Kleene Theorems for Free Choice Nets Labelled with Distributed Alphabets

TL;DR

This paper extends Kleene theorems to free choice nets with distributed alphabets, removing previous restrictions and providing new expressions and characterizations for broader classes of these nets.

Contribution

It introduces Kleene theorems for free choice nets with distributed alphabets without the product condition restriction, including new characterizations and polynomial-time checkable properties.

Findings

Expressions for free choice nets with distributed choice property

Characterization of free choice nets via polynomial-time properties

Extension to free choice nets without the product condition

Abstract

We provided (PNSE'2014) expressions for free choice nets having "distributed choice property" which makes the nets "direct product" representable. In a recent work (PNSE'2016), we gave equivalent syntax for a larger class of free choice nets obtained by dropping distributed choice property. In both these works, the classes of free choice nets were restricted by a "product condition" on the set of final markings. In this paper we do away with this restriction and give expressions for the resultant classes of nets which correspond to "free choice synchronous products and Zielonka automata". For free choice nets with distributed choice property, we give an alternative characterization using properties checkable in polynomial time. Free choice nets we consider are 1-bounded, S-coverable, and are labelled with distributed alphabets, where S-components of the associated S-cover respect the given alphabet distribution.