FASTer Acceleration of Counter Automata in Practice

Abstract

We compute reachability sets of counter automata. Even if the reachability set is not necessarily recursive, we use symbolic representation and acceleration to increase convergence. For functions defined by translations over a polyhedral domain, we give a new acceleration algorithm which is polynomial in the size of the function and exponential in its dimension, while the more generic algorithm is exponential in both the size of the function and its dimension. This algorithm has been implemented in the tool Fast. We apply it to a complex industrial protocol, the TTP membership algorithm. This protocol has been widely studied. For the first time, the protocol is automatically proved to be correct for 1 fault and N stations, and using abstraction we prove the correctness for 2 faults and N stations also.

Towards a Model-Checker for Counter Systems

“…The tool FAST [BFL04] generates flattenings via an exhaustive search algorithm. However, verification of FOCTL (Pr) properties of C by using a flattening C can only be done for those FOCTL (Pr) properties that are preserved under such flattenings.…”

“…Transition systems defined by Presburger relations provide a large natural class of infinite-state transition systems [BFLS05], suitable for modeling in various applications such as TTP Protocol (embedded system) [BFL04] and broadcast protocols [EFM99], to quote a few examples. Important cases of such transition systems with computable reachability have been established in [Iba78,FO97,CJ98,FL02].…”

“…Important cases of such transition systems with computable reachability have been established in [Iba78,FO97,CJ98,FL02]. The method of acceleration for computing reachability has been developed in [Boi98,FL02] and completely implemented in the verification tool FAST [BFL04]. Motivation For practical (computer-aided) model-checking, an infinite-state system must be provided with an effective finitary presentation, and in particular, must admit a symbolic representation of sets of states and transitions.…”

“…5. We design a complete semi-algorithm to check whether a given Presburger counter system satisfies a Presburger-LTL formula extending the underlying reachability semi-algorithm used in the tool FAST [BFL04].…”

Towards Model-Checking Programs with Lists

“…Among the different models, counter systems enjoy a central position for both theoretical results and maturity of tools like FAST [3], ASPIC [19], LASH [20] and TREX [1]. Moreover, counter systems, defined by Presburger relations, allow to model and to verify quantitative properties over various applications such as the TTP protocol [2] and broadcast protocols [16]. Different acceleration methods for computing the reachability relation of such counter systems have been developed .…”