Регулярные выражения для некоторых языков сетей Петри в задаче о производителе и потребителе

We consider a Petri net for the producer/consumer problem (one of the classical synchronization problems) with the bounded buffer of size n and the regular formal languages Ln, generated by the net. We propose regular expressions denoting these languages in the recursive form, in case of the bounded buffer of size from 1 to 3 the explicit formulas are proposed. We transform a reachability graph into a finite automaton and use the state elimination method. We give an upper estimate for the star-height of the mentioned languages, in case of the bounded buffer of size 1 and 2 the exact values are calculated. We also consider union, intersection, Kleene closure, concatenation and set difference operations on mentioned languages. We give the finite automaton and propose regular expressions denoting the set difference of languages Ln \ L1 in the recursive form, for L2 \ L1 the explicit formula is proposed