13,490 research outputs found
Deterministic Automata for Unordered Trees
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
A regular language is -lookahead deterministic (resp. -block
deterministic) if it is specified by a -lookahead deterministic (resp.
-block deterministic) regular expression. These two subclasses of regular
languages have been respectively introduced by Han and Wood (-lookahead
determinism) and by Giammarresi et al. (-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 -block
deterministic language is the alphabetic image of some one-unambiguous
language. Moreover, we show that the conversion from a minimal DFA of a
-block deterministic regular language to a -block deterministic automaton
not only requires state elimination, and that the proof given by Han and Wood
of a proper hierarchy in -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 -block deterministic regular languages.
We also prove that there is a proper hierarchy in -lookahead deterministic
regular languages by studying particular properties of unary regular
expressions. Finally, using our valid results, we confirm that the family of
-block deterministic regular languages is strictly included into the one of
-lookahead deterministic regular languages by showing that any -block
deterministic unary language is one-unambiguous
Forward Analysis and Model Checking for Trace Bounded WSTS
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 -regular properties on the
set of infinite traces of the system
Two-Way Visibly Pushdown Automata and Transducers
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
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
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
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