Automatic Verification of Hybrid Systems with Large Discrete State Space

Abstract

Abstract.We address the problem of model checking hybrid systems which exhibit nontrivial discrete behavior and thus cannot be treated by considering the discrete states one by one, as most currently available verification tools do. Our procedure relies on a deep integration of several techniques and tools. An extension of AND-Inverter-Graphs (AIGs) with first-order constraints serves as a compact representation format for sets of configurations which are composed of continuous regions and discrete states. Boolean reasoning on the AIGs is complemented by firstorder reasoning in various forms and on various levels. These include implication checks for simple constraints, test vector generation for fast inequality checks of boolean combinations of constraints, and an exact subsumption check for representations of two configurations.These techniques are integrated within a model checker for universal CTL. Technically, it deals with discrete-time hybrid systems with linear differentials. The paper presents the approach, its prototype implementation, and first experimental data.

Computing Optimized Representations for Non-convex Polyhedra by Detection and Removal of Redundant Linear Constraints

“…Yices [13] is used for all SMT solver calls except the generation of the don't care set. This means that Yices performs all equivalence checks needed for LinAIG compaction ( [4,5], Sect. 2.1) and moreover, it is also used for the redundancy detection algorithm described in Sect.…”

“…Experimental results in Sect. 4 show that the method is indeed essential in order to enable sequences of quantifier eliminations.…”

“…As a underlying data structure for our method we use representations of formulas from P(B, C) by LinAIGs [4,5]. LinAIGs are And-Inverter-Graphs (AIGs) enriched by linear constraints.…”

“…1) we use a set of new (boolean) constraint variables Q as encodings for the linear constraints, where each occurring i ∈ L(C) is encoded by some q i ∈ Q. For keeping the representation as compact as possible we use a multitude of methods; e.g., inserting different nodes representing the same predicate is avoided using an SMT (SAT modulo theories) solver which combines DPLL with linear programming as a decision procedure [4,5].…”

“…Whereas approaches like [2,3] consider unions of convex polyhedra (i.e. unions of conjunctions of linear constraints) together with an explicit representation of discrete states, in [4,5] a data structure called LinAIGs was used as a single symbolic representation for sets of states of hybrid systems with large discrete state spaces (in the context of model checking by backward analysis). LinAIGs in turn represent an extension of non-convex polyhedra by additional boolean variables, i.e., they represent arbitrary boolean combinations of boolean variables and linear constraints.…”