We introduce two abstract models for multithreaded programs based on dynamic networks of pushdown systems. We address the problem of symbolic reachability analysis for these models. More precisely, we consider the problem of computing effective representations of their reachability sets using finite-state automata. We show that, while forward reachability sets are not regular in general, backwa...

This paper introduces a class of cuts, called reachability cuts, for the Vehicle Routing Problem with Time Windows (VRPTW). Reachability cuts are closely related to cuts derived from precedence constraints in the Asymmetric Traveling Salesman Problem with Time Windows and to k-path cuts for the VRPTW. In particular, any reachability cut dominates one or more k-path cuts. The paper presents sepa...

Matching logic reachability has been recently proposed as an alternative program verification approach. Unlike Hoare logic, where one defines a language-specific proof system that needs to be proved sound for each language separately, matching logic reachability provides a language-independent and sound proof system that directly uses the trusted operational semantics of the language as axioms....

The reachability problem for Petri nets is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immediate. However, in this case, the computation of a Presburger formula denoting the reachability set...

We generalise Constrained Dynamic Pushdown Networks, introduced by Bouajjani et al., to Constrained Dynamic Tree Networks. In this model, we have trees of processes which may monitor their children. We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable. We address the problem of symbolic reachability analysis for this model. Mo...

Motivated by the objective to further reduce the storage and computation time required by finite-horizon discrete-time optimal reduced-order LQG compensators, this paper introduces the modified reachability canonical form of a minimal finite-horizon discrete-time compensator and an algorithm to compute it. Next recursive algorithms for efficient storage and recovery of the compensator matrices ...

This thesis deals with verification algorithms for inhomogeneous continuous time Markov chains (ICTMC), discrete time stochastic hybrid systems (DTSHS) and Markovian timed automata (MTA). For all of these three models we define the notions of time-bounded and time-unbounded reachability. We use time-bounded and time-unbounded reachability in order to compute the satisfiability probability of an...

The decidability of the reachability problem for VASS has been open for a long time, and today the computational complexity of the problem is still open. Obviously, there is more hope of obtaining elementary complexity upper bounds by restricting the class of VASS, for example by considering those for which the reachability sets are effectively semilinear. Presburger arithmetic would then provi...