Systematic Construction of Abstractions for Model-Checking

Abstract

This paper describes a framework, based on Abstract Interpretation, for creating abstractions for model-checking. Specifically, we study how to abstract models of µ-calculus and systematically derive abstractions that are constructive, sound, and precise, and apply them to abstracting Kripke structures. The overall approach is based on the use of bilattices to represent partial and inconsistent information.

Mixed Transition Systems Revisited

“…We write U(e) and O(e) to denote U and O, respectively. We use operators ⊓ and ∼ defined as follows: ∼ U, O O, U , and [1,5,12,14,20]. Let M = M, L M be a model, M = S, R may , R must , V ar a set of fixpoint variables, and σ : V ar → 2 S ×2 S .…”

“…Every MixTS can be translated to an equivalent monotone one without affecting the concrete models it approximates [12]. Thus, Theorem 3 can also be used to check semantic consistency of non-monotone MixTSs.…”

“…Monotone models are as expressive as their regular counterparts [12]. The monotonicity condition simply ensures that all information that can be derived from the existing may and must transitions is made explicit in the model.…”

“…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 places no restrictions on the relationship between may and must transitions and thus extends KMTSs.…”

Why Waste a Perfectly Good Abstraction?

“…4-valued Kripke structures and their application to abstraction are equivalent to Mixed Transition Systems [8,18]. They can also be seen as an extension of Modal Transition Systems [11] that are defined using Kleene logic.…”