checking is a generalization of classical modelchecking, useful for analyzing models that contain uncertainty (lack of essential information) or inconsistency (contradictory information, often occurring when information is gathered from multiple sources). Multi-valued logics support the explicit modeling of uncertainty and disagreement by providing additional truth values in the logic.This article provides a theoretical basis for multi-valued model-checking and discusses some of its applications. A companion article [Chechik et al. 2002b] describes implementation issues in detail. The model-checker works for any member of a large class of multi-valued logics. Our modeling language is based on a generalization of Kripke structures, where both atomic propositions and transitions between states may take any of the truth values of a given multi-valued logic. Properties are expressed in χ CTL, our multi-valued extension of the temporal logic CTL.We define the class of logics, present the theory of multi-valued sets and multi-valued relations used in our model-checking algorithm, and define the multi-valued extensions of CTL and Kripke structures. We explore the relationship between χ CTL and CTL, and provide a symbolic modelchecking algorithm for χ CTL. We also address the use of fairness in multi-valued model-checking. Finally, we discuss some applications of the multi-valued model-checking approach.

Finding Environment Guarantees

“…The multi-valued model-checking algorithm that reasons over 4-valued Kripke structures has been implemented in the tool χ Chek [5]. We can use χ Chek to check models of the environment directly or reduce the multi-valued model-checking problem to two classical ones, via a reduction described in [12], and then use a classical model-checker such as NuSMV [6].…”

“…Given the environment rules, (1) construct the associated 4-valued Kripke structure (using Definition 6); (2) use the multi-valued model-checking algorithm to check the property on this structure; (3) if the algorithm answers t or f, the property is guaranteed by the environment. An interpretation of CTL formulas over multi-valued Kripke structures and a corresponding model-checking algorithm have been defined [5], and apply to our 4-valued Kripke structures without modification. We illustrate how the property "there is a next state where the light is on", written as EX Light, is modelchecked in state u 5 of the structure in Fig.…”

Mixed Transition Systems Revisited

“…The first is Kripke Modal Transition Systems (KMTSs) [14] and their equivalent variants, Modal TSs [16], Partial Kripke Structures (PKSs) [2], and 3-valued KSs [3]. It requires that every must transition is also a may transition.…”

“…It requires that every must transition is also a may transition. KMTSs were first introduced as computational models for partial specifications of reactive systems [16], and later adapted for model-checking [2,3,14]. The second family is Mixed Transition Systems (MixTSs) [5], or, equivalently, Belnap TSs [12].…”

“…It extends MixTSs by allowing must hyper-transitions, i.e., transitions into sets of states. Both MixTSs and KMTSs have been used in practical symbolic model-checkers (e.g., [3,11,13]), while the direct use of GKMTSs has been hampered by the difficulty of compactly encoding hyper-transitions into BDDs.…”