8,003 research outputs found
The Fibers and Range of Reduction Graphs in Ciliates
The biological process of gene assembly has been modeled based on three types
of string rewriting rules, called string pointer rules, defined on so-called
legal strings. It has been shown that reduction graphs, graphs that are based
on the notion of breakpoint graph in the theory of sorting by reversal, for
legal strings provide valuable insights into the gene assembly process. We
characterize which legal strings obtain the same reduction graph (up to
isomorphism), and moreover we characterize which graphs are (isomorphic to)
reduction graphs.Comment: 24 pages, 13 figure
On Constructor Rewrite Systems and the Lambda Calculus
We prove that orthogonal constructor term rewrite systems and lambda-calculus
with weak (i.e., no reduction is allowed under the scope of a
lambda-abstraction) call-by-value reduction can simulate each other with a
linear overhead. In particular, weak call-by- value beta-reduction can be
simulated by an orthogonal constructor term rewrite system in the same number
of reduction steps. Conversely, each reduction in a term rewrite system can be
simulated by a constant number of beta-reduction steps. This is relevant to
implicit computational complexity, because the number of beta steps to normal
form is polynomially related to the actual cost (that is, as performed on a
Turing machine) of normalization, under weak call-by-value reduction.
Orthogonal constructor term rewrite systems and lambda-calculus are thus both
polynomially related to Turing machines, taking as notion of cost their natural
parameters.Comment: 27 pages. arXiv admin note: substantial text overlap with
arXiv:0904.412
Functional Dependencies Unleashed for Scalable Data Exchange
We address the problem of efficiently evaluating target functional
dependencies (fds) in the Data Exchange (DE) process. Target fds naturally
occur in many DE scenarios, including the ones in Life Sciences in which
multiple source relations need to be structured under a constrained target
schema. However, despite their wide use, target fds' evaluation is still a
bottleneck in the state-of-the-art DE engines. Systems relying on an all-SQL
approach typically do not support target fds unless additional information is
provided. Alternatively, DE engines that do include these dependencies
typically pay the price of a significant drop in performance and scalability.
In this paper, we present a novel chase-based algorithm that can efficiently
handle arbitrary fds on the target. Our approach essentially relies on
exploiting the interactions between source-to-target (s-t) tuple-generating
dependencies (tgds) and target fds. This allows us to tame the size of the
intermediate chase results, by playing on a careful ordering of chase steps
interleaving fds and (chosen) tgds. As a direct consequence, we importantly
diminish the fd application scope, often a central cause of the dramatic
overhead induced by target fds. Moreover, reasoning on dependency interaction
further leads us to interesting parallelization opportunities, yielding
additional scalability gains. We provide a proof-of-concept implementation of
our chase-based algorithm and an experimental study aiming at gauging its
scalability with respect to a number of parameters, among which the size of
source instances and the number of dependencies of each tested scenario.
Finally, we empirically compare with the latest DE engines, and show that our
algorithm outperforms them
!-Graphs with Trivial Overlap are Context-Free
String diagrams are a powerful tool for reasoning about composite structures
in symmetric monoidal categories. By representing string diagrams as graphs,
equational reasoning can be done automatically by double-pushout rewriting.
!-graphs give us the means of expressing and proving properties about whole
families of these graphs simultaneously. While !-graphs provide elegant proofs
of surprisingly powerful theorems, little is known about the formal properties
of the graph languages they define. This paper takes the first step in
characterising these languages by showing that an important subclass of
!-graphs--those whose repeated structures only overlap trivially--can be
encoded using a (context-free) vertex replacement grammar.Comment: In Proceedings GaM 2015, arXiv:1504.0244
Dimensional Confluence Algebra of Information Space Modulo Quotient Abstraction Relations in Automated Problem Solving Paradigm
Confluence in abstract parallel category systems is established for net
class-rewriting in iterative closed multilevel quotient graph structures with
uncountable node arities by multi-dimensional transducer operations in
topological metrics defined by alphabetically abstracting net block
homomorphism. We obtain minimum prerequisites for the comprehensive connector
pairs in a multitude dimensional rewriting closure generating confluence in
Participatory algebra for different horizontal and vertical level projections
modulo abstraction relations constituting formal semantics for confluence in
information space. Participatory algebra with formal automata syntax in its
entirety representing automated problem solving paradigm generates rich variety
of multitude confluence harmonizers under each fundamental abstraction relation
set, horizontal structure mapping and vertical process iteration cardinality.Comment: The current work is an application as a continuation for my previous
works in arXiv:1305.5637 and arXiv:1308.5321 using the key definitions of
them sustaining consistency, consequently references being minimized. Readers
are strongly advised to resort to the mentioned previous works for
preliminaries. arXiv admin note: text overlap with arXiv:1408.137
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