Approximate automata for omega-regular languages

Automata over infinite words, also known as ω -automata, play a key role in the verification and synthesis of reactive systems. The spectrum of ω -automata is defined by two characteristics: the acceptance condition (e.g. Büchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic ω -automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism. In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition

On the Completeness of Verifying Message Passing Programs Under Bounded Asynchrony

International audienceWe address the problem of verifying message passing programs , defined as a set of processes communicating through unbounded FIFO buffers. We introduce a bounded analysis that explores a special type of computations, called k-synchronous. These computations can be viewed as (unbounded) sequences of interaction phases, each phase allowing at most k send actions (by different processes), followed by a sequence of receives corresponding to sends in the same phase. We give a procedure for deciding k-synchronizability of a program, i.e., whether every computation is equivalent (has the same happens-before relation) to one of its k-synchronous computations. We show that reachability over k-synchronous computations and checking k-synchronizability are both PSPACE-complete

On the Completeness of Verifying Message Passing Programs under Bounded Asynchrony

We address the problem of verifying message passing programs, defined as a set of parallel processes communicating through unbounded FIFO buffers. We introduce a bounded analysis that explores a special type of computations, called k-synchronous. These computations can be viewed as (unbounded) sequences of interaction phases, each phase allowing at most k send actions (by different processes), followed by a sequence of receives corresponding to sends in the same phase. We give a procedure for deciding k-synchronizability of a program, i.e., whether every computation is equivalent (has the same happens-before relation) to one of its k-synchronous computations. We also show that reachability over k-synchronous computations and checking k-synchronizability are both PSPACE-complete. Furthermore, we introduce a class of programs called {\em flow-bounded} for which the problem of deciding whether there exists a k>0 for which the program is k-synchronizable, is decidable

Model-based quality assurance of instrumented context-free systems

The ever-growing complexity of today’s software and hardware systems makes quality assurance (QA) a challenging task. Abstraction is a key technique for dealing with this complexity because it allows one to skip non-essential properties of a system and focus on the important ones. Crucial for the success of this approach is the availability of adequate abstraction models that strike a fine balance between simplicity and expressiveness. This thesis presents the formalisms of systems of procedural automata (SPAs), systems of behavioral automata (SBAs), and systems of procedural Mealy machines (SPMMs). The three model types describe systems which consist of multiple procedures that can mutually call each other, including recursion. While the individual procedures are described by regular automata and therefore are easy to understand, the aggregation of procedures towards systems captures the semantics of context-free systems, offering the expressiveness necessary for representing procedural systems. A central concept of the proposed model types is an instrumentation that exposes the internal structure of systems by making calls to and returns from procedures observable. This instrumentation allows for a notion of rigorous (de-) composition which enables a translation between local (procedural) views and global (holistic) views on a system. On the basis of this translation, this thesis presents algorithms for the verification, testing, and learning of (instrumented) context-free systems, covering a broad spectrum of practical QA tasks. Starting with SPAs as a “base” formalism for context-free systems, the flexibility of this concept is shown by including features such as prefix-closure (SBAs) and dialog-based transductions (SPMMs). In a comparison with related formalisms, this thesis shows that the simplicity of the proposed model types not only increases the understandability of models but can also improve the performance of QA tasks. This makes SPAs, SBAs, and SPMMs a powerful tool for tackling the practical challenges of assuring the quality of today’s software and hardware systems