Deterministic λ-free Petri net languages and their application to the supervisory control of discrete event dynamic systems

In this paper we introduce a family of languages called deterministic λ-free Petri net languages (DPNLs). We show that the controllability of a DPNL K⊆Σ* with respect to a DPNL L⊆Σ* is decidable. That is, it is possible to decide if (i) K⊆L, and (ii) KΣ_u∩L⊆K, where Σ=Σ_u∪Σ_c and Σ_u ∩Σ_c=φ. We also show that this family of languages strictly includes the family of Free-labeled Petri net languages (FLPNLs), another family of languages where the controllability of one language with respect to another is decidable