An Automaton Group with PSPACE-Complete Word Problem

Jan Philipp Wächter, Armin Weiß, Christophe Paul, Markus Bläser
2020 Symposium on Theoretical Aspects of Computer Science  
We construct an automaton group with a PSPACE-complete word problem, proving a conjecture due to Steinberg. Additionally, the constructed group has a provably more difficult, namely EXPSPACE-complete, compressed word problem. Our construction directly simulates the computation of a Turing machine in an automaton group and, therefore, seems to be quite versatile. It combines two ideas: the first one is a construction used by D'Angeli, Rodaro and the first author to obtain an inverse automaton
more » ... nverse automaton semigroup with a PSPACE-complete word problem and the second one is to utilize a construction used by Barrington to simulate circuits of bounded degree and logarithmic depth in the group of even permutations over five elements.
doi:10.4230/lipics.stacs.2020.6 dblp:conf/stacs/WachterW20 fatcat:x6dzx5e6xrftfdzm3wo7wp5pxe