19,717 research outputs found
Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the
state-complexity of representing sub- or superword closures of context-free
grammars (CFGs): (1) We prove a (tight) upper bound of on
the size of nondeterministic finite automata (NFAs) representing the subword
closure of a CFG of size . (2) We present a family of CFGs for which the
minimal deterministic finite automata representing their subword closure
matches the upper-bound of following from (1).
Furthermore, we prove that the inequivalence problem for NFAs representing sub-
or superword-closed languages is only NP-complete as opposed to PSPACE-complete
for general NFAs. Finally, we extend our results into an approximation method
to attack inequivalence problems for CFGs
A Note on the Complexity of Restricted Attribute-Value Grammars
The recognition problem for attribute-value grammars (AVGs) was shown to be
undecidable by Johnson in 1988. Therefore, the general form of AVGs is of no
practical use. In this paper we study a very restricted form of AVG, for which
the recognition problem is decidable (though still NP-complete), the R-AVG. We
show that the R-AVG formalism captures all of the context free languages and
more, and introduce a variation on the so-called `off-line parsability
constraint', the `honest parsability constraint', which lets different types of
R-AVG coincide precisely with well-known time complexity classes.Comment: 18 pages, also available by (1) anonymous ftp at
ftp://ftp.fwi.uva.nl/pub/theory/illc/researchReports/CT-95-02.ps.gz ; (2) WWW
from http://www.fwi.uva.nl/~mtrautwe
Implicit learning of recursive context-free grammars
Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning
experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have
not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing
features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured
the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both
distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes
even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between
individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for
tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex
context-free structures, which model some features of natural languages. They support the relevance of artificial grammar
learning for probing mechanisms of language learning and challenge existing theories and computational models of
implicit learning
On non-recursive trade-offs between finite-turn pushdown automata
It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive tradeoffs. Considering the number of turns of the stack height as a consumable resource of PDAs, we can show the existence of non-recursive trade-offs between PDAs performing k+ 1 turns and k turns for k >= 1. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. Finally, several decidability questions are shown to be undecidable and not semidecidable
Search and Result Presentation in Scientific Workflow Repositories
We study the problem of searching a repository of complex hierarchical
workflows whose component modules, both composite and atomic, have been
annotated with keywords. Since keyword search does not use the graph structure
of a workflow, we develop a model of workflows using context-free bag grammars.
We then give efficient polynomial-time algorithms that, given a workflow and a
keyword query, determine whether some execution of the workflow matches the
query. Based on these algorithms we develop a search and ranking solution that
efficiently retrieves the top-k grammars from a repository. Finally, we propose
a novel result presentation method for grammars matching a keyword query, based
on representative parse-trees. The effectiveness of our approach is validated
through an extensive experimental evaluation
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
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