2,439 research outputs found
Streamability of nested word transductions
We consider the problem of evaluating in streaming (i.e., in a single
left-to-right pass) a nested word transduction with a limited amount of memory.
A transduction T is said to be height bounded memory (HBM) if it can be
evaluated with a memory that depends only on the size of T and on the height of
the input word. We show that it is decidable in coNPTime for a nested word
transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In
this case, the required amount of memory may depend exponentially on the height
of the word. We exhibit a sufficient, decidable condition for a VPT to be
evaluated with a memory that depends quadratically on the height of the word.
This condition defines a class of transductions that strictly contains all
determinizable VPTs
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Which Classes of Origin Graphs Are Generated by Transducers.
We study various models of transducers equipped with origin information. We consider the semantics of these models as particular graphs, called origin graphs, and we characterise the families of such graphs recognised by streaming string transducers
Streaming Tree Transducers
Theory of tree transducers provides a foundation for understanding
expressiveness and complexity of analysis problems for specification languages
for transforming hierarchically structured data such as XML documents. We
introduce streaming tree transducers as an analyzable, executable, and
expressive model for transforming unranked ordered trees in a single pass.
Given a linear encoding of the input tree, the transducer makes a single
left-to-right pass through the input, and computes the output in linear time
using a finite-state control, a visibly pushdown stack, and a finite number of
variables that store output chunks that can be combined using the operations of
string-concatenation and tree-insertion. We prove that the expressiveness of
the model coincides with transductions definable using monadic second-order
logic (MSO). Existing models of tree transducers either cannot implement all
MSO-definable transformations, or require regular look ahead that prohibits
single-pass implementation. We show a variety of analysis problems such as
type-checking and checking functional equivalence are solvable for our model.Comment: 40 page
Weak MSO+U with Path Quantifiers over Infinite Trees
This paper shows that over infinite trees, satisfiability is decidable for
weak monadic second-order logic extended by the unbounding quantifier U and
quantification over infinite paths. The proof is by reduction to emptiness for
a certain automaton model, while emptiness for the automaton model is decided
using profinite trees.Comment: version of an ICALP 2014 paper with appendice
Learning to Prove Safety over Parameterised Concurrent Systems (Full Version)
We revisit the classic problem of proving safety over parameterised
concurrent systems, i.e., an infinite family of finite-state concurrent systems
that are represented by some finite (symbolic) means. An example of such an
infinite family is a dining philosopher protocol with any number n of processes
(n being the parameter that defines the infinite family). Regular model
checking is a well-known generic framework for modelling parameterised
concurrent systems, where an infinite set of configurations (resp. transitions)
is represented by a regular set (resp. regular transducer). Although verifying
safety properties in the regular model checking framework is undecidable in
general, many sophisticated semi-algorithms have been developed in the past
fifteen years that can successfully prove safety in many practical instances.
In this paper, we propose a simple solution to synthesise regular inductive
invariants that makes use of Angluin's classic L* algorithm (and its variants).
We provide a termination guarantee when the set of configurations reachable
from a given set of initial configurations is regular. We have tested L*
algorithm on standard (as well as new) examples in regular model checking
including the dining philosopher protocol, the dining cryptographer protocol,
and several mutual exclusion protocols (e.g. Bakery, Burns, Szymanski, and
German). Our experiments show that, despite the simplicity of our solution, it
can perform at least as well as existing semi-algorithms.Comment: Full version of FMCAD'17 pape
Linearly bounded infinite graphs
Linearly bounded Turing machines have been mainly studied as acceptors for
context-sensitive languages. We define a natural class of infinite automata
representing their observable computational behavior, called linearly bounded
graphs. These automata naturally accept the same languages as the linearly
bounded machines defining them. We present some of their structural properties
as well as alternative characterizations in terms of rewriting systems and
context-sensitive transductions. Finally, we compare these graphs to rational
graphs, which are another class of automata accepting the context-sensitive
languages, and prove that in the bounded-degree case, rational graphs are a
strict sub-class of linearly bounded graphs
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