138 research outputs found

    Regular and First Order List Functions

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    We define two classes of functions, called regular (respectively, first-order) list functions, which manipulate objects such as lists, lists of lists, pairs of lists, lists of pairs of lists, etc. The definition is in the style of regular expressions: the functions are constructed by starting with some basic functions (e.g. projections from pairs, or head and tail operations on lists) and putting them together using four combinators (most importantly, composition of functions). Our main results are that first-order list functions are exactly the same as first-order transductions, under a suitable encoding of the inputs; and the regular list functions are exactly the same as MSO-transductions

    The formal power of one-visit attribute grammars

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    An attribute grammar is one-visit if the attributes can be evaluated by walking through the derivation tree in such a way that each subtree is visited at most once. One-visit (1V) attribute grammars are compared with one-pass left-to-right (L) attribute grammars and with attribute grammars having only one synthesized attribute (1S).\ud \ud Every 1S attribute grammar can be made one-visit. One-visit attribute grammars are simply permutations of L attribute grammars; thus the classes of output sets of 1V and L attribute grammars coincide, and similarly for 1S and L-1S attribute grammars. In case all attribute values are trees, the translation realized by a 1V attribute grammar is the composition of the translation realized by a 1S attribute grammar with a deterministic top-down tree transduction, and vice versa; thus, using a result of Duske e.a., the class of output languages of 1V (or L) attribute grammars is the image of the class of IO macro tree languages under all deterministic top-down tree transductions

    Macro tree transducers

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    Macro tree transducers are a combination of top-down tree transducers and macro grammars. They serve as a model for syntax-directed semantics in which context information can be handled. In this paper the formal model of macro tree transducers is studied by investigating typical automata theoretical topics like composition, decomposition, domains, and ranges of the induced translation classes. The extension with regular look-ahead is considered

    Three hierarchies of transducers

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    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

    Streaming Tree Transducers

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    Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming tree transducers as an analyzable, executable, and expressive model for transforming unranked ordered trees in a single pass. Given a linear encoding of the input tree, the transducer makes a single left-to-right pass through the input, and computes the output in linear time using a finite-state control, a visibly pushdown stack, and a finite number of variables that store output chunks that can be combined using the operations of string-concatenation and tree-insertion. We prove that the expressiveness of the model coincides with transductions definable using monadic second-order logic (MSO). Existing models of tree transducers either cannot implement all MSO-definable transformations, or require regular look ahead that prohibits single-pass implementation. We show a variety of analysis problems such as type-checking and checking functional equivalence are solvable for our model.Comment: 40 page

    Decision Problems for Origin-Close Top-Down Tree Transducers

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    Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to tree transductions, i.e., tagging each output node with the input node it originates from, is a known way to recover decidability for inclusion and equivalence. The origin semantics is rather rigid, in this work, we introduce a similarity measure for transducers with origin semantics and show that we can decide inclusion, equivalence and synthesis problems for origin-close non-deterministic top-down tree transducers
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