Kleene theorems for product systems

  • Authors:

  • Kamal Lodaya;Madhavan Mukund;Ramchandra Phawade

  • Affiliations:

  • The Institute of Mathematical Sciences, Chennai, India;Chennai Mathematical Institute, Siruseri, India;The Institute of Mathematical Sciences, Chennai, India

  • Venue:
  • DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
  • Year:
  • 2011

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Abstract

We prove Kleene theorems for two subclasses of labelled product systems which are inspired from well-studied subclasses of 1- bounded Petri nets. For product T-systems we define a corresponding class of expressions. The algorithms from systems to expressions and in the reverse direction are both polynomial time. For product free choice systems with a restriction of structural cyclicity, that is, the initial global state is a feedback vertex set, going from systems to expressions is still polynomial time; in the reverse direction it is polynomial time with access to an NP oracle for finding deadlocks.