Efficient verification of sequential and concurrent systems

Formal methods provide means for rigorously specifying the desired behaviour of a hardware or software system, making a precise model of its actual behaviour, and then verifying whether that actual behaviour corresponds to the specification. My habiliation thesis reports on various contributions to this realm, where my main interest has been on algorithmic aspects. This is motivated by the observation that asymptotic worst-case complexity, often used to characterize the difficulty of algorithmic problems, is only loosely related to the difficulty encountered in solving those problems in practice. The two main types of system I have been working on are pushdown systems and Petri nets. Both are fundamental notions of computation, and both offer, in my opinion, particularly nice opportunities for combining theory and algorithmics. Pushdown systems are finite automata equipped with a stack; since the height of the stack is not bounded, they represent a class of infinite-state systems that model programs with (recursive) procedure calls. Moreover, we shall see that specifying authorizations is another, particularly interesting application of pushdown systems. While pushdown systems are primarily suited to express sequential systems, Petri nets model concurrent systems. My contributions in this area all concern unfoldings. In a nutshell, the unfolding of a net N is an acyclic version of N in which loops have been unrolled. Certain verification problems, such as reachability, have a lower complexity on unfoldings than on general Petri nets.