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A central decision problem in Petri net theory is reachability asking whether a given marking can be reached from the initial marking. Related is the covering problem (or sub-marking reachbility), which decides whether there is a reachable…

In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds…

A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…

The reachability problem in vector addition systems is a central question, not only for the static verification of these systems, but also for many inter-reducible decision problems occurring in various fields. The currently best known…

We consider the model-checking problem for freeze LTL on one-counter automata (OCA). Freeze LTL extends LTL with the freeze quantifier, which allows one to store different counter values of a run in registers so that they can be compared…

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

The reachability problem is a central decision problem for formal verification based on vector addition systems with states (VASS), which are equivalent to Petri nets and form one of the most studied and applied models of concurrency.…

In a previous paper we have presented a CEGAR approach for the verification of parameterized systems with an arbitrary number of processes organized in an array or a ring. The technique is based on the iterative computation of parameterized…

Vector addition systems with states (VASS) are widely used for the formal verification of concurrent systems. Given their tremendous computational complexity, practical approaches have relied on techniques such as reachability relaxations,…

Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is…

The recent years have seen remarkable progress in establishing the complexity of the reachability problem for vector addition systems with states (VASS), equivalently known as Petri nets. Existing work primarily considers the case in which…

We study the complexity of invariant inference and its connections to exact concept learning. We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept…

There are many physical processes that have inherent discontinuities in their mathematical formulations. This paper is motivated by the specific case of collisions between two rigid or deformable bodies and the intrinsic nature of that…

Vector addition systems with states (VASS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VASS, which consists of deciding whether a target…

We consider the master/slave parameterised reachability problem for networks of pushdown systems, where communication is via a global store using only non-atomic reads and writes. We show that the control-state reachability problem is…

The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a feasible point does not exist. However,…

The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are…

Given a Probabilistic Finite Automata (PFA), a set of states S, and an error threshold e > 0, our algorithm approximates the infimum probability (quantifying over all infinite words) that the automata reaches S. Our result contrasts with…

The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem.…

In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This…