Assume-Guarantee Reasoning With Local Specifications

Abstract

Abstract. We investigate assume-guarantee reasoning for global specifications consisting of conjunctions of local specifications. We present a sound and complete assume-guarantee rule that permits reasoning about individual modules for local specifications and draws conclusions on global specifications. We illustrate our approach with an example from the field of network congestion control, where different agents are responsible for controlling packet flow across a shared infrastructure. In this context, we derive an assume-guarantee rule for system stability, and show that this rule is valuable to reason about any number of agents, any initial flow configuration, and any topology of bounded degree.

Practical verification of decision-making in agent-based autonomous systems

“…It would therefore be beneficial to move in the direction of [41] and represent the continuous parts of the system as an abstract automata, or a similar formulation, which allowed us to control the number of possible states. This would draw on work such as [64,73,80].…”

Compositional Model Checking of Concurrent Systems

“…4. 22 , t 23 , t 24 }; where t 21 = (w = 1 ∧ z = 1, w := 0); t 22 = (w = 0 ∧ z = 0, w := 1); t 23 = (x = 1 ∧ w = 1, x := 0); t 24 = (x = 0 ∧ w = 0, x := 1); 31 , t 32 , t 33 , t 34 }; where t 31 = (u = 1 ∧ x = 0 ∧ y = 0, u := 0); t 32 = (u = 0 ∧ x = 1 ∧ y = 1, u := 1); t 33 = (z = 1 ∧ u = 1, z := 0); t 34 = (z = 0 ∧ u = 0, z := 1); Fig. 2.…”

“…An automated interface refinement method is presented in [39] where the models of the system modules are refined, and the extra behavior is removed by extracting the interface interactions among these modules. Although the capability of compositional reasoning methods has been demonstrated by verifying large examples, and advances of these methods have demonstrated the ability to reason about a global property represented as a conjunctive form of local specifications in [31], it is difficult in general for them to handle inherently global properties such as deadlock freedom. To address issues with learning based methods, [16], [4] present alternative compositional reasoning methods based on computing local invariants.…”

“…While the focus of this manuscript is on explicit state model checking, there are no mentions to works based on symbolic, abstraction-refinement based model checking. Two missing references on explicit state model checking are given below (see [31] and [4]). …”

“…They are compositional reasoning method that verifies global properties in a limited form ( [31]), compositional reasoning methods that use interface constraints ( [24]), compositional reachability ( [17]), and applications of compositional reachability methods ( [9], [8], [23], [38]). This paper does make a comparison with traditional abstraction techniques in [12] in Section IV-B.…”