2,984 research outputs found
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
Logical and Algebraic Characterizations of Rational Transductions
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
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
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
A word-to-word function is continuous for a class of languages~
if its inverse maps _languages to~. 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
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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