Tearing Based Automatic Abstraction for CTL Model Checking

In this paper we present the tearing paradigm as a way to automatically abstract behavior to obtain upper and lower bound approximations of a reactive system. We present algorithms that exploit the bounds to perform conservative ECTL and ACTL model checking. We also give an algorithm for false negative (or false positive) resolution for verification based on a theory of a lattice of approximations. We show that there exists a bipartition of the lattice set based on positive versus negative verification results. Our resolution methods are based on determining a pseudo-optimal shortest path from a given, possibly coarse but tractable approximation, to a nearest point on the contour separating one set of the bipartition from the other

Techniques for the formal verification of analog and mixed- signal designs

Embedded systems are becoming a core technology in a growing range of electronic devices. Cornerstones of embedded systems are analog and mixed signal (AMS) designs, which are integrated circuits required at the interfaces with the real world environment. The verification of AMS designs is concerned with the assurance of correct functionality, in addition to checking whether an AMS design is robust with respect to different types of inaccuracies like parameter tolerances, nonlinearities, etc. The verification framework described in this thesis is composed of two proposed methodologies each concerned with a class of AMS designs, i.e., continuous-time AMS designs and discrete-time AMS designs. The common idea behind both methodologies is built on top of Bounded Model Checking (BMC) algorithms. In BMC, we search for a counter-example for a property verified against the design model for bounded number of verification steps. If a concrete counter-example is found, then the verification is complete and reports a failure, otherwise, we need to increment the number of steps until property validation is achieved. In general, the verification is not complete because of limitations in time and memory needed for the verification. To alleviate this problem, we observed that under certain conditions and for some classes of specification properties, the verification can be complete if we complement the BMC with other methods such as abstraction and constraint based verification methods. To test and validate the proposed approaches, we developed a prototype implementation in Mathematica and we targeted analog and mixed signal systems, like oscillator circuits, switched capacitor based designs, Delta-Sigma modulators for our initial tests of this approach

Interaction in Concurrent Systems

This dissertation is concerned with the theoretical analysis of component-based models for concurrent systems. We focus on interaction systems, which were introduced by Sifakis et al. in 2003. Centered around interaction systems, we also cover Minsky machines, Petri nets and the Linda calculus and establish relations between the models by giving translations from one to the other. Thus, we gain an insight concerning the expressiveness of the models and learn, given a system described in one syntax, how to simulate it in another. Additionally, these translations allow us to deduce complexity and undecidability results. Namely, we show that the questions whether a LinCa process terminates or diverges under a maximum progress semantics are undecidable. We also prove that the problems of reachability, progress, local and global deadlock and availability are PSPACE-complete in interaction systems. This complexity-theoretic classification serves as a motivation for the sufficient condition approach that is presented in the second half of this work: We present a generic approach to prove properties for component-based systems that allow for decomposition into subsystems. To avoid the problem of state space explosion, we consider overlapping projections and thus compute over-approximations of the reachable global state space. We enhance the quality of these over-approximations by a technique we call Cross-Checking. Based on the enhanced over-approximations, we may then prove properties of the global system in polynomial time. We demonstrate our ideas by means of interaction systems and for the property of local deadlock