Algorithms of Elementary Net Synthesis

Abstract

In this chapter, we consider finite transition systems exclusively. The chapter contains two sections. The first section shows that the net synthesis problem is NP-complete, hence one cannot construct very efficient synthesis algorithms. The second section constructs a flexible algorithm, based on minimal regions, that can be tailored to all forms of the net synthesis problem by selecting the relevant separation axioms. Most developments presented in the chapter, in spite of the title, are independent of elementary nets and valid in the larger framework of quasi-elementary nets. By nets and net systems, to restate the convention adopted in Chapter 1, we always mean quasi-elementary nets and quasi-elementary net systems, thus elementary is never meant unless it is explicit.