5,037 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
Logics with rigidly guarded data tests
The notion of orbit finite data monoid was recently introduced by Bojanczyk
as an algebraic object for defining recognizable languages of data words.
Following Buchi's approach, we introduce a variant of monadic second-order
logic with data equality tests that captures precisely the data languages
recognizable by orbit finite data monoids. We also establish, following this
time the approach of Schutzenberger, McNaughton and Papert, that the
first-order fragment of this logic defines exactly the data languages
recognizable by aperiodic orbit finite data monoids. Finally, we consider
another variant of the logic that can be interpreted over generic structures
with data. The data languages defined in this variant are also recognized by
unambiguous finite memory automata
Learning probability distributions generated by finite-state machines
We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference
in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft
Well-Pointed Coalgebras
For endofunctors of varieties preserving intersections, a new description of
the final coalgebra and the initial algebra is presented: the former consists
of all well-pointed coalgebras. These are the pointed coalgebras having no
proper subobject and no proper quotient. The initial algebra consists of all
well-pointed coalgebras that are well-founded in the sense of Osius and Taylor.
And initial algebras are precisely the final well-founded coalgebras. Finally,
the initial iterative algebra consists of all finite well-pointed coalgebras.
Numerous examples are discussed e.g. automata, graphs, and labeled transition
systems
A split-and-perturb decomposition of number-conserving cellular automata
This paper concerns -dimensional cellular automata with the von Neumann
neighborhood that conserve the sum of the states of all their cells. These
automata, called number-conserving or density-conserving cellular automata, are
of particular interest to mathematicians, computer scientists and physicists,
as they can serve as models of physical phenomena obeying some conservation
law. We propose a new approach to study such cellular automata that works in
any dimension and for any set of states . Essentially, the local rule of
a cellular automaton is decomposed into two parts: a split function and a
perturbation. This decomposition is unique and, moreover, the set of all
possible split functions has a very simple structure, while the set of all
perturbations forms a linear space and is therefore very easy to describe in
terms of its basis. We show how this approach allows to find all
number-conserving cellular automata in many cases of and . In
particular, we find all three-dimensional number-conserving CAs with three
states, which until now was beyond the capabilities of computers
On the Synchronizing Probability Function and the Triple Rendezvous Time for Synchronizing Automata
Cerny's conjecture is a longstanding open problem in automata theory. We
study two different concepts, which allow to approach it from a new angle. The
first one is the triple rendezvous time, i.e., the length of the shortest word
mapping three states onto a single one. The second one is the synchronizing
probability function of an automaton, a recently introduced tool which
reinterprets the synchronizing phenomenon as a two-player game, and allows to
obtain optimal strategies through a Linear Program.
Our contribution is twofold. First, by coupling two different novel
approaches based on the synchronizing probability function and properties of
linear programming, we obtain a new upper bound on the triple rendezvous time.
Second, by exhibiting a family of counterexamples, we disprove a conjecture on
the growth of the synchronizing probability function. We then suggest natural
follow-ups towards Cernys conjecture.Comment: A preliminary version of the results has been presented at the
conference LATA 2015. The current ArXiv version includes the most recent
improvement on the triple rendezvous time upper bound as well as formal
proofs of all the result
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