25 research outputs found
On Boundedness Problems for Pushdown Vector Addition Systems
We study pushdown vector addition systems, which are synchronized products of
pushdown automata with vector addition systems. The question of the boundedness
of the reachability set for this model can be refined into two decision
problems that ask if infinitely many counter values or stack configurations are
reachable, respectively.
Counter boundedness seems to be the more intricate problem. We show
decidability in exponential time for one-dimensional systems. The proof is via
a small witness property derived from an analysis of derivation trees of
grammar-controlled vector addition systems
On Functions Weakly Computable by Pushdown Petri Nets and Related Systems
We consider numerical functions weakly computable by grammar-controlled
vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can
weakly compute all fast growing functions for
, hence they are computationally more powerful than
standard vector addition systems. On the other hand they cannot weakly compute
the inverses or indeed any sublinear function. The proof relies
on a pumping lemma for runs of GVASes that is of independent interest
New Lower Bounds for Reachability in Vector Addition Systems
We investigate the dimension-parametric complexity of the reachability
problem in vector addition systems with states (VASS) and its extension with
pushdown stack (pushdown VASS). Up to now, the problem is known to be
-hard for VASS of dimension (the complexity class
corresponds to the th level of the fast-growing hierarchy),
and no essentially better bound is known for pushdown VASS. We provide a new
construction that improves the lower bound for VASS: -hardness
in dimension . Furthermore, building on our new insights we show a new
lower bound for pushdown VASS: -hardness in dimension . This dimension-parametric lower bound is strictly stronger than the upper
bound for VASS, which suggests that the (still unknown) complexity of the
reachability problem in pushdown VASS is higher than in plain VASS (where it is
Ackermann-complete)
What makes petri nets harder to verify : stack or data?, Concurrency, security, and puzzles : Festschrift for A.W. Roscoe on the occasion of his 60th birthday
We show how the yardstick construction of Stockmeyer, also developed as counter bootstrapping by Lipton, can be adapted and extended to obtain new lower bounds for the coverability problem for two prominent classes of systems based on Petri nets: Ackermann-hardness for unordered data Petri nets, and Tower-hardness for pushdown vector addition systems
On Functions Weakly Computable by Pushdown Petri Nets and Related Systems
We consider numerical functions weakly computable by grammar-controlled
vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can
weakly compute all fast growing functions for
, hence they are computationally more powerful than
standard vector addition systems. On the other hand they cannot weakly compute
the inverses or indeed any sublinear function. The proof relies
on a pumping lemma for runs of GVASes that is of independent interest
A lower bound for the coverability problem in acyclic pushdown VAS
We investigate the coverability problem for a one-dimensional restriction of pushdown vector addition systems with states. We improve the lower complexity bound to PSpace, even in the acyclic case
Timed Basic Parallel Processes
Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching rules, and as such may be used to model networks of independent timed automata with process creation. We show that the coverability and reachability problems (with unary encoded target multiplicities) are PSPACE-complete and EXPTIME-complete, respectively. For the special case of 1-clock TBPP, both are NP-complete and hence not more complex than for untimed BPP. This contrasts with known super-Ackermannian-completeness and undecidability results for general timed Petri nets. As a result of independent interest, and basis for our NP upper bounds, we show that the reachability relation of 1-clock TA can be expressed by a formula of polynomial size in the existential fragment of linear arithmetic, which improves on recent results from the literature