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An ever present, common sense idea in language modelling research is that, for a
word to be a valid phrase, it should comply with multiple constraints at
once. A new language definition model is studied, based on agreement or consensus
between similar strings. Considering a regular set of strings over a bipartite
alphabet made by pairs of unmarked/marked symbols, a match relation is
introduced, in order to specify when such strings agree. Then a regular set
over the bipartite alphabet can be interpreted...
A deterministic automaton recognizing a given
ω-regular language
is constructed from an ω-regular expression
with the help of derivatives.
The construction is related to Safra's algorithm,
in about the same way as the classical
derivative method is related to the subset construction.
Since recognizable tree languages are closed under the rational operations, every regular tree expression denotes a recognizable tree language. We provide an alternative proof to this fact that results in smaller tree automata. To this aim, we transfer Antimirov's partial derivatives from regular word expressions to regular tree expressions. For an analysis of the size of the resulting automaton as well as for algorithmic improvements, we also transfer the methods of Champarnaud and Ziadi from words...
Since recognizable tree languages are closed under the rational
operations, every regular tree expression denotes a recognizable
tree language. We provide an alternative proof to this fact that
results in smaller tree automata. To this aim, we transfer
Antimirov's partial derivatives from regular word expressions to
regular tree expressions. For an analysis of the size of the
resulting automaton as well as for algorithmic improvements, we also
transfer the methods of Champarnaud and Ziadi...
We consider conversions of regular expressions into k-realtime
finite state automata, i.e., automata in which the number of
consecutive uses of ε-transitions, along any computation path,
is bounded by a fixed constant k. For 2-realtime automata,
i.e., for automata that cannot change the state, without reading
an input symbol, more than two times in a row, we show that the
conversion of a regular expression into such an automaton produces
only O(n) states, O(nlogn) ε-transitions, and O(n)
alphabet-transitions....
We formulate a few basic concepts of J. H. Conway's theory of games based on his book [6]. This is a first step towards formalizing Conway's theory of numbers into Mizar, which is an approach to proving the existence of a FIELD (i.e., a proper class that satisfies the axioms of a real-closed field) that includes the reals and ordinals, thus providing a uniform, independent and simple approach to these two constructions that does not go via the rational numbers and hence does for example not need...
In a previous paper, we have described the construction of an
automaton from a rational expression which has the property that
the automaton built from an expression which is itself computed
from a co-deterministic automaton by the state elimination method
is co-deterministic.
It turned out that the definition on which the construction is
based was inappropriate, and thus the proof of the property was
flawed.
We give here the correct definition of the broken derived terms
of an...
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