Completeness of bounded model checking temporal logic of knowledge

In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system＇s reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed.

Bounded Model Checking of CTL＊

Bounded Model Checking has been recently introduced as an efficient verification method for reactive systems. This technique reduces model checking of linear temporal logic to propositional satisfiability. In this paper we first present how quantified Boolean decision procedures can replace BDDs. We introduce a bounded model checking procedure for temporal logic CTL＊ which reduces model checking to the satisfiability of quantified Boolean formulas. Our new technique avoids the space blow up of BDDs, and extends the concept of bounded model checking.

Improved Bounded Model Checking for the Universal Fragment of CTL

SAT-based bounded model checking （BMC） has been introduced as a complementary technique to BDD-based symbolic model checking in recent years, and a lot of successful work has been done in this direction. The approach was first introduced by A. Biere et al. in checking linear temporal logic （LTL） formulae and then also adapted to check formulae of the universal fragment of computation tree logic （ACTL） by W. Penczek et al. As the efficiency of model checking is still an important issue, we present an improved BMC approach for ACTL based on Penczek＇s method. We consider two aspects of the approach. One is reduction of the number of variables and transitions in the κ-model by distinguishing the temporal operator EX from the others. The other is simplification of the transformation of formulae by using uniform path encoding instead of a disjunction of all paths needed in the κ-model. With these improvements, for an ACTL formula, the length of the final encoding of the formula in the worst case is reduced. The improved approach is implemented in the tool BMV and is compared with the original one by applying both to two well known examples, mutual exclusion and dining philosophers. The comparison shoves the advantages of the improved approach with respect to the efficiency of model checking.