6,525 research outputs found
Context-Free Path Querying with Structural Representation of Result
Graph data model and graph databases are very popular in various areas such
as bioinformatics, semantic web, and social networks. One specific problem in
the area is a path querying with constraints formulated in terms of formal
grammars. The query in this approach is written as grammar, and paths querying
is graph parsing with respect to given grammar. There are several solutions to
it, but how to provide structural representation of query result which is
practical for answer processing and debugging is still an open problem. In this
paper we propose a graph parsing technique which allows one to build such
representation with respect to given grammar in polynomial time and space for
arbitrary context-free grammar and graph. Proposed algorithm is based on
generalized LL parsing algorithm, while previous solutions are based mostly on
CYK or Earley algorithms, which reduces time complexity in some cases.Comment: Evaluation extende
Computation of distances for regular and context-free probabilistic languages
Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe
Sparse Automatic Differentiation for Large-Scale Computations Using Abstract Elementary Algebra
Most numerical solvers and libraries nowadays are implemented to use
mathematical models created with language-specific built-in data types (e.g.
real in Fortran or double in C) and their respective elementary algebra
implementations. However, built-in elementary algebra typically has limited
functionality and often restricts flexibility of mathematical models and
analysis types that can be applied to those models. To overcome this
limitation, a number of domain-specific languages with more feature-rich
built-in data types have been proposed. In this paper, we argue that if
numerical libraries and solvers are designed to use abstract elementary algebra
rather than language-specific built-in algebra, modern mainstream languages can
be as effective as any domain-specific language. We illustrate our ideas using
the example of sparse Jacobian matrix computation. We implement an automatic
differentiation method that takes advantage of sparse system structures and is
straightforward to parallelize in MPI setting. Furthermore, we show that the
computational cost scales linearly with the size of the system.Comment: Submitted to ACM Transactions on Mathematical Softwar
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