Comparing the Expressive Power of Well-Structured Transition Systems

Abstract

Abstract. We compare the expressive power of a class of well-structured transition systems that includes relational automata, Petri nets, lossy channel systems, and constrained multiset rewriting systems. For each one of these models we study the class of languages generated by labelled transition systems describing their semantics. We consider here two types of accepting conditions: coverability and reachability of a given configuration. In both cases we obtain a strict hierarchy in which constrained multiset rewriting systems is the the most expressive model.

Ordinal Theory for Expressiveness of Well Structured Transition Systems

“…As in the previous result, we remark that LCS (1,2) and AWN are selfwitnessing. Thus, we only need to apply Prop.…”

“…However, analogously to what happens with reachability, repeated coverability is generally undecidable, which makes ω-languages a bad candidate to study the relative expressive power of WSTS. In conclusion, we will use the class of coverability languages, as in [10,1,2,15].…”

“…More precisely, the language of an instance of a model is defined as the class of finite words accepted by it, with discriminate between extensions of Petri Nets. In [1,2] the expressive power of Petri Nets is proved to be strictly below that of Affine Well Nets, and Affine Well Nets are proved to be strictly less expressive than Lossy Channel Systems. Similar results are obtained in [15], though some significant problems are left open, like the distinction between ν-Petri Nets [14] and Data Nets [13] that we solve here.…”

“…We use + and − for multiset operations. If X is a wpo then so is X ⊕ ordered by ≤ ⊕ defined by {|x 1 …”

A Language-Based Comparison of Extensions of Petri Nets with and without Whole-Place Operations

“…For instance, with this notion of acceptance transfer/reset nets are equivalent to Turing machines. As shown in [6][7][8], a finer classification of wsts can be obtained by considering the class of languages recognized with coverability acceptance conditions (clanguages for short). A classification of wsts based on c-languages is particularly interesting since it can be used to extend the applicability of a decision procedure for coverability (e.g.…”