On the Topological Complexity of omega-Languages of Non-Deterministic Petri Nets

Wadge Degrees of $\omega$-Languages of Petri Nets

We prove that ω-languages of (non-deterministic) Petri nets and ω-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Turing machines which also form the class of effective...

On the topological complexity of ω-languages of non-deterministic Petri nets

We show that there are Σ3-complete languages of infinite words accepted by non-deterministic Petri nets with Büchi acceptance condition, or equivalently by Büchi blind counter automata. This shows that ω-languages accepted by non-deterministic Petri nets are topologically more complex than those accepted by deterministic Petri nets.

A rule-based evaluation of ladder logic diagram and timed petri nets for programmable logic controllers

This paper describes an evaluation through a case study by measuring a rule-based approach, which proposed for ladder logic diagrams and Petri nets. In the beginning, programmable logic controllers were widely designed by ladder logic diagrams. When complexity and functionality of manufacturing systems increases, developing their software is becoming more difficult. Thus, Petri nets as a high l...

Topological Complexity of Context-Free omega-Languages: A Survey

We survey recent results on the topological complexity of context-free ω-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free ω-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of amb...

The Wadge Hierarchy of Petri Nets omega-Languages