It is proved that the FC-rank of every tree-automatic linear ordering is below omega^omega, and an analogue for tree- automatic linear orderings where the branching complexity of the trees involved is bounded is shown.Expand

We model the behavior of a fifo-queue as a monoid of transformations that are induced by sequences of writing and reading. We describe this monoid by means of a confluent and terminating semi-Thue… Expand

It is proved that the problem of whether a given tree automatic structure is already word automatic is decidable for tree automatic scattered linear orderings and in case of a positive answer a word automatic presentation is computable from the tree automatic presentation.Expand

It is proved that wACAs and wFAs which satisfy an I-diamond property are equally expressive, and a characterization of this expressiveness by weighted monadic second-order logic.Expand

The main theorem shows that a given fragment satisfies some identity of omega-terms if and only if Duplicator has a winning strategy for the game on the resulting linear orders, and it is shown that one can decide in exponential time whether all aperiodic monoids satisfy some given identity of Omega-terms.Expand

It is shown that the isomorphism problem for tree-automatic well-founded trees is complete for level Delta^0_{omega^omega} of the hyperarithmetical hierarchy with respect to Turing-reductions.Expand

A pumping lemma for alpha-automata (processing finite alpha-words, i.e., words of length alpha that have one fixed letter at all but finitely many positions) is developed and a sharp bound on the height of the finite word alpha-automatic well-founded order forests is provided.Expand

It is shown that while several properties concerning its rational subsets are undecidable, their uniform membership problem is NL-complete and it is proved that the monoid is not Thurston-automatic.Expand

It is shown that if both operations of the bimonoid are locally finite, then the classes of recognizable and mc-rational trace series coincide and, in general, are properly contained in the class of c-rational series.Expand

It is proved that weighted asynchronous cellular automata and weighted finite automata which satisfy an I-diamond property are equally expressive.Expand