12,208 research outputs found
Isomorphisms of scattered automatic linear orders
We prove that the isomorphism of scattered tree automatic linear orders as
well as the existence of automorphisms of scattered word automatic linear
orders are undecidable. For the existence of automatic automorphisms of word
automatic linear orders, we determine the exact level of undecidability in the
arithmetical hierarchy
Advances and applications of automata on words and trees : abstracts collection
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
On the classification of automorphisms of trees
We identify the complexity of the classification problem for automorphisms of
a given countable regularly branching tree up to conjugacy. We consider both
the rooted and unrooted cases. Additionally, we calculate the complexity of the
conjugacy problem in the case of automorphisms of several non-regularly
branching trees
The Isomorphism Relation Between Tree-Automatic Structures
An -tree-automatic structure is a relational structure whose domain
and relations are accepted by Muller or Rabin tree automata. We investigate in
this paper the isomorphism problem for -tree-automatic structures. We
prove first that the isomorphism relation for -tree-automatic boolean
algebras (respectively, partial orders, rings, commutative rings, non
commutative rings, non commutative groups, nilpotent groups of class n >1) is
not determined by the axiomatic system ZFC. Then we prove that the isomorphism
problem for -tree-automatic boolean algebras (respectively, partial
orders, rings, commutative rings, non commutative rings, non commutative
groups, nilpotent groups of class n >1) is neither a -set nor a
-set
Tree-Automatic Well-Founded Trees
We investigate tree-automatic well-founded trees. Using Delhomme's
decomposition technique for tree-automatic structures, we show that the
(ordinal) rank of a tree-automatic well-founded tree is strictly below
omega^omega. Moreover, we make a step towards proving that the ranks of
tree-automatic well-founded partial orders are bounded by omega^omega^omega: we
prove this bound for what we call upwards linear partial orders. As an
application of our result, we show 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.Comment: Will appear in Logical Methods of Computer Scienc
The FC-rank of a context-free language
We prove that the finite condensation rank (FC-rank) of the lexicographic
ordering of a context-free language is strictly less than
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