On computing a liveness enforcing supervisory policy for a class of general petri nets

Discrete-Event/Discrete-State (DEDS) Systems are prone to livelocks. Once a system enters a livelocked-state, there is at least one activity of the modeled system that cannot be executed from all subsequent states of the system. This phenomenon is common to many operating systems where some process enters into a state of suspended animation for perpetuity, and the user is left with no other option than to terminate the process, or reboot the machine. This thesis is about computing Liveness Enforcing Supervisory Policies (LESPs) for Petri net (PN) models of DEDS systems. The existence of an LESP for general PNs is not even semi-decidable. This thesis identifies two classes of PNs F and H for which the existence of a LESP is decidable. It also describes an object-oriented implementation of a procedure for the synthesis of the minimally-restrictive LESP for any instance from these classes. The minimally-restrictive LESP prevents the occurrence of events in a DEDS system only when it is absolutely necessary. A suite of methods, based on refinement/abstraction concepts, is developed to reduce the complexity of LESP-synthesis. This involves the synthesis of a LESP for a simplified-version of a complex PN structure, which is subsequently refined to serve as a LESP for the original complex PN. Two PNs are in a simulation relationship if their behaviors are "similar" in a formal sense. The thesis concludes with a result that shows that the above mentioned procedure can be generalized to PNs in simulation relationships. That is, a LESP for a PN can be modified to serve as a LESP for another PN that is "similar". The implementation of this theoretical observation is suggested as a topic for future work

On the convexity of right-closed sets and its application to liveness enforcement in Petri Nets

A set of n-dimensional integral vectors, Nn, is said to be right-closed if for any x 2 , any vector y x also belongs to it. An integral-set Nn is convex if and only if there is a convex set C Rn such that = Int(C), where Int( ) denotes the integral points in the set argument. In this dissertation, we show that the problem of verifying convexity of a right-closed set is decidable. Following this, we present a polynomial time, LP-based algorithm, for verifying the convexity of a right-closed set of integral vectors, when the dimension n is xed. This result is to be viewed against the backdrop of the fact that checking the convexity of a real-valued, geometric set can only be accomplished in an approximate sense; and, the fact that most algorithms involving sets of real-valued vectors do not apply directly to their integral counterparts. Also, we discuss a grid-search based algorithm for verifying the convexity of such a set, although not a polynomial time procedure, it is a method that veri es the convexity of right-closed sets in a reasonable time complexity. On the application side, right-closed sets feature in the synthesis of Liveness Enforcing Supervisory Policies (LESPs) for a large family of Petri Nets (PNs). For any PN structure N from this family, the set of initial markings, (N), for which there is a LESP, is right-closed. A LESP determines the transitions of a PN that are to be permitted to re at any marking in such a manner that, irrespective of the past, every transition can be red at some marking in the future. A system that is modeled by a live PN does not experience livelocks, which serves as the motivation for investigating implementation paradigms for LESPs in practice. If a transition is prevented from ring at a marking by a LESP, and all LESPs, irrespective of the implementation-paradigm that is chosen, prescribe the same control for the marking, then it is a minimally restrictive LESP. It is possible to synthesize the minimally restrictive LESP for any instance N of the aforementioned family that uses the right-closed set of markings (N). The literature also contains an implementation paradigm called invariant-based monitors for liveness enforcement in PNs. This paradigm is popular due to the fact that the resulting supervisor can be directly incorporated into the semantics of the PN model of the controlled system. In this work, we show that there is an invariant-based monitor that is equivalent to the minimally restrictive LESP that uses the right-closed set (N) if and only if (N) is convex. This result serves as the motivation behind exploring the convexity of right-closed sets

Obstructions in Security-Aware Business Processes

This Open Access book explores the dilemma-like stalemate between security and regulatory compliance in business processes on the one hand and business continuity and governance on the other. The growing number of regulations, e.g., on information security, data protection, or privacy, implemented in increasingly digitized businesses can have an obstructive effect on the automated execution of business processes. Such security-related obstructions can particularly occur when an access control-based implementation of regulations blocks the execution of business processes. By handling obstructions, security in business processes is supposed to be improved. For this, the book presents a framework that allows the comprehensive analysis, detection, and handling of obstructions in a security-sensitive way. Thereby, methods based on common organizational security policies, process models, and logs are proposed. The Petri net-based modeling and related semantic and language-based research, as well as the analysis of event data and machine learning methods finally lead to the development of algorithms and experiments that can detect and resolve obstructions and are reproducible with the provided software