Analysis of Parameterized Networks

In particular, the thesis will focus on parameterized networks of discrete-event systems. These are collections of interacting, isomorphic subsystems, where the number of subsystems is, for practical purposes, arbitrary; thus, the system parameter of interest is, in this case, the size of the network as characterized by the number of subsystems. Parameterized networks are reasonable models of real systems where the number of subsystems is large, unknown, or time-varying: examples include communication, computer and transportation networks. Intuition and engineering practice suggest that, in checking properties of such networks , it should be sufficient to consider a ``testbed'' network of limited size. However, there is presently little rigorous support for such an approach. In general, the problem of deciding whether a temporal property holds for a parameterized network of finite-state systems is undecidable; and the only decidable subproblems that have so far been identified place unreasonable restrictions on the means by which subsystems may interact. The key to ensuring decidability, and therefore the existence of effective solutions to the problem, is to identify restrictions that limit the computational power of the network. This can be done not only by limiting communication but also by restricting the structure of individual subsystems. In this thesis, we take both approaches, and also their combination on two different network topologies: ring networks and fully connected networks

Algorithmic Analysis of Infinite-State Systems

Many important software systems, including communication protocols and concurrent and distributed algorithms generate infinite state-spaces. Model-checking which is the most prominent algorithmic technique for the verification of concurrent systems is restricted to the analysis of finite-state models. Algorithmic analysis of infinite-state models is complicated--most interesting properties are undecidable for sufficiently expressive classes of infinite-state models. In this thesis, we focus on the development of algorithmic analysis techniques for two important classes of infinite-state models: FIFO Systems and Parameterized Systems. FIFO systems consisting of a set of finite-state machines that communicate via unbounded, perfect, FIFO channels arise naturally in the analysis of distributed protocols. We study the problem of computing the set of reachable states of a FIFO system composed of piecewise components. This problem is closely related to calculating the set of all possible channel contents, i.e. the limit language. We present new algorithms for calculating the limit language of a system with a single communication channel and important subclasses of multi-channel systems. We also discuss the complexity of these algorithms. Furthermore, we present a procedure that translates a piecewise FIFO system to an abridged structure, representing an expressive abstraction of the system. We show that we can analyze the infinite computations of the more concrete model by analyzing the computations of the finite, abridged model. Parameterized systems are a common model of computation for concurrent systems consisting of an arbitrary number of homogenous processes. We study the reachability problem in parameterized systems of infinite-state processes. We describe a framework that combines Abstract Interpretation with a backward-reachability algorithm. Our key idea is to create an abstract domain in which each element (a) represents the lower bound on the number of processes at a control location and (b) employs a numeric abstract domain to capture arithmetic relations among variables of the processes. We also provide an extrapolation operator for the domain to guarantee sound termination of the backward-reachability algorithm