CS780 Project: The Weighted Automata Network Analyzer

Weighted automata generalize a number of concepts found in discrete event dynamics systems of various kind. Semirings are used as a base algebra for describing weights which implies a variety different interpretations for particular application cases. In this project, we want to explore how theoretical results in fact boil down to algorithms and techniques that work in practice. The goal of this project is to derive a proof-of-concept implementation of approaches based on weighted automata. 1 Motivation and Overview Model checking discrete event dynamic systems is an area that combines a variety of types of automata with a variety of types of modal logics to evaluate if a given system has a particular property or not. Those automata models differ in important aspects; for instance untimed automata are used for standard model checking, probabilistic automata for timed and probabilistic model checking, stochastic automata for stochastic model checking and various other forms of timed automata have been considered as well. By considering the wide area of finite state automata, one can notice that in addition to these types of automata other models have been proposed and applied successfully in different application areas. Examples are min/plus, max/plus, or min/max automata that have been used for the analysis of real time systems, communication system, and discrete event systems. Furthermore, similar models have been applied for natural language processing or image compression. It is quite natural and for most of the mentioned applications also very useful to extend model checking approaches to all these types of automata. Since the class of weighted automata provides in some sense a superset of different automata types, which includes different forms of probabilistic automata and also untimed automata, one may strive for a general framework of model checking which can be applied to a wide variety of different types of weighted automata without defining a new approach for each type. Such a framework is of theoretical interest to get a better understanding of model checking and to get a common ground for model checking in various application areas. From a methodological point of view, it gives direct access to model checking techniques for various types of automata that do not profit from these techniques yet. Finally, it supports tool development: in an object oriented setting, implementation of a specific model checker can inherit basic techniques from a more general class that implements techniques valid for the whole framework. Weighted automata are a well known class of automata where transitions are labeled with labels from a finite alphabet and, additionally, receive weights or costs that are elements of some semiring. A key observation is that the algebraic structure of a semiring is sufficient to define model checking for weighted automata. The advantage is that by selecting appropriate semirings, one obtains different types of automata that include most of the above mentioned types. This general type of automata is suitable to define a bisimulation as we did in [4, 2]. In [3], the process algebra GPA has been introduced for the specification of models in a compositional way such that the underlying semantic model is a weighted automaton in the case of a finite set of states. In [1] we propose a model checking approach