Corpus ID: 233393969

The Reachability Problem for Petri Nets is Not Primitive Recursive

@article{Leroux2021TheRP,
  title={The Reachability Problem for Petri Nets is Not Primitive Recursive},
  author={J{\'e}r{\^o}me Leroux},
  journal={ArXiv},
  year={2021},
  volume={abs/2104.12695}
}
We provide an Ackermannian complexity lower bound for the reachability problem for checking programs, a model equivalent to Petri nets. Moreover in fixed dimension 2d + 4, we show that the problem is Fd-hard. As a direct corollary, the reachability problem in dimension 10 is not elementary. 
Petri Net Invariant Synthesis
TLDR
This work formulated a CEGAR-loop, an algorithm that decides whether a given half space is indeed inductive, and implemented it in the tool Inequalizer, showing that it is competitive against state-of-the-art techniques. Expand
Improved Ackermannian lower bound for the VASS reachability problem
TLDR
This draft provides a simplification of the former construction of VASS, thus improving the lower bound for VASS in fixed dimension, and proves Fk-hardness in dimension 6k, and Leroux in dimension 4k + 9, the simplified construction. Expand
On Opacity Verification for Discrete-Event Systems
TLDR
This work considers two kinds of automata models: (i) acyclic automata, and (ii) automata where all cycles are only in the form of self-loops, and shows that the opacity verification for these systems is still hard. Expand
Synthetic Undecidability of MSELL via FRACTRAN Mechanised in Coq
TLDR
This work presents an alternate undecidability proof for entailment in (intuitionistic) multiplicative subexponential linear logic (MSELL) and gives an alternate presentation of those two counters machines as sequent rules, where computation is performed by proof-search, and halting reduced to provability. Expand
Improved Ackermannian lower bound for the Petri nets reachability problem
TLDR
This work improves the lower bound for vector addition systems with states in fixed dimension (or, equivalently, Petri nets with fixed number of places), and improves the former construction, making it conceptually simpler and more direct. Expand
Reachability in Vector Addition Systems is Ackermann-complete
TLDR
It is proved that the problem is Fk-hard for Vector Addition Systems with States in dimension 6k, where Fk is the k-th complexity class from the hierarchy of fast-growing complexity classes. Expand
A Linear-Time Nominal μ-Calculus with Name Allocation
Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly toExpand
Linear equations for unordered data vectors
Following a recently considered generalisation of linear equations to unordereddata vectors and to ordered-data vectors, we perform a further generalisation to k-elementsets-of-unordered-dataExpand
Long Runs Imply Big Separators in Vector Addition Systems
TLDR
It is shown that in VASSes fulfilling certain conditions existence of only long runs between some configurations implies existence ofonly big separators between some other configurations, and it is proved that a few known examples of hard VASSs fulfil the mentioned conditions. Expand
Nominal Büchi Automata with Name Allocation
TLDR
It is proved that, in contrast to most other nondeterministic automata models over infinite alphabets, language inclusion of Büchi RNNAs is decidable and in fact elementary, which makes B Müchi RnnAs a suitable tool for applications in model checking. Expand
...
1
2
...

References

SHOWING 1-10 OF 22 REFERENCES
An Algorithm for the General Petri Net Reachability Problem
  • E. Mayr
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1984
An algorithm is presented for the general Petri net reachability problem. It is based on a generalization of the basic reachability tree construction which is made symmetric with respect to theExpand
A Structure to Decide Reachability in Petri Nets
TLDR
A new structure to analyse Petri nets and decide reachability is presented, simplified, cleared and made more flexible by the introduction of the new structure of precovering graph. Expand
Reachability in Vector Addition Systems is Primitive-Recursive in Fixed Dimension
  • Jérôme Leroux, S. Schmitz
  • Mathematics, Computer Science
  • 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
  • 2019
TLDR
This work provides significant refinements to the classical decomposition algorithm of Mayr, Kosaraju, and Lambert and to its termination proof, which yield an ACKERMANN upper bound in the general case, and primitive-recursive upper bounds in fixed dimension. Expand
The reachability problem for Petri nets is not elementary
TLDR
A non-elementary lower bound is established, i.e. that the reachability problem needs a tower of exponentials of time and space, which implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachable problem, are also not elementary. Expand
Decidability Questions for Petri Nets
  • M. Hack
  • Mathematics, Computer Science
  • Outstanding Dissertations in the Computer Sciences
  • 1975
TLDR
A number of Petri Net problems are shown to be recursively equivalent to the Reachability Problem for Vector Addition Systems, and the equality of Reachability Sets and the equivalence of two Petri Nets in terms of their language-generating capability are recursive undecidable. Expand
Decidability of reachability in vector addition systems (Preliminary Version)
TLDR
A convincing proof of the decidability of reachability in vector addition systems is presented, and the complicated tree constructions in the earlier proofs are completely eliminated. Expand
The complexity of reachability in vector addition systems
TLDR
The problem was attacked by providing the first tight complexity bounds in the case of dimension 2 systems with states, while Leroux and Schmitz proved the first complexity upper bound in the general case. Expand
On the Reachability Problem for 5-Dimensional Vector Addition Systems
The reachability set for vector addition systems of dimension less than or equal to five are shown to be effectively computable semilinear sets. Thus reachability, equvalence and containment areExpand
The decidability of the reachability problem for vector addition systems (Preliminary Version)
TLDR
The reachability problem for the vector addition system (&abarbelow;,V) asks for an algorithm to decide which integral points &bbarbelow; are in R, which is the set of integral points in the first orthant of N-space. Expand
Demystifying Reachability in Vector Addition Systems
TLDR
This work offers a justification for this decomposition technique, and applies recent results on the complexity of termination thanks to well quasi orders and well orders to obtain a cubic Ackermann upper bound for the decomposition algorithms, thus providing the first known upper bounds for general VAS reach ability. Expand
...
1
2
3
...