The goal of the lab course is to investigate set of rules (chemical reactions) and for “interesting” combinations answer the following questions:

• Does the rule under investigation lead to an infinite amount of molecules?
• Is there a starting molecule where the graph language (yielded by the rule) is infinite?
• Is there a combination of (two rules) where every single rule yields a finite language, but both rules together give something infinite?
• Systematic summary which rules are finite, which are infinite

• Given a set of rules that yield an infinite language, which is the minimal set of rules yielding it / yielding an infinite language? (Minimality in this context means that there is no (proper) subset that generates the language)
• Given a set of rules that yield an infinite language, which is the maximal set of rules yielding a finite language? (Maximality in this context means that there is no rule that (unionized with the given set of rules) yield an infinite set)

Answer how the language generated by the rule / set of rules depends on the starting molecule

• case 0: trivial: no rule can be applied
• case 1: rules can be applied, but finite set is yielded; iterate until exhausted -> finite language
• case 2: Is there a starting set that will give an infinite chemical universe?
• Extend systematic summary of finiteness of rules depending on the starting molecule(s)

• (until tuesday:) What are good stopping conditions for the analysis of the networks?
• Since infinite grammar can’t be computationally generated: what are good bounds for stopping the computation?
  • Limit the size of chemical networks with a total number of graphs
  • Limit the size of chemical networks with a total size of molecules
• Create a comparison of stopping conditions (how large is network or what size of molecules to expand (coordinate between groups))

• Analysis of finiteness of rules
• For infinite rules: do the finite subsets contain any other networks inside of them?
• Comparison of these rules to rules with several infinite cycles, since it is easier to find autocatalytic cycles in these

• Which combinations of groups are interesting / boring? (interesting: maximal finiteness / minimal infiniteness?)
• Who investigates which combination of rules?
• How can we parallelize the search tree through the lab course (numerical experiments & and arguing whether and why rule set / universe is (in-)finite)