4,886 research outputs found
A Note on Limited Pushdown Alphabets in Stateless Deterministic Pushdown Automata
Recently, an infinite hierarchy of languages accepted by stateless
deterministic pushdown automata has been established based on the number of
pushdown symbols. However, the witness language for the n-th level of the
hierarchy is over an input alphabet with 2(n-1) elements. In this paper, we
improve this result by showing that a binary alphabet is sufficient to
establish this hierarchy. As a consequence of our construction, we solve the
open problem formulated by Meduna et al. Then we extend these results to
m-state realtime deterministic pushdown automata, for all m at least 1. The
existence of such a hierarchy for m-state deterministic pushdown automata is
left open
Transition Property For Cube-Free Words
We study cube-free words over arbitrary non-unary finite alphabets and prove
the following structural property: for every pair of -ary cube-free
words, if can be infinitely extended to the right and can be infinitely
extended to the left respecting the cube-freeness property, then there exists a
"transition" word over the same alphabet such that is cube free. The
crucial case is the case of the binary alphabet, analyzed in the central part
of the paper.
The obtained "transition property", together with the developed technique,
allowed us to solve cube-free versions of three old open problems by Restivo
and Salemi. Besides, it has some further implications for combinatorics on
words; e.g., it implies the existence of infinite cube-free words of very big
subword (factor) complexity.Comment: 14 pages, 5 figure
Automata theory in nominal sets
We study languages over infinite alphabets equipped with some structure that
can be tested by recognizing automata. We develop a framework for studying such
alphabets and the ensuing automata theory, where the key role is played by an
automorphism group of the alphabet. In the process, we generalize nominal sets
due to Gabbay and Pitts
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
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