Parametric Verification of Weighted Systems

This paper addresses the problem of parametric model checking for weighted transition systems. We consider transition systems labelled with linear equations over a set of parameters and we use them to provide semantics for a parametric version of weighted CTL where the until and next operators are themselves indexed with linear equations. The parameters change the model-checking problem into a problem of computing a linear system of inequalities that characterizes the parameters that guarantee the satisfiability. To address this problem, we use parametric dependency graphs (PDGs) and we propose a global update function that yields an assignment to each node in a PDG. For an iterative application of the function, we prove that a fixed point assignment to PDG nodes exists and the set of assignments constitutes a well-quasi ordering, thus ensuring that the fixed point assignment can be found after finitely many iterations. To demonstrate the utility of our technique, we have implemented a prototype tool that computes the constraints on parameters for model checking problems

Local Model Checking Algorithm Based on Mu-calculus with Partial Orders

The propositionalμ-calculus can be divided into two categories, global model checking algorithm and local model checking algorithm. Both of them aim at reducing time complexity and space complexity effectively. This paper analyzes the computing process of alternating fixpoint nested in detail and designs an efficient local model checking algorithm based on the propositional μ-calculus by a group of partial ordered relation, and its time complexity is O(d2(dn)d/2+2) (d is the depth of fixpoint nesting,  is the maximum of number of nodes), space complexity is O(d(dn)d/2). As far as we know, up till now, the best local model checking algorithm whose index of time complexity is d. In this paper, the index for time complexity of this algorithm is reduced from d to d/2. It is more efficient than algorithms of previous research