On Languages Accepted by P/T Systems Composed of joins

TL;DR

This paper introduces J languages accepted by Petri nets composed of joins, linking their topology to computational power and comparing them to other language families.

Contribution

It defines J languages, proves their acceptance by join-only Petri nets, and explores their relation to other formal languages and computational models.

Findings

J languages can be accepted by log n space-bounded nondeterministic Turing machines.

J languages have semilinear Parikh maps.

J languages and context-free languages are incomparable.

Abstract

Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood by just looking at their topology, that is, information flow. Here we continue this line of research introducing J languages and proving that they can be accepted by place/transition systems whose underlying net is composed only of joins. Moreover, we investigate how J languages relate to other families of formal languages. In particular, we show that every J language can be accepted by a log n space-bounded non-deterministic Turing machine with a one-way read-only input. We also show that every J language has a semilinear Parikh map and that J languages and context-free languages (CFLs) are incomparable.