663 research outputs found
On the k-Boundedness for Existential Rules
The chase is a fundamental tool for existential rules. Several chase variants
are known, which differ on how they handle redundancies possibly caused by the
introduction of nulls. Given a chase variant, the halting problem takes as
input a set of existential rules and asks if this set of rules ensures the
termination of the chase for any factbase. It is well-known that this problem
is undecidable for all known chase variants. The related problem of boundedness
asks if a given set of existential rules is bounded, i.e., whether there is a
predefined upper bound on the number of (breadth-first) steps of the chase,
independently from any factbase. This problem is already undecidable in the
specific case of datalog rules. However, knowing that a set of rules is bounded
for some chase variant does not help much in practice if the bound is unknown.
Hence, in this paper, we investigate the decidability of the k-boundedness
problem, which asks whether a given set of rules is bounded by an integer k. We
prove that k-boundedness is decidable for three chase variants, namely the
oblivious, semi-oblivious and restricted chase.Comment: 20 pages, revised version of the paper published at RuleML+RR 201
A Nearly Optimal Lower Bound on the Approximate Degree of AC
The approximate degree of a Boolean function is the least degree of a real polynomial that
approximates pointwise to error at most . We introduce a generic
method for increasing the approximate degree of a given function, while
preserving its computability by constant-depth circuits.
Specifically, we show how to transform any Boolean function with
approximate degree into a function on variables with approximate degree at least . In particular, if , then
is polynomially larger than . Moreover, if is computed by a
polynomial-size Boolean circuit of constant depth, then so is .
By recursively applying our transformation, for any constant we
exhibit an AC function of approximate degree . This
improves over the best previous lower bound of due to
Aaronson and Shi (J. ACM 2004), and nearly matches the trivial upper bound of
that holds for any function. Our lower bounds also apply to
(quasipolynomial-size) DNFs of polylogarithmic width.
We describe several applications of these results. We give:
* For any constant , an lower bound on the
quantum communication complexity of a function in AC.
* A Boolean function with approximate degree at least ,
where is the certificate complexity of . This separation is optimal
up to the term in the exponent.
* Improved secret sharing schemes with reconstruction procedures in AC.Comment: 40 pages, 1 figur
Type-Based Detection of XML Query-Update Independence
This paper presents a novel static analysis technique to detect XML
query-update independence, in the presence of a schema. Rather than types, our
system infers chains of types. Each chain represents a path that can be
traversed on a valid document during query/update evaluation. The resulting
independence analysis is precise, although it raises a challenging issue:
recursive schemas may lead to infer infinitely many chains. A sound and
complete approximation technique ensuring a finite analysis in any case is
presented, together with an efficient implementation performing the chain-based
analysis in polynomial space and time.Comment: VLDB201
Meta-model Pruning
Large and complex meta-models such as those of Uml and its profiles are growing due to modelling and inter-operability needs of numerous\ud
stakeholders. The complexity of such meta-models has led to coining\ud
of the term meta-muddle. Individual users often exercise only a small\ud
view of a meta-muddle for tasks ranging from model creation to construction\ud
of model transformations. What is the effective meta-model that represents\ud
this view? We present a flexible meta-model pruning algorithm and\ud
tool to extract effective meta-models from a meta-muddle. We use\ud
the notion of model typing for meta-models to verify that the algorithm\ud
generates a super-type of the large meta-model representing the meta-muddle.\ud
This implies that all programs written using the effective meta-model\ud
will work for the meta-muddle hence preserving backward compatibility.\ud
All instances of the effective meta-model are also instances of the\ud
meta-muddle. We illustrate how pruning the original Uml metamodel\ud
produces different effective meta-models
Definitions by Rewriting in the Calculus of Constructions
The main novelty of this paper is to consider an extension of the Calculus of
Constructions where predicates can be defined with a general form of rewrite
rules. We prove the strong normalization of the reduction relation generated by
the beta-rule and the user-defined rules under some general syntactic
conditions including confluence. As examples, we show that two important
systems satisfy these conditions: a sub-system of the Calculus of Inductive
Constructions which is the basis of the proof assistant Coq, and the Natural
Deduction Modulo a large class of equational theories.Comment: Best student paper (Kleene Award
- âŠ