Applying CEGAR to the Petri Net State Equation

Abstract

Abstract. We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence, we replace the search through the set of reachable states by a search through the space of solutions of the state equation. We demonstrate the excellent performance of the technique on several real-world examples. The technique is particularly useful in those cases where the reachability query yields a negative result: While state space based techniques need to fully expand the state space in this case, our technique often terminates promptly. In addition, we can derive some diagnostic information in case of unreachability while state space methods can only provide witness paths in the case of reachability.

New Search Strategies for the Petri Net CEGAR Approach

“…The solution space of the state equation m + Cx = m is semi-linear. Each solution x can be written as the sum of a base solution and the linear combination of T-invariants [18], which can formally be written as x = b + i n i y i , where b ∈ N |T | is the base solution and n i ∈ N is the coefficient of the T-invariant y i ∈ N |T | .…”

“…In this section we introduce the CEGAR approach generally (Section 3.1) and we present an algorithm published by Wimmel and Wolf [18], which applies the CEGAR approach to the reachability problem of Petri nets (Section 3.2). After its publication, we examined the correctness and completeness of their algorithm [8].…”

“…Wimmel and Wolf published an algorithm [18], which applies the CEGAR approach to the reachability analysis of Petri nets, using the state equation. Figure 1 shows an overview of their algorithm, while each step is detailed in this section.…”

“…Wimmel and Wolf published an algorithm [18], which applies counterexample guided abstraction refinement to the reachability problem of Petri nets. Their algorithm proved its efficiency at the model checking contest in 2013 [10].…”

“…In Section 2 we introduce the theoretical background of our work. We present the algorithm of Wimmel and Wolf [18] and a brief overview of our previous findings [8] in Section 3. Then, we introduce our current results.…”