On the analysis of Petri nets and their synthesis from process languages

Processes in Place/Transition (P/T) nets are defined inductively by a peculiar numbering of place occurrences. Along with an associative sequential composition called catenation and a neutral process, a monoid of processes is obtained. The power algebra of this monoid contains all process languages with appropriate operations on them. Hence the problems of analysis and synthesis, analogous to those in the formal languages and automata theory, arise. Here, the analysis problem is: for a given P/T net with an initial marking find the set of all processes the net may evoke. The synthesis problem is: given a process language L decide if there exists a marked net whose evolutions (presented by processes) are collected in L and, in the positive case, find such net and its initial marking. The problems are posed and given a general solution.