Bounded model checking of Time Petri Nets using SAT solver

Abstract

To carry out performance evaluation of an asynchronous system, the system is modeled as Time Petri Net (TPN) and an iteration of Petri net simulations produces its performance index. The TPN model needs to satisfy required properties such as deadlock freeness. We proposed a symbolic representation of TPN for SAT-based bounded model checking. In the proposed encoding scheme, firing of transitions and elapsing of place delays are expressed as boolean formulas discretely. Our representation can work with relaxed ∃-step semantics which enables to perform each step by two or more transitions. We applied the encoding to example TPN models and checked the deadlock freeness using SAT solver. The results of experiments demonstrated the effectiveness of the proposed representation.

Symbolic Representation of Time Petri Nets for Efficient Bounded Model Checking

“…We prepare differentsized TPN examples to evaluate the scalability of the encoding. We also demonstrate that the formula size reduction [10] has a greater effect on the proposed encoding.…”

“…For evaluation, the proposed encoding was compared with the existing encoding based on Linear Arithmetic (LA) shown in [10]. This experiment was performed on the computer with Ubuntu 16.04 LTS OS, Intel Core i7 7700 3.6 GHz CPU, and 64 GB Memory.…”

“…To express time constraints in DL, we introduce the additional variable c which represents the global time for each state and the additional constraints over the value of c. Thus the formula to be solved increases in the number of variables. In [10], we provided the method for reducing formula size by replacing unchanged variables. Since the value of z i will be unchanged until the place p i gets a new token in the proposed encoding, there are many terms formed as (z i = z i ) which can be removed by replacing z i with z i .…”

“…In [10], we proposed a verification method for TPN based on bounded model checking that extended an SATbased bounded model checking method for Petri Nets [11] and showed the advantage of our method over existing model checker. The method expressed time constraints in linear arithmetic (LA) and enabled to use an SMT (Satisfiability Modulo Theories) solver for verification.…”