Efficient Computation of Recurrence Diameters

Abstract

SAT based Bounded Model Checking (BMC) is an efficient method for detecting logical errors in finite-state transition systems. Given a transition system, an LTL property, and a user defined bound k, a bounded model checker generates a propositional formula that is satisfiable if and only if a counterexample to the property of length up to k exists. Standard SAT checkers can be used to check this formula.BMCis complete if k is larger than some pre-computed threshold. It is still unknown how to compute this threshold for general properties.We show that the longest initialized loop-free path in the state graph, also known as the recurrence diameter, is sufficient for Fp properties. The recurrence diameter is also a known over-approximation for the threshold of simple safety properties (Gp).We discuss various techniques to compute the recurrence diameter efficiently and provide experimental results that demonstrate the benefits of using the new approach.

This research was sponsored by the Semiconductor Research Corporation (SRC) under contract no. 99-TJ-684, the National Science Foundation (NSF) under grant no. CCR-9803774, the Office of Naval Research (ONR), and the Naval Research Laboratory (NRL) under contract no. N00014-01-1-0796. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of SRC, NSF, ONR, NRL, the U.S. government or any other entity.

In all previous publications on this matter, the term ‘diameter’ was used to denote what we refer to as the completeness threshold. Since the term diameter has a specific meaning in graph theory that coincides with the completeness threshold only for some properties (as we explain later), it is unsuitable for describing the general case.