In this paper we study the home marking problem for Petri nets, and some related concepts to it l... more In this paper we study the home marking problem for Petri nets, and some related concepts to it like confluence, noetherianity, and state space inclusion. We show that the home marking problem for inhibitor Petri nets is undecidable. We relate then the existence of home markings to confluence and noetherianity and prove that confluent and noetherian Petri nets have an unique home marking. Finally, we define some versions of the state space inclusion problem related to the home marking and sub-marking problems, and discuss their decidability status.
A Petri net is confluent if its firing relation is confluent, i.e., for any two reachable marking... more A Petri net is confluent if its firing relation is confluent, i.e., for any two reachable markings there exists a marking reachable from both of them. We prove that confluence is a decidable property for Petri nets and it is preserved by asynchronous parallel composition. Applications to Petri net structural transformations and term rewriting systems are then pointed out.
This paper presents a control synthesis software tool for manufacturing systems with a driven dyn... more This paper presents a control synthesis software tool for manufacturing systems with a driven dynamic event. This tool is based on an original control synthesis algorithm which solves the forbidden state problem (FSP) under the following hypothesis: 1) each event may occur at time instants specified by an interval or a union of intervals; 2) two types of events are considered: controllable and uncontrollable events and 3) the evolution of time is discrete. This tool generates a live and maximally permissive controller which can 1) act on the arriving date of controllable events or 2) completely forbid some controllable events. The aim is to guaranty the respect of the given specifications
Linear Algebraic Approach for Home Markings in Live and Bounded Equal Conflict Systems
The paper proposes a linear algebraic based approach to finding a set of home markings in a bound... more The paper proposes a linear algebraic based approach to finding a set of home markings in a bounded and live Equal Conflict System. Our algorithm is based on the theory of T-invariants, controlled-siphons and traps. The idea is to decompose the initial net in a certain subset of T-components, which are Choice-Free nets, find a set of live and potentially
Uploads
Papers by Ioana Leahu