An Automaton Group with PSPACE-Complete Word Problem

Abstract We construct an automaton group with a -complete word problem, proving conjecture due to Steinberg. Additionally, the constructed has provably more difficult, namely -complete, compressed problem and acts over binary alphabet. Thus, it is optimal in terms of alphabet size. Our construction directly simulates computation Turing machine and, therefore, seems be quite versatile. It combines two ideas: first one used by D’Angeli, Rodaro author obtain inverse semigroup second utilize Barrington simulate Boolean circuits bounded degree logarithmic depth even permutations five elements.