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.
SUMMARY
To evaluate the performance of a large‐scale digital system, the system can be modeled by stochastic timed Petri nets (STPN) and a performance index can be estimated based on the number of iterations in a Petri net simulation. When the performance evaluation is carried out in a large distributed environment, parallel calculation with incidence matrices for the STPN can make the Petri net simulation more efficient. In this paper, we propose an ordering method for the incidence matrices to reduce the communication costs in the parallel calculation of matrix operations. For this purpose, we first propose a method of blocking the incidence matrices based on the structure of the system by taking into consideration synchronous and asynchronous buses as structural elements. We also propose a method for converting submatrices of the incidence matrices into band matrices. This method is based on breadth‐first search in the STPN as represented by the submatrices. Finally, we demonstrate the benefits of ordering on the time required for a performance evaluation by carrying out a performance evaluation using the incidence matrices generated under the proposed method. In addition, we show that the ordering method can reduce the communication costs in a large distributed environment by estimating the utilization rate of calculation nodes.
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