192 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
Multiple Context-Free Tree Grammars: Lexicalization and Characterization
Multiple (simple) context-free tree grammars are investigated, where "simple"
means "linear and nondeleting". Every multiple context-free tree grammar that
is finitely ambiguous can be lexicalized; i.e., it can be transformed into an
equivalent one (generating the same tree language) in which each rule of the
grammar contains a lexical symbol. Due to this transformation, the rank of the
nonterminals increases at most by 1, and the multiplicity (or fan-out) of the
grammar increases at most by the maximal rank of the lexical symbols; in
particular, the multiplicity does not increase when all lexical symbols have
rank 0. Multiple context-free tree grammars have the same tree generating power
as multi-component tree adjoining grammars (provided the latter can use a
root-marker). Moreover, every multi-component tree adjoining grammar that is
finitely ambiguous can be lexicalized. Multiple context-free tree grammars have
the same string generating power as multiple context-free (string) grammars and
polynomial time parsing algorithms. A tree language can be generated by a
multiple context-free tree grammar if and only if it is the image of a regular
tree language under a deterministic finite-copying macro tree transducer.
Multiple context-free tree grammars can be used as a synchronous translation
device.Comment: 78 pages, 13 figure
Revisiting the growth of polyregular functions: output languages, weighted automata and unary inputs
Polyregular functions are the class of string-to-string functions definable
by pebble transducers (an extension of finite automata) or equivalently by MSO
interpretations (a logical formalism). Their output length is bounded by a
polynomial in the input length: a function computed by a -pebble transducer
or by a -dimensional MSO interpretation has growth rate .
Boja\'nczyk has recently shown that the converse holds for MSO
interpretations, but not for pebble transducers. We give significantly
simplified proofs of those two results, extending the former to first-order
interpretations by reduction to an elementary property of -weighted
automata. For any , we also prove the stronger statement that there is some
quadratic polyregular function whose output language differs from that of any
-fold composition of macro tree transducers (and which therefore cannot be
computed by any -pebble transducer).
In the special case of unary input alphabets, we show that pebbles
suffice to compute polyregular functions of growth . This is obtained
as a corollary of a basis of simple word sequences whose ultimately periodic
combinations generate all polyregular functions with unary input. Finally, we
study polyregular and polyblind functions between unary alphabets (i.e. integer
sequences), as well as their first-order subclasses.Comment: 27 pages, not submitted ye
Tree transducers, L systems, and two-way machines
A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results
The copying power of one-state tree transducers
One-state deterministic top-down tree transducers (or, tree homomorphisms) cannot handle "prime copying," i.e., their class of output (string) languages is not closed under the operation L → {)f(n) w ε L, f(n) ≥ 1}, where f is any integer function whose range contains numbers with arbitrarily large prime factors (such as a polynomial). The exact amount of nonclosure under these copying operations is established for several classes of input (tree) languages. These results are relevant to the extended definable (or, restricted parallel level) languages, to the syntax-directed translation of context-free languages, and to the tree transducer hierarchy.\ud
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Three hierarchies of transducers
Composition of top-down tree transducers yields a proper hierarchy of transductions and of output languages. The same is true for ETOL systems (viewed as transducers) and for two-way generalized sequential machines
Comparison-Free Polyregular Functions.
This paper introduces a new automata-theoretic class of string-to-string functions with polynomialgrowth. Several equivalent definitions are provided: a machine model which is a restricted variant ofpebble transducers, and a few inductive definitions that close the class of regular functions undercertain operations. Our motivation for studying this class comes from another characterization,which we merely mention here but prove elsewhere, based on a λ-calculus with a linear type system.As their name suggests, these comparison-free polyregular functions form a subclass of polyregularfunctions; we prove that the inclusion is strict. We also show that they are incomparable withHDT0L transductions, closed under usual function composition – but not under a certain “map”combinator – and satisfy a comparison-free version of the pebble minimization theorem.On the broader topic of polynomial growth transductions, we also consider the recently introducedlayered streaming string transducers (SSTs), or equivalently k-marble transducers. We prove that afunction can be obtained by composing such transducers together if and only if it is polyregular,and that k-layered SSTs (or k-marble transducers) are closed under “map” and equivalent to acorresponding notion of (k + 1)-layered HDT0L systems
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