On the finite containment problem for Petri nets

doi:10.1016/0304-3975(86)90169-6

Theoretical Computer Science

Volume 43, 1986, Pages 99-105

https://doi.org/10.1016/0304-3975(86)90169-6 Get rights and content

Under an Elsevier user license

open archive

Abstract

We prove that the Finite Containment Problem (FCP) for Petri nets is Dtime(Ackermann) complete for the reducibility ⩽^P_T, thus sharpening previous results due to McAloon (1984) and to Mayr and Meyer (1981). Our principal technique is to replace an application of the infinite Ramsey Theorem by a certain finite Ramsey Theorem previously studied by Paris (1980) and by Ketonen and Solovay (1981). Such techniques may have further applications in obtaining upper bounds for combinatorial problems.

Keywords

Petri net

vector addition set

finite containment problem

Ackermann function

Ramsey's Theorem

Cited by (0)

^*: This research was partially supported by NSF funding while the author was visiting the Department of Mathematics at the University of Illinois in Urbana, as well as by a Boston College faculty summer research grant.