191 research outputs found
The Equivalence Problem for Deterministic MSO Tree Transducers is Decidable
It is decidable for deterministic MSO definable graph-to-string or
graph-to-tree transducers whether they are equivalent on a context-free set of
graphs
Linear Bounded Composition of Tree-Walking Tree Transducers: Linear Size Increase and Complexity
Compositions of tree-walking tree transducers form a hierarchy with respect
to the number of transducers in the composition. As main technical result it is
proved that any such composition can be realized as a linear bounded
composition, which means that the sizes of the intermediate results can be
chosen to be at most linear in the size of the output tree. This has
consequences for the expressiveness and complexity of the translations in the
hierarchy. First, if the computed translation is a function of linear size
increase, i.e., the size of the output tree is at most linear in the size of
the input tree, then it can be realized by just one, deterministic,
tree-walking tree transducer. For compositions of deterministic transducers it
is decidable whether or not the translation is of linear size increase. Second,
every composition of deterministic transducers can be computed in deterministic
linear time on a RAM and in deterministic linear space on a Turing machine,
measured in the sum of the sizes of the input and output tree. Similarly, every
composition of nondeterministic transducers can be computed in simultaneous
polynomial time and linear space on a nondeterministic Turing machine. Their
output tree languages are deterministic context-sensitive, i.e., can be
recognized in deterministic linear space on a Turing machine. The membership
problem for compositions of nondeterministic translations is nondeterministic
polynomial time and deterministic linear space. The membership problem for the
composition of a nondeterministic and a deterministic tree-walking tree
translation (for a nondeterministic IO macro tree translation) is log-space
reducible to a context-free language, whereas the membership problem for the
composition of a deterministic and a nondeterministic tree-walking tree
translation (for a nondeterministic OI macro tree translation) is possibly
NP-complete
Tree transducers, L systems, and two-way machines
A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the âcopying powerâ 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
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
XQuery Streaming by Forest Transducers
Streaming of XML transformations is a challenging task and only very few
systems support streaming. Research approaches generally define custom
fragments of XQuery and XPath that are amenable to streaming, and then design
custom algorithms for each fragment. These languages have several shortcomings.
Here we take a more principles approach to the problem of streaming
XQuery-based transformations. We start with an elegant transducer model for
which many static analysis problems are well-understood: the Macro Forest
Transducer (MFT). We show that a large fragment of XQuery can be translated
into MFTs --- indeed, a fragment of XQuery, that can express important features
that are missing from other XQuery stream engines, such as GCX: our fragment of
XQuery supports XPath predicates and let-statements. We then rely on a
streaming execution engine for MFTs, one which uses a well-founded set of
optimizations from functional programming, such as strictness analysis and
deforestation. Our prototype achieves time and memory efficiency comparable to
the fastest known engine for XQuery streaming, GCX. This is surprising because
our engine relies on the OCaml built in garbage collector and does not use any
specialized buffer management, while GCX's efficiency is due to clever and
explicit buffer management.Comment: Full version of the paper in the Proceedings of the 30th IEEE
International Conference on Data Engineering (ICDE 2014
Pebble alternating tree-walking automata and their recognizing power
