Complexity Results for Reachability in Cooperating Systems and Approximated Reachability by Abstract Over-Approximations

This work deals with theoretic aspects of cooperating systems, i.e., systems that consists of cooperating subsystems. Our main focus lies on the complexity theoretic classification of deciding the reachability problem and on efficiently establishing deadlock-freedom in models of cooperating systems. The formal verification of system properties is an active field of research, first attempts of which go back to the late 60's. The behavior of cooperating systems suffers from the state space explosion problem and can become very large. This is, techniques that are based on an analysis of the reachable state space have a runtime exponential in the number of subsystems. The consequence is that even modern techniques that decide whether or not a system property holds in a system can become unfeasible. We use interaction systems, introduced by Sifakis et al. in 2003, as a formalism to model cooperating systems. The reachability problem and deciding deadlock-freedom in interaction systems was proved to be PSPACE-complete. An approach to deal with this issue is to investigate subclasses of systems in which these problems can be treated efficiently. We show here that the reachability problem remains PSPACE-complete in subclasses of interaction systems with a restricted communication structure. We consider structures that from trees, stars and linear arrangements of subsystems. Our result motivates the research of techniques that treat the reachability problem in these subclasses based on sufficient conditions which exploit characteristics of the structural restrictions. In a second part of this work we investigate an approach to efficiently establish the reachability of states and deadlock-freedom in general interaction systems. We introduce abstract over-approximations -- a concept of compact representations of over-approximations of the reachable behavior of interaction systems. Families of abstract over-approximations are the basis for our approach to establish deadlock-freedom in interaction systems in polynomial time in the size of the underlying interaction system. We introduce an operator called Edge-Match for refining abstract over-approximations. The strength of our approach is illustrated on various parametrized instances of interaction systems. Furthermore, we establish a link between our refinement approach and the field of relational database theory and use this link in order to make a preciseness statement about our refinement approach