Quorum Based Conflict Resolution Algorithms In Distributed Systems

Mutual exclusion is one of the most fundamental issues in the study of distributed systems. The problem arises when two or more processes are competing to use a mutual exclusive resource concurrently, i.e., the resource can only be used by at most one process at a time. Synchronizations adopting quorum systems are an important class of distributed algorithms since they are gracefully and significantly tolerate process and communication failures that may lead to network partitioning. Coterie based algorithm is a typical quorum based algorithm for mutual exclusion: A process can use the resource  only if it obtains permissions from all processes in any quorum ofcoterie, and since each quorum intersects with each other and each process only issues one permission, the mutual exclusion can be guaranteed. Many quorum systems have been defined based on the relaxation of the properties of coterie system. Each of them is designed to resolve its corresponding problem, e.g., k-coterie based algorithm to resolve the k-mutual exclusion, local coterie for the generalized mutual exclusion, (h, k)-arbiter for h-out of-k resource allocation problem, etc. Therefore, design an algorithm for any distributed conflict resolution problem is only meant to define a new quorum system which can be implemented to the corresponding problem. Since most of distributed conflict resolution problems are designed based on the relaxation of the safety property of mutual exclusion, understanding the way to relaxing the safety property and its quorum system is important to study any kind of conflict resolution problem in distributed systems

An asynchronous message-passing distributed algorithm for the global critical section problem

This paper considers the global $(l,k)$-CS problem which is the problem of controlling the system in such a way that, at least $l$ and at most $k$ processes must be in the CS at a time in the network. In this paper, a distributed solution is proposed in the asynchronous message-passing model. Our solution is a versatile composition method of algorithms for $l$-mutual inclusion and $k$-mutual exclusion. Its message complexity is $O(|Q|)$, where $|Q|$ is the maximum size for the quorum of a coterie used by the algorithm, which is typically $|Q| = \sqrt{n}$.Comment: This is a modified version of the conference paper in PDAA201

Group Mutual Exclusion in Linear Time and Space

We present two algorithms for the Group Mutual Exclusion (GME) Problem that satisfy the properties of Mutual Exclusion, Starvation Freedom, Bounded Exit, Concurrent Entry and First Come First Served. Both our algorithms use only simple read and write instructions, have O(N) Shared Space complexity and O(N) Remote Memory Reference (RMR) complexity in the Cache Coherency (CC) model. Our first algorithm is developed by generalizing the well-known Lamport's Bakery Algorithm for the classical mutual exclusion problem, while preserving its simplicity and elegance. However, it uses unbounded shared registers. Our second algorithm uses only bounded registers and is developed by generalizing Taubenfeld's Black and White Bakery Algorithm to solve the classical mutual exclusion problem using only bounded shared registers. We show that contrary to common perception our algorithms are the first to achieve these properties with these combination of complexities.Comment: A total of 21 pages including 5 figures and 3 appendices. The bounded shared registers algorithm in the old version has a subtle error (that has no easy fix) necessitating replacement. A correct, but fundamentally different, bounded shared registers algorithm, which has the same properties claimed in the old version is presented in this new version. Also, this version has an additional autho

Synthesis of Parametric Programs using Genetic Programming and Model Checking

Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into constructing it automatically. Classical algorithmic synthesis theory provides interesting algorithms but also alarming high complexity and undecidability results. The use of genetic programming, in combination with model checking and testing, provides a powerful heuristic to synthesize programs. The method is not completely automatic, as it is fine tuned by a user that sets up the specification and parameters. It also does not guarantee to always succeed and converge towards a solution that satisfies all the required properties. However, we applied it successfully on quite nontrivial examples and managed to find solutions to hard programming challenges, as well as to improve and to correct code. We describe here several versions of our method for synthesizing sequential and concurrent systems.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

On the Enforcement of a Class of Nonlinear Constraints on Petri Nets

International audienceThis paper focuses on the enforcement of nonlinear constraints in Petri nets. First, a supervisory structure is proposed for a nonlinear constraint. The proposed structure consists of added places and transitions. It controls the transitions in the net to be controlled only but does not change its states since there is no arc between the added transitions and the places in the original net. Second, an integer linear programming model is proposed to transform a nonlinear constraint to a minimal number of conjunc-tive linear constraints that have the same control performance as the nonlinear one. By using a place invariant based method, the obtained linear constraints can be easily enforced by a set of control places. The control places consist to a supervisor that can enforce the given nonlinear constraint. On condition that the admissible markings space of a nonlinear constraint is non-convex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint. Finally, a number of examples are provided to demonstrate the proposed approach