Ahmed Nazeem

Designing Compact and Maximally Permissive Deadlock Avoidance Policies for Complex Resource Allocation Systems Through Classification Theory: The Nonlinear Case

Most of the past research on the problem of deadlock avoidance for complex resource allocation systems (RAS) has acknowledged the fact that the computation of the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and therefore, it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this paper, we distinguish between the off-line and the on-line computation that is required for the effective implementation of the maximally permissive DAP, and we seek to develop representations of this policy that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Furthermore, in this first study of the aforementioned problem, we restrict our attention to a particular RAS class that is motivated by an ongoing project of ours called Gadara, and accepts separation of the safe and unsafe subspaces of its instantiations through a set of linear inequalities. Through a series of reductions of the derived classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. We formally establish completeness and optimality properties for the proposed design procedures. We also offer heuristics that, if necessary, can alleviate the computational effort that is necessary for the construction of the sought classifier. Finally, we demonstrate the efficacy of the developed approaches through a series of computational experiments. To the best of our knowledge, these experiments also establish the ability of the proposed methodology to effectively compute tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literature.

Designing Optimal Deadlock Avoidance Policies for Sequential Resource Allocation Systems Through Classification Theory: Existence Results and Customized Algorithms

A recent line of work has sought the implementation of the maximally permissive deadlock avoidance policy (DAP) for a broad class of complex resource allocation systems (RAS) as a classifier that gives effective and parsimonious representation to the dichotomy of the underlying behavioral space into the admissible and inadmissible subspaces defined by that policy. The work presented in this paper complements the past developments in this area by providing 1) succinct conditions regarding the possibility of expressing the aforementioned classifier as a set of linear inequalities in the RAS state variables, and 2) an efficient customized algorithm for the synthesis of pertinent nonlinear classifiers that implement the target DAP with minimum run-time computational overhead, in the case that a linear-classifier-based representation of this policy is not possible.

Supervisory Control of Software Execution for Failure Avoidance: Experience from the Gadara Project

Abstract We discuss our experience in the Gadara project, whose objective is to control the execution of software to avoid potential failures using discrete-event control techniques. We summarize our accomplishments so far and discuss future challenges. After initial work on safety of workflow scripts via supervisory control techniques, we have focused our efforts on deadlock avoidance in multithreaded C programs that use locking primitives to control access to shared data. We describe how we automatically construct automata models of workflows and Petri net models of concurrent programs. In the case of multithreaded C programs, the resulting models characterize a new class of resource-allocation Petri nets called Gadara nets. These nets enjoy structural properties that facilitate the synthesis of liveness-enforcing control policies that are maximally-permissive. We describe our strategy for run-time implementation of these control policies, especially by a technique known as code instrumentation. It is hoped that the lessons learned so far in the Gadara project will be useful in other application areas and will suggest avenues for future theoretical investigations.

Designing maximally permissive deadlock avoidance policies for sequential resource allocation systems through classification theory

Most of the past research on the problem of deadlock avoidance for sequential resource allocation systems (RAS) has acknowledged the fact that the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this work, we seek the effective implementation of the maximally permissive DAP for sequential RAS, by distinguishing between the off-line and the on-line computation required for the specification of this policy, and developing a representation of the derived result that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. The reported results establish that the proposed method can support the effective deployment of maximally permissive DAP for RAS with very large state spaces.

Maximally permissive deadlock avoidance for sequential resource allocation systems using disjunctions of linear classifiers

A recent line of work has sought the implementation of the maximally permissive deadlock avoidance policy (DAP) for a broad class of complex resource allocation systems (RAS) as a classifier that gives effective and parsimonious representation to the dichotomy of the underlying behavioral space into the admissible and inadmissible subspaces defined by the target policy. The considered RAS class pertains also to the management of the lock allocation in multi-threaded software. The work presented in this paper complements the past developments in this area by providing (i) succinct conditions regarding the possibility of expressing the aforementioned classifier as a set of linear inequalities in the RAS state variables, and (ii) an efficient customized algorithm for the synthesis of pertinent non-linear classifiers that implement the target DAP with minimum run-time computational overhead, in the case that a linear-classifier-based representation of this policy is not possible.

Optimal deadlock avoidance for complex resource allocation systems through classification theory

Abstract Most of the past research on the problem of deadlock avoidance for sequential complex resource allocation systems (RAS) has acknowledged the fact that the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this work, we seek the effective implementation of the maximally permissive DAP for a broad spectrum of RAS, by distinguishing between the off-line and the on-line computation that is required for the specification of this policy, and developing a representation of the derived result that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Through a series of reductions of the posed classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. A series of computational experiments demonstrate the efficacy of the proposed approach and establish its ability to provide tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literature.

Maximally permissive deadlock avoidance for resource allocation systems with R/W-locks

This paper extends the existing theory on maximally permissive liveness-enforcing supervision of resource allocation systems (RAS) so that it can handle RAS with reader / writer (R/W-) locks. A key challenge that is posed by this new RAS class stems from the fact that the underlying state space is not necessarily finite. We effectively address this obstacle by taking advantage of special structure that exists in the set of inadmissible states and enables a finite representation of this set through its minimal elements.

A practical approach to the design of maximally permissive liveness-enforcing supervisors for complex resource allocation systems

The problem of designing and deploying liveness-enforcing supervisors (LES) for sequential resource allocation systems is well-documented and extensively researched in the current literature. Acknowledging the fact that the computation of the maximally permissive LES is an NP-hard problem, most of the present solutions tend to trade off maximal permissiveness for computational tractability and ease of the policy design and implementation. In this work, we demonstrate that the maximally permissive LES can be a viable solution for the resource allocation taking place in many practical applications, by (a) effectively differentiating between the off-line and on-line problem complexity, and (b) controlling the latter through the development of succinct and compact representations of the information that is necessary for the characterization of the maximal permissive LES.

Efficient Enumeration of Minimal Unsafe States in Complex Resource Allocation Systems

An earlier work of ours has proposed a novel approach for the deployment of the maximally permissive deadlock avoidance policy for complex resource allocation systems (RAS), that is based on the identification and the efficient storage of a critical subset of states of the underlying RAS state space; the availability of this information enables an expedient one-step-lookahead scheme for the identification and blockage of transitions that will take the system behavior outside its safe region. This paper complements the aforementioned results by introducing a novel algorithm that provides those critical states while avoiding the complete enumeration of the RAS state space.

Optimal Linear Separation of the Safe and Unsafe Subspaces of Sequential Resource Allocation Systems as a Set-Covering Problem: Algorithmic Procedures and Geometric Insights

A recent line of work has posed the design of the maximally permissive deadlock avoidance policy for a particular class of sequential resource allocation systems as a linear classification problem. It has also identified a connection between the classifier design problem addressed by it and the classical set-covering problem that has been studied in operations research and computer science. This paper seeks to explore and formalize further this connection, in an effort to (i) develop novel insights regarding the geometric and combinatorial structure of the classifier design problem mentioned above; (ii) set an analytical base for the development of additional customized and computationally (more) efficient algorithms for its solution; and (iii) identify necessary and sufficient conditions, and the corresponding computational tests, for the effective application and the extension of the representational results in the aforementioned work to broader classes of resource allocation systems.