On the finite containment problem for Petri nets

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.