4,845 research outputs found
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
On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism
In this paper we address the problem of the uniform random generation of non
deterministic automata (NFA) up to isomorphism. First, we show how to use a
Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use
the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism.
Using labeling techniques, we show that in practice it is possible to move into
the modified Markov Chain efficiently, allowing the random generation of NFAs
up to isomorphism with dozens of states. This general approach is also applied
to several interesting subclasses of NFAs (up to isomorphism), such as NFAs
having a unique initial states and a bounded output degree. Finally, we prove
that for these interesting subclasses of NFAs, moving into the Metropolis
Markov chain can be done in polynomial time. Promising experimental results
constitute a practical contribution.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223,
pp.12, 2015, Implementation and Application of Automata - 20th International
Conferenc
Self-Automaton Semigroups
After reviewing automaton semigroups, we introduce Cayley Automata and the
corresponding Cayley Automaton semigroups. We investigate which semigroups are
isomorphic to their Cayley Automaton semigroup and give some results for
special classes of semigroups. We answer a question posed by Cain relating to
the dual construction.Comment: 18 page
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
The isomorphism problem for tree-automatic ordinals with addition
This paper studies tree-automatic ordinals (or equivalently, well-founded
linearly ordered sets) together with the ordinal addition operation +.
Informally, these are ordinals such that their elements are coded by finite
trees for which the linear order relation of the ordinal and the ordinal
addition operation can be determined by tree automata. We describe an algorithm
that, given two tree-automatic ordinals with the ordinal addition operation,
decides if the ordinals are isomorphic
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