MULTILISP: a language for concurrent symbolic computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
X10: an object-oriented approach to non-uniform cluster computing
OOPSLA '05 Proceedings of the 20th annual ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Interprocedural analysis of asynchronous programs
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Alternating two-way AC-tree automata
Information and Computation
FMOODS '09/FORTE '09 Proceedings of the Joint 11th IFIP WG 6.1 International Conference FMOODS '09 and 29th IFIP WG 6.1 International Conference FORTE '09 on Formal Techniques for Distributed Systems
The design of a task parallel library
Proceedings of the 24th ACM SIGPLAN conference on Object oriented programming systems languages and applications
Journal of Computer and System Sciences
Expand, Enlarge and Check: New algorithms for the coverability problem of WSTS
Journal of Computer and System Sciences
Complexity analysis of the backward coverability algorithm for VASS
RP'11 Proceedings of the 5th international conference on Reachability problems
Analysis of recursively parallel programs
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Algorithmic verification of asynchronous programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
The covering and boundedness problems for branching vector addition systems
Journal of Computer and System Sciences
Efficient coverability analysis by proof minimization
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
| Hi-index | 0.00 |
Expand, enlarge, and check (EEC) is a successful heuristic for the coverability problem of well-structured transition systems. EEC constructs a sequence of under- and over-approximations with the property that the presence of a bug is eventually exhibited by some under-approximation and the absence of a bug is eventually exhibited by some over-approximation. In this paper, we consider the application of EEC to the coverability problem for branching vector addition systems (BVAS), an expressive model that subsumes Petri nets. We describe an EEC algorithm for BVAS, and prove its termination and correctness. We prove an upper bound on the number of iterations for our EEC algorithm, both for BVAS and, as a special case, vector addition systems (or Petri nets). We show that in addition to practical effectiveness, the EEC heuristic is asymptotically optimal. For BVAS, it requires at most doubly-exponentially many iterations, thus matching the optimal 2EXPTIME upper bound. For Petri nets, it can be implemented in EXPSPACE, again matching the optimal bound. We have implemented our algorithm and used it to verify safety properties of concurrent programs with asynchronous tasks.