Pumping for ordinal-automatic structures

  title={Pumping for ordinal-automatic structures},
  author={Martin Huschenbett and Alexander Kartzow and Philipp Schlicht},
An alpha-automaton (for alpha some ordinal) is an automaton similar to a Muller automaton that processes words of length alpha. A structure is called alpha-automatic if it can be presented by alpha-automata (completely analogous to the notion of automatic structures which can be presented by the well-known finite automata). We call a structure ordinal-automatic if it is alpha-automatic for some ordinal alpha. We continue the study of ordinal-automatic structures initiated by Schlicht and… Expand
The Field of the Reals and the Random Graph are not Finite-Word Ordinal-Automatic
This work lifts Delhomm\'e's relative-growth-technique from the automatic and tree-automatic setting to the ordinal- automatic setting, which implies that the random graph is not Ordinal-automatic and infinite integral domains are not ordinals below $\omega_1+\omega^ \omega$ where $\omegas_1$ is the first uncountable ordinal. Expand
Tree-automatic scattered linear orders
It is shown that there is no tree-automatic scattered linear order, and therefore no tree's automatic well-order, on the set of all finite labeled trees, and that a regular tree language admits a tree- automatic scattered linear orders if and only if for some n, no binary tree of height n can be embedded into the union of the domains of its trees. Expand
L O ] 2 0 Ju l 2 01 7 Space-bounded OTMs and REG ∞
An important theorem in classical complexity theory is that LOGLOGSPACE=REG, i.e. that languages decidable with doublelogarithmic space bound are regular. We consider a transfinite analogue of thisExpand
A Complete Bibliography of Computability
above [CDHTM20]. admissible [Joh20]. affine [BA15]. Algebraic [DHS13]. algebras [AZ19]. algorithm [CD18, CD20]. Algorithmic [FrKHNS14, STZDG13, Muc16]. algorithmically [HTKT19]. Analog [PZ18, Mil20].Expand


Automatic structures
  • Achim Blumensath, E. Grädel
  • Computer Science
  • Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
  • 2000
This work determines the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic and gives model-theoretic characterisations for automatic structures via interpretations. Expand
A hierarchy of tree-automatic structures
It is obtained that there exist infinitely many ωn- automatic, hence also ω-tree-automatic, atomless boolean algebras, which are pairwise isomorphic under the continuum hypothesis CH and pairwise non isomorph under an alternate axiom AT, strengthening a result of [14]. Expand
Model-theoretic complexity of automatic structures
The following results are proved: The ordinal height of any automatic well-founded partial order is bounded by ωω, and the ordinal heights of automaticWell-founded relations are unbounded below (ω1CK). Expand
The isomorphism problem on classes of automatic structures with transitive relations
Automatic structures are finitely presented structures where the universe and all relations can be recognized by finite automata. It is known that the isomorphism problem for automatic structures isExpand
The Rank of Tree-Automatic Linear Orderings
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
Automatic linear orders and trees
It is shown that every infinite path in an automatic tree with countably many infinite paths is a regular language. Expand
Tree-Automatic Well-Founded Trees
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 (under Turing-reductions). Expand
Structures without Scattered-Automatic Presentation
This paper proves the following limitations on the class of \(\mathfrak{L}\)-automatic structures for a fixed \(\ mathfrak {L}\) of finite condensation rank 1 + α. Expand
Automatic Ordinals
It is proved that the injectively ω-tree-automatic ordinals are the ordinals smaller than ω ω and that the hierarchy of injectivelyω-automatic structures, n ≥ 1, which was considered in [FT12], is strict. Expand
Automata on ordinals and automaticity of linear orders
A method for proving non-automaticity is described and this is applied to determine the optimal bounds for the ranks of linear orders recognized by finite state automata. Expand