1,334 research outputs found
On Functionality of Visibly Pushdown Transducers
Visibly pushdown transducers form a subclass of pushdown transducers that
(strictly) extends finite state transducers with a stack. Like visibly pushdown
automata, the input symbols determine the stack operations. In this paper, we
prove that functionality is decidable in PSpace for visibly pushdown
transducers. The proof is done via a pumping argument: if a word with two
outputs has a sufficiently large nesting depth, there exists a nested word with
two outputs whose nesting depth is strictly smaller. The proof uses technics of
word combinatorics. As a consequence of decidability of functionality, we also
show that equivalence of functional visibly pushdown transducers is
Exptime-Complete.Comment: 20 page
Singularities of Type-Q ABS Equations
The type-Q equations lie on the top level of the hierarchy introduced by
Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts
of KdV-type integrable partial differential equations. We ask what
singularities are possible in the solutions of these equations, and examine the
relationship between the singularities and the principal integrability feature
of multidimensional consistency. These questions are considered in the global
setting and therefore extend previous considerations of singularities which
have been local. What emerges are some simple geometric criteria that determine
the allowed singularities, and the interesting discovery that generically the
presence of singularities leads to a breakdown in the global consistency of
such systems despite their local consistency property. This failure to be
globally consistent is quantified by introducing a natural notion of monodromy
for isolated singularities.Comment: contribution to the SIDE-9 special issue of SIGM
Turing degrees of limit sets of cellular automata
Cellular automata are discrete dynamical systems and a model of computation.
The limit set of a cellular automaton consists of the configurations having an
infinite sequence of preimages. It is well known that these always contain a
computable point and that any non-trivial property on them is undecidable. We
go one step further in this article by giving a full characterization of the
sets of Turing degrees of cellular automata: they are the same as the sets of
Turing degrees of effectively closed sets containing a computable point
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