4,278 research outputs found

    Formal Properties of XML Grammars and Languages

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    XML documents are described by a document type definition (DTD). An XML-grammar is a formal grammar that captures the syntactic features of a DTD. We investigate properties of this family of grammars. We show that every XML-language basically has a unique XML-grammar. We give two characterizations of languages generated by XML-grammars, one is set-theoretic, the other is by a kind of saturation property. We investigate decidability problems and prove that some properties that are undecidable for general context-free languages become decidable for XML-languages. We also characterize those XML-grammars that generate regular XML-languages.Comment: 24 page

    One-Tape Turing Machine Variants and Language Recognition

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    We present two restricted versions of one-tape Turing machines. Both characterize the class of context-free languages. In the first version, proposed by Hibbard in 1967 and called limited automata, each tape cell can be rewritten only in the first dd visits, for a fixed constant d≥2d\geq 2. Furthermore, for d=2d=2 deterministic limited automata are equivalent to deterministic pushdown automata, namely they characterize deterministic context-free languages. Further restricting the possible operations, we consider strongly limited automata. These models still characterize context-free languages. However, the deterministic version is less powerful than the deterministic version of limited automata. In fact, there exist deterministic context-free languages that are not accepted by any deterministic strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of the September 2015 issue of SIGACT New

    A Characterization of ET0L and EDT0L Languages

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    There exists a PT0L language L0L_0 such that the following holds. A language LL is an ET0L language if and only if there exists a mapping TT induced by an a-NGSM (nondeterministic generalized sequential machine with accepting states) such that L=T(L0)L = T(L_0). There exists an infinite collection of EPDT0L languages Dmn⊆Σmn⋆D_{mn}\subseteq\Sigma_{mn}^\star (n≥m≥1n\geq m\geq 1) such that the family EDT0L is characterized in the following way. A language LL is an EDT0L language if and only if there exists n≥m≥1n\geq m\geq 1, a homomorphism hh and a regular language R⊆Σmn⋆R \subseteq \Sigma_{mn}^\star such that L=h(Dmn∩R)L = h(D_{mn} \cap R).\u

    Analytic aspects of the shuffle product

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    There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of D-finite generating functions, a class which contains algebraic. We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. In the process, we define a grammar class that models D-finite generating functions

    Introspective Pushdown Analysis of Higher-Order Programs

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    In the static analysis of functional programs, pushdown flow analysis and abstract garbage collection skirt just inside the boundaries of soundness and decidability. Alone, each method reduces analysis times and boosts precision by orders of magnitude. This work illuminates and conquers the theoretical challenges that stand in the way of combining the power of these techniques. The challenge in marrying these techniques is not subtle: computing the reachable control states of a pushdown system relies on limiting access during transition to the top of the stack; abstract garbage collection, on the other hand, needs full access to the entire stack to compute a root set, just as concrete collection does. \emph{Introspective} pushdown systems resolve this conflict. Introspective pushdown systems provide enough access to the stack to allow abstract garbage collection, but they remain restricted enough to compute control-state reachability, thereby enabling the sound and precise product of pushdown analysis and abstract garbage collection. Experiments reveal synergistic interplay between the techniques, and the fusion demonstrates "better-than-both-worlds" precision.Comment: Proceedings of the 17th ACM SIGPLAN International Conference on Functional Programming, 2012, AC
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