Process/reaction synthesis usually are described by (Petri-) graphs and are investigated by graph theoretical methods.
In this lecture we present a linear algebraic approach of the problem, and discuss some theoretical and computational results, comparing the outputs and running time to the old ones.
In some more detail, a Petri-graph is a usual directed graph but has two types of vertices: representing compounds and processes. These latter ones represent processing states in which outgoing compounds are produced from the input ones. Let us highlight, that of course each vertex is connected with vertices of the other type! (In the language of graph theory: this is a bipartite graph.)
Now our idea shortly is: represent each process-state vertex with an n-dimensional vector (for suitable fixed n), as we usually represent any chemical reaction with a vector. Then methods of linear algebra and our former investigations offer solutions for question about such vectorsets and so for Petri-graphs.
(Die Teilnahme an der Konferenz wird durch die Stiftung von Hans Pape, Dortmund, Dr. h.c. der Universität Veszprém unterstützt.)