Anna Philippou

Weak Bisimulation for Probabilistic Systems

In this paper, we introduce weak bisimulation in the framework of Labeled Concurrent Markov Chains, that is, probabilistic transition systems which exhibit both probabilistic and nondeterministic behavior. By resolving the nondeterminism present, these models can be decomposed into a possibly infinite number of computation trees. We show that in order to compute weak bisimulation it is sufficient to restrict attention to only a finite number of these computations. Finally, we present an algorithm for deciding weak bisimulation which has polynomial-time complexity in the number of states of the transition system.

Symbolic schedulability analysis of real-time systems

We propose a unifying method for analysis of scheduling problems in real-time systems. The method is based on ACSR-VP, a real-time process algebra with value-passing capabilities. We use ACSR-VP to describe an instance of a scheduling problem as a process that has parameters of the problem as free variables. The specification is analyzed by means of a symbolic algorithm. The outcome of the analysis is a set of equations, a solution to which yields the values of the parameters that make the system schedulable. Equations are solved using integer programming or constraint logic programming. The paper presents specifications of two scheduling problems as examples.

Resources in process algebra

Abstract The Algebra of Communicating Shared Resources (ACSR) is a timed process algebra which extends classical process algebras with the notion of a resource . It takes the view that the timing behavior of a real-time system depends not only on delays due to process synchronization, but also on the availability of shared resources. Thus, ACSR employs resources as a basic primitive and it represents a real-time system as a collection of concurrent processes which may communicate with each other by means of instantaneous events and compete for the usage of shared resources. Resources are used to model physical devices such as processors, memory modules, communication links, or any other reusable resource of limited capacity. Additionally, they provide a convenient abstraction mechanism for capturing a variety of aspects of system behavior. In this paper we give an overview of ACSR and its probabilistic extension, PACSR, where resources can fail with associated failure probabilities. We present associated analysis techniques for performing qualitative analysis (such as schedulability analysis) and quantitative analysis (such as resource utilization analysis) of process-algebraic descriptions. We also discuss mappings between probabilistic and non-probabilistic models, which allow us to use analysis techniques from one algebra on models from the other.

Network uncertainty in selfish routing

We study the problem of selfish routing in the presence of incomplete network information. Our model consists of a number of users who wish to route their traffic on a network of m parallel links with the objective of minimizing their latency. However, in doing so, they face the challenge of lack of precise information on the capacity of the network links. This uncertainty is modelled via a set of probability distributions over all the possibilities, one for each user. The resulting model is an amalgamation of the KP-model of (E. Koutsoupias and C. H. Papadimitriou, 1999) and the congestion games with user-specific functions of (I. Milchtaich, 1996). We embark on a study of Nash equilibria and the price of anarchy in this new model. In particular, we propose polynomial-time algorithms for computing some special cases of pure Nash equilibria and we show that negative results of (I. Milchtaich, 1996), for the non-existence of pure Nash equilibria in the case of three users, do not apply to our model. Consequently, we propose an interesting open problem in this area, that of the existence of pure Nash equilibria in the general case of our model. Furthermore, we consider appropriate notions for the social cost and the price of anarchy and obtain upper bounds for the latter. With respect to fully mixed Nash equilibria, we propose a method to compute them and show that when they exist they are unique. Finally we prove that the fully mixed Nash equilibrium maximizes the social welfare

Network game with attacker and protector entities

Consider an information network with harmful procedures called attackers (e.g., viruses); each attacker uses a probability distribution to choose a node of the network to damage. Opponent to the attackers is the system protector scanning and cleaning from attackers some part of the network (e.g., an edge or a path), which it chooses independently using another probability distribution. Each attacker wishes to maximize the probability of escaping its cleaning by the system protector; towards a conflicting objective, the system protector aims at maximizing the expected number of cleaned attackers. We model this network scenario as a non-cooperative strategic game on graphs. We focus on the special case where the protector chooses a single edge. We are interested in the associated Nash equilibria, where no network entity can unilaterally improve its local objective. We obtain the following results: – No instance of the game possesses a pure Nash equilibrium. –Every mixed Nash equilibrium enjoys a graph-theoretic structure, which enables a (typically exponential) algorithm to compute it. – We coin a natural subclass of mixed Nash equilibria, which we call matching Nash equilibria, for this game on graphs. Matching Nash equilibria are defined using structural parameters of graphs, such as independent sets and matchings. –We derive a characterization of graphs possessing matching Nash equilibria. The characterization enables a linear time algorithm to compute a matching Nash equilibrium on any such graph with a given independent set and vertex cover. – Bipartite graphs are shown to satisfy the characterization. So, using a polynomial-time algorithm to compute a perfect matching in a bipartite graph, we obtain, as our main result, an efficient graph-theoretic algorithm to compute a matching Nash equilibrium on any instance of the game with a bipartite graph.

On Confluence in the pi-Calculus

An account of the basic theory of confluence in the π-calculus is presented, techniques for showing confluence of mobile systems are given, and the utility of some of the theory presented is illustrated via an analysis of a distributed algorithm.

On Transformations of Concurrent Object Programs

Transformation rules which increase the scope for concurrent activity within systems prescribed by programs of concurrent object languages are given. The correctness of the rules is proved using a semantic definition by translation to a mobile-process calculus. The main theoretical development concerns the notions of confluence and partial confluence.

A Family of Resource-Bound Real-Time Process Algebras

This paper describes three real-time process algebras, ACSR, PACSR and ACSR- VP. ACSR is a resource-bound real-time process that supports synchronous timed actions and asynchronous instantaneous events as well as the notions of resource, priority, exception, and interrupt. PACSR is a probabilistic extension of ACSR with resources that can fail and associated failure probabilities. ACSR-VP extends ACSR with value passing between processes and parameterized process definitions. This paper also provides three simple real-time system examples to illustrate the expressive power and analysis technique of each process algebra.

Praobabilistic Resource Failure in Real-Time Process Algebra

PACSR, a probabilistic extension of the real-time process algebra ACSR, is presented. The extension is built upon a novel treatment of the notion of a resource. In ACSR, resources are used to model contention in accessing physical devices. Here, resources are invested with the ability to fail and are associated with a probability of failure. The resulting formalism allows one to perform probabilistic analysis of real-time system specifications in the presence of resource failures. A probabilistic variant of Hennessy-Milner logic with until is presented. The logic features an until operator which is parameterized by both a probabilistic constraint and a regular expression over observable actions. This style of parameterization allows the application of probabilistic constraints to complex execution fragments. A model-checking algorithm for the proposed logic is also given. Finally, PACSR and the logic are illustrated with a telecommunications example.

The price of defense

We consider a strategic game with two classes of confronting randomized players on a graph G(V, E): νattackers, each choosing vertices and wishing to minimize the probability of being caught, and a defender, who chooses edges and gains the expected number of attackers it catches. The Price of Defense is the worst-case ratio, over all Nash equilibria, of the optimal gain of the defender over its gain at a Nash equilibrium. We provide a comprehensive collection of trade-offs between the Price of Defense and the computational efficiency of Nash equilibria. – Through reduction to a Two-Players, Constant-Sum Game, we prove that a Nash equilibrium can be computed in polynomial time. The reduction does not provide any apparent guarantees on the Price of Defense. – To obtain such, we analyze several structured Nash equilibria: – In a Matching Nash equilibrium, the support of the defender is an Edge Cover. We prove that they can be computed in polynomial time, and they incur a Price of Defense of α(G), the Independence Number of G. – In a Perfect Matching Nash equilibrium, the support of the defender is a Perfect Matching. We prove that they can be computed in polynomial time, and they incur a Price of Defense of