13,490 research outputs found

    Deterministic Automata for Unordered Trees

    Get PDF
    Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of determinism, which makes it difficult to distinguish subclasses of automata for which problems such as inclusion, equivalence, and minimization can be solved efficiently. In this paper, we propose and investigate different notions of "horizontal determinism", starting from automata for unranked trees in which the horizontal evaluation is performed by finite state automata. We show that a restriction to confluent horizontal evaluation leads to polynomial-time emptiness and universality, but still suffers from coNP-completeness of the emptiness of binary intersections. Finally, efficient algorithms can be obtained by imposing an order of horizontal evaluation globally for all automata in the class. Depending on the choice of the order, we obtain different classes of automata, each of which has the same expressiveness as CMso.Comment: In Proceedings GandALF 2014, arXiv:1408.556

    On the Hierarchy of Block Deterministic Languages

    Full text link
    A regular language is kk-lookahead deterministic (resp. kk-block deterministic) if it is specified by a kk-lookahead deterministic (resp. kk-block deterministic) regular expression. These two subclasses of regular languages have been respectively introduced by Han and Wood (kk-lookahead determinism) and by Giammarresi et al. (kk-block determinism) as a possible extension of one-unambiguous languages defined and characterized by Br\"uggemann-Klein and Wood. In this paper, we study the hierarchy and the inclusion links of these families. We first show that each kk-block deterministic language is the alphabetic image of some one-unambiguous language. Moreover, we show that the conversion from a minimal DFA of a kk-block deterministic regular language to a kk-block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper hierarchy in kk-block deterministic languages based on this result is erroneous. Despite these results, we show by giving a parameterized family that there is a proper hierarchy in kk-block deterministic regular languages. We also prove that there is a proper hierarchy in kk-lookahead deterministic regular languages by studying particular properties of unary regular expressions. Finally, using our valid results, we confirm that the family of kk-block deterministic regular languages is strictly included into the one of kk-lookahead deterministic regular languages by showing that any kk-block deterministic unary language is one-unambiguous

    Forward Analysis and Model Checking for Trace Bounded WSTS

    Full text link
    We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all ω\omega-regular properties on the set of infinite traces of the system

    Two-Way Visibly Pushdown Automata and Transducers

    Full text link
    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

    Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages

    Full text link
    For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular properties, in contrast to pure PDL. For regular, visibly pushdown and deterministic context-free languages, the separation of the respective PDLs can be proven by automata-theoretic techniques. However, these techniques introduce non-determinism on the automata side. As non-determinism is also the difference between DCFL and CFL, these techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL]. Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081

    Forms of Determinism for Automata

    Get PDF
    International audienceWe survey in this paper some variants of the notion of determinism, refining the spectrum between non-determinism and determinism. We present unambiguous automata, strongly unambiguous automata, prophetic automata, guidable automata, and history-deterministic automata. We instantiate these various notions for finite words, infinite words, finite trees, infinite trees, data languages, and cost functions. The main results are underlined and some open problems proposed
    corecore