Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.Comment: 18 pages, 4 figure

Complexity bounds for the verification of real-time software

We present uniform approaches to establish complexity bounds for decision problems such as reachability and simulation, that arise naturally in the verification of timed software systems. We model timed software systems as timed automata augmented with a data store (like a pushdown stack) and show that there is at least an exponential blowup in complexity of verification when compared with untimed systems. Our proof techniques also establish complexity results for boolean programs, which are automata with stores that have additional boolean variables.published or submitted for publicationis peer reviewe

Efficient On-the-fly Algorithm for Checking Alternating Timed Simulation

In this paper we focus on property-preserving preorders between timed game automata and their application to control of partially observable systems. We define timed weak alternating simulation as a preorder between timed game automata, which preserves controllability. We define the rules of building a symbolic turn-based two-player game such that the existence of a winning strategy is equivalent to the simulation being satisfied. We also propose an on-the-fly algorithm for solving this game. This simulation checking method can be applied to the case of non-alternating or strong simulations as well. We illustrate our algorithm by a case study and report on results

Preemptive Job-Shop Scheduling using Stopwatch Automata

In this paper we show how the problem of job-shop scheduling where the jobs are preemptible can be modeled naturally as a shortest path problem defined on an extension of timed automata, namely stopwatch automata where some of the clocks might be freezed at certain states. Although standard verification problems on stopwatch automata are known to be undecidable, we show that due to well-known properties of optimal schedules, the shortest path in the automaton belongs to a finite class of acyclic paths where transitions occur at integer points in time, and hence the problem is solvable. We present several algorithms and heuristics for finding the shortest paths in such automata and test their implementation on numerous benchmark examples