Parameterized Verification with Automatically Computed Inductive Assertions?

Abstract

The paper presents a method, called the method of verification by invisible invariants, for the automatic verification of a large class of parameterized systems. The method is based on the automatic calculation of candidate inductive assertions and checking for their inductiveness, using symbolic model-checking techniques for both tasks. First, we show how to use model-checking techniques over finite (and small) instances of the parameterized system in order to derive candidates for invariant assertions. Next, we show that the premises of the standard deductive inv rule for proving invariance properties can be automatically resolved by finite-state (bdd-based) methods with no need for interactive theorem proving. Combining the automatic computation of invariants with the automatic resolution of the VCs (verification conditions) yields a (necessarily) incomplete but fully automatic sound method for verifying large classes of parameterized systems. The generated invariants can be transferred to the VC-validation phase without ever been examined by the user, which explains why we refer to them as "invisible". The efficacy of the method is demonstrated by automatic verification of diverse parameterized systems in a fully automatic and efficient manner.

Handling Parameterized Systems with Non-atomic Global Conditions

“…All existing automatic verification methods (e.g., [12,4,6,8,9,3,2]) are defined for parameterized systems where universal and existential conditions are evaluated atomically. Non-atomic versions of parameterized mutual exclusion protocols such as the Bakery algorithm and two-phase commit protocol have been studied with heuristics to discover invariants, ad-hoc abstractions, or semi-automated methods in [5,13,16,7]. In contrast to these methods, our verification procedure is fully automated and is based on a generic approximation scheme for quantified conditions.…”

Transformational Verification of Parameterized Protocols Using Array Formulas

“…We only want to mention the technique proposed in [3], which has also been applied for the veri cation of the parameterized Peterson's protocol. That technique can be applied for verifying in an automatic way safety properties of all systems that satisfy a so-called strati cation condition.…”

“…Indeed, when this condition holds for a given parameterized system, then the veri cation task can be reduced to the veri cation of a nite number of nite state systems that are instances of the given parameterized system for suitable values of the parameter. However, Peterson's protocol does not satisfy the strati cation condition and its treatment with the technique proposed in [3] requires a signi cant amount of ingenuity.…”

“…These protocols are said to be parameterized with respect to the number of processes. Several extensions of the model checking technique based upon abstraction and induction have been proposed in the literature for the veri cation of parameterized protocols (see, for instance, [3,18,27,29]). However, since the general problem of verifying temporal properties of parameterized protocols is undecidable [2], these extensions cannot be fully mechanical.…”

“…Indeed, since the parameter N is unbounded, the parameterized Peterson's protocol, as it stands, cannot be viewed as a nite state system. Now, one can reduce it to a nite state system, thereby enabling the application of model checking, by using the above mentioned techniques based on abstraction [3]. However, it is not easy to nd a powerful abstraction function which works for the many protocols and concurrent systems one encounters in practice.…”