Pebble tree-walking automata with alternation were first investigated by Milo, Suciu and Vianu (2003), who showed that tree languages recognized by these devices are exactly the regular tree languages. We strengthen this by proving the same result for pebble automata with "strong pebble handling" which means that pebbles can be lifted independently of the position of the reading head and without moving the reading head. Then we make a comparison among some restricted versions of these automata. We will show that the deterministic and non-looping pebble alternating tree-walking automata are strictly less powerful than their nondeterministic counterparts, i.e., they do not recognize all the regular tree languages. Moreover, there is a proper hierarchy of recognizing capacity of deterministic and non-looping n-pebble alternating tree-walking automata with respect to the number of pebbles, i.e., for each n â„ 0, deterministic and non-looping (n+1)-pebble alternating tree-walking automata are more powerful than their n-pebble counterparts
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 â but not under a certain âmapâcombinator â 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 âmapâ and equivalent to acorresponding notion of (k + 1)-layered HDT0L systems
AutomatĂĄk, fĂĄk Ă©s logika = Automata, trees and logic
Elemi idejƱ exponenciĂĄlis algoritmus adtunk meg regulĂĄris szavak ekvivalenciĂĄjĂĄnak eldönthetĆsĂ©gĂ©re. ĂltalĂĄnosĂtottuk Kleene tĂ©telĂ©t vĂ©gtelen szavakat is felismerĆ sĂșlyozott automatĂĄkra. KifejlesztettĂŒnk egy algebrai mĂłdszert, amellyel a CTL logika szĂĄmos szegmense estĂ©n eldönthetĆ, hogy egy regulĂĄris fanyelv definiĂĄlhatĂł-e a szegmensben. VizsgĂĄltuk a faautomatĂĄk algebrai tulajdonsĂĄgait, megadtuk a felismerhetĆsĂ©g egy algebrai jellemzĂ©sĂ©t. DefiniĂĄltunk a multi-leszĂĄllĂł fatranszformĂĄtort Ă©s megmutattuk, hogy ekvivalens a determinisztikus regulĂĄris szƱkĂtĂ©sƱ felszĂĄllĂł fatranszformĂĄtorral. MeghatĂĄroztuk a lineĂĄris multi-leszĂĄllĂł osztĂĄly szĂĄmĂtĂĄsi erejĂ©t. Megmutattuk, hogy az alakmegĆrzĆ leszĂĄllĂł fatranszformĂĄtorok ekvivalensek az ĂĄtcĂmkĂ©zĆkkel Ă©s bebizonyĂtottuk, hogy az alakmegĆrzĆ tulajdonsĂĄg eldönthetĆ. Megadtuk a kavics makrĂł fatranszformĂĄciĂłk egy felbontĂĄsĂĄt Ă©s megmutattuk, hogy a kĂŒlönbözĆ cirkularitĂĄsi tulajdonsĂĄgok eldönthetĆk. Ugyancsak megadtuk a felbontĂĄst erĆs kavics kezelĂ©s estĂ©n is. ĂltalĂĄnosĂtottuk J. Engelfriet hiararchia tĂ©telĂ©t sĂșlyozott fatranszformĂĄtorokra. SĂșlyozott faautomatĂĄkra definiĂĄltuk a termĂĄtĂrĂł szemantikĂĄt Ă©s megmutattuk, hogy ekvivalens az algebari szenmatikĂĄval. Algoritmust adtunk annak eldöntĂ©sĂ©re, hogy egy polinomiĂĄlisan sĂșlyozott faautomata vĂ©ges költsĂ©gƱ-e. VizsgĂĄltuk a sĂșlyozott faautomata kĂŒlönbözĆ vĂĄltozatait: fuzzy faautomata, multioperĂĄtor monoid feletti faautomata, Ez utĂłbbi esetre ĂĄltalĂĄnosĂtottuk a Kleene tĂ©telt. | We gave an elementary algorithm for deciding the equivalence of regular words. We generalized Kleene's theorem to weighted automata processing infinite words. We developed an algebraic method that, for several segments of the CTL logic, can be applied to decide if a regular tree language can be defined in that segment. We examined algebraic properties of tree automata, and gave an algebraic characterization of recognizability. We defined multi bottom-up tree transducers and showed that they are equivalent to top-down tree transducers with regular look-ahead. We determined the computation power of the linear subclass. We showed that shape preserving bottom-up tree transducers are equivalent to relabelings. We proved that the shape preserving property is decidable. We gave a decomposition for pebble macro tree transducers and showed that certain circularity properties are decidable. We also gave a decomposition for the strong pebble handling. We have generalized the hierarchy theorem of J. Engelfriet to weighted tree transducers. We defined the term rewrite semantics of weighted tree transducers and showed that it is equivalent to the algebraic semantics. We gave a decision algorithm for the finite cost property of a polynomially weighted tree automata. We defined different versions of weighted tree automata: fuzzy tree automata, weighted tree automata over a multioperator monoid. For the latter we generalized Kleene's theorem
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