Teaching Principles of Petri Nets in Hardware Courses and Students Projects

Introduction

Petri nets (PN) are a well established mechanism for system modeling. They are a mathematically defined formal model, and can be subjected to a large variety of systems. PN based models have been widely used due to their ease of understanding, declarative, logic based and modular modeling principles, and finally because they can be represented graphically. Since Petri nets began to be exploited in the 1960s, many different types of models have been introduced and used. The most popular models are presented in this paper, their main advantages are shown and the differences between them are mentioned. Everything is described according the teaching of formal methods used in digital systems design especially during the design of peripheral devices of computers, where some asynchronous and parallel actions without any coupling to internal clock frequency have to be designed and modeled.

This basic knowledge and method of the model construction is enlarged and exploited in student group projects. Petri net based models have been used e.g. in the design of a processor or a control system architecture with special properties, e.g. fault-tolerant or fault-secure, hardware-software co-design, computer networks architecture, etc. This has led to the development of PN models in some Petri net design tools and then the analysis and simulation of models using these tools. After this high-level design has been developed and validated it becomes possible, through automatic translation to a Hardware Description Language obviously used in digital hardware design (VHDL or Verilog design languages), to employ proper implementation in a programmable hardware (FPGA – field programmable gate array or CPLD – complex programmable logic device).

Our students have been teaching and making many experiments based on the massive using of FPGA or CPLD development kit. They have practical skills from the 3^rd semester of bachelor studies (Kubátová, 2005; Bečvář, 2006). It enables a custom device to be rapidly prototyped and tested (however the ASIC implementation is also possible). An FPGA version of a digital circuit is likely to be slower than the equivalent ASIC version, due to the regularly structured FPGA wiring channels compared to the ASIC custom logic. However, the easier custom design changes, the possibility of easy FPGA reconfiguration, and relatively easy manipulation make FPGAs very good final implementation bases for our experiments. This is most important due to strict time schedule of these student group projects – everything must be finished during one semester.

Most models used in the hardware design process are equivalent to the Finite State Machine (FSM), (Adamski, 2001; Erhard, 2001; Gomes, 2001; Uzam, 2001). It is said that the resulting hardware must be deterministic, but we have found real models that are not equivalent to an FSM. Therefore we have concentrated on those models with really concurrent actions, with various types of dependencies (mutual exclusion, parallel, scheduled), and have studied their hardware implementation.

Petri nets are a good platform and tool in the “multiple-level” design process. They can serve as a specification language on all levels of specifications, and as a formal verification tool throughout these specification and architectural description levels. The first problem to be solved during the design process is the construction of a good model, which will enable the specification and further handling and verification of the different levels of this design. Therefore this paper presents such model constructions on the basis of a number of simple examples. These experiments can use the automatic translation process from PNML language to the synthesized VHDL description that can be easily implemented in FPGA. We have used universal VHDL description divided into several blocks. The blocks can be easily modified.