2,984 research outputs found

    Two-Way Visibly Pushdown Automata and Transducers

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    Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three following models are equivalent: deterministic two-way transducers, monadic second-order (MSO) transducers, and deterministic one-way automata equipped with a finite number of registers. Nested words are words with a nesting structure, allowing to model unranked trees as their depth-first-search linearisations. In this paper, we consider transformations from nested words to words, allowing in particular to produce unranked trees if output words have a nesting structure. The model of visibly pushdown transducers allows to describe such transformations, and we propose a simple deterministic extension of this model with two-way moves that has the following properties: i) it is a simple computational model, that naturally has a good evaluation complexity; ii) it is expressive: it subsumes nested word-to-word MSO transducers, and the exact expressiveness of MSO transducers is recovered using a simple syntactic restriction; iii) it has good algorithmic/closure properties: the model is closed under composition with a unambiguous one-way letter-to-letter transducer which gives closure under regular look-around, and has a decidable equivalence problem

    Logical and Algebraic Characterizations of Rational Transductions

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    Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic congruences allows to decide whether a regular language is aperiodic. We lift this decidability result to rational transductions, i.e., word-to-word functions defined by finite state transducers. In this context, logical and algebraic characterizations have also been proposed. Our main result is that one can decide if a rational transduction (given as a transducer) is in a given decidable congruence class. We also establish a transfer result from logic-algebra equivalences over languages to equivalences over transductions. As a consequence, it is decidable if a rational transduction is first-order definable, and we show that this problem is PSPACE-complete

    Relational Constraint Driven Test Case Synthesis for Web Applications

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    This paper proposes a relational constraint driven technique that synthesizes test cases automatically for web applications. Using a static analysis, servlets can be modeled as relational transducers, which manipulate backend databases. We present a synthesis algorithm that generates a sequence of HTTP requests for simulating a user session. The algorithm relies on backward symbolic image computation for reaching a certain database state, given a code coverage objective. With a slight adaptation, the technique can be used for discovering workflow attacks on web applications.Comment: In Proceedings TAV-WEB 2010, arXiv:1009.330

    Synchronous Subsequentiality and Approximations to Undecidable Problems

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    We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an infinite automaton, then most decision problems (apart from membership) still remain undecidable (as they are for synchronous and subsequential rational relations), but on the positive side, they can be approximated in a meaningful way we make precise in this paper. This might make the class useful for some applications, and might serve to establish an intermediate position in the trade-off between issues of expressivity and (un)decidability.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

    Continuity of Functional Transducers: A Profinite Study of Rational Functions

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    A word-to-word function is continuous for a class of languages~V\mathcal{V} if its inverse maps V\mathcal{V}_languages to~V\mathcal{V}. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some circuit complexity classes. Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages. To this end, we develop a robust theory rooted in the standard profinite analysis of regular languages. Since previous algebraic studies of transducers have focused on the sole structure of the underlying input automaton, we also compare the two algebraic approaches. We focus on two questions: When are the automaton structure and the continuity properties related, and when does continuity propagate to superclasses

    Aperiodic String Transducers

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    Regular string-to-string functions enjoy a nice triple characterization through deterministic two-way transducers (2DFT), streaming string transducers (SST) and MSO definable functions. This result has recently been lifted to FO definable functions, with equivalent representations by means of aperiodic 2DFT and aperiodic 1-bounded SST, extending a well-known result on regular languages. In this paper, we give three direct transformations: i) from 1-bounded SST to 2DFT, ii) from 2DFT to copyless SST, and iii) from k-bounded to 1-bounded SST. We give the complexity of each construction and also prove that they preserve the aperiodicity of transducers. As corollaries, we obtain that FO definable string-to-string functions are equivalent to SST whose transition monoid is finite and aperiodic, and to aperiodic copyless SST
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