11,124 research outputs found
Splittability of bilexical context-free grammars is undecidable
Bilexical context-free grammars (2-LCFGs) have proved to be accurate models for statistical natural language parsing. Existing dynamic programming algorithms used to parse sentences under these models have running time of O(|w|^4), where w is the input string. A 2-LCFG is splittable if the left arguments of a lexical head are always independent of the right arguments, and vice versa. When a 2-LCFGs is splittable, parsing time can be asymptotically improved to O(|w|^3). Testing this propertyis therefore of central interest to parsing efficiency. In this article, however, we show the negative result that splittability of 2-LCFGs is undecidable.Publisher PDFPeer reviewe
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
Digraph Complexity Measures and Applications in Formal Language Theory
We investigate structural complexity measures on digraphs, in particular the
cycle rank. This concept is intimately related to a classical topic in formal
language theory, namely the star height of regular languages. We explore this
connection, and obtain several new algorithmic insights regarding both cycle
rank and star height. Among other results, we show that computing the cycle
rank is NP-complete, even for sparse digraphs of maximum outdegree 2.
Notwithstanding, we provide both a polynomial-time approximation algorithm and
an exponential-time exact algorithm for this problem. The former algorithm
yields an O((log n)^(3/2))- approximation in polynomial time, whereas the
latter yields the optimum solution, and runs in time and space O*(1.9129^n) on
digraphs of maximum outdegree at most two. Regarding the star height problem,
we identify a subclass of the regular languages for which we can precisely
determine the computational complexity of the star height problem. Namely, the
star height problem for bideterministic languages is NP-complete, and this
holds already for binary alphabets. Then we translate the algorithmic results
concerning cycle rank to the bideterministic star height problem, thus giving a
polynomial-time approximation as well as a reasonably fast exact exponential
algorithm for bideterministic star height.Comment: 19 pages, 1 figur
Phrase structure grammars as indicative of uniquely human thoughts
I argue that the ability to compute phrase structure grammars is indicative of a particular kind of thought. This type of thought that is only available to cognitive systems that have access to the computations that allow the generation and interpretation of the structural descriptions of phrase structure grammars. The study of phrase structure grammars, and formal language theory in general, is thus indispensable to studies of human cognition, for it makes explicit both the unique type of human thought and the underlying mechanisms in virtue of which this thought is made possible
An Introduction to Programming for Bioscientists: A Python-based Primer
Computing has revolutionized the biological sciences over the past several
decades, such that virtually all contemporary research in the biosciences
utilizes computer programs. The computational advances have come on many
fronts, spurred by fundamental developments in hardware, software, and
algorithms. These advances have influenced, and even engendered, a phenomenal
array of bioscience fields, including molecular evolution and bioinformatics;
genome-, proteome-, transcriptome- and metabolome-wide experimental studies;
structural genomics; and atomistic simulations of cellular-scale molecular
assemblies as large as ribosomes and intact viruses. In short, much of
post-genomic biology is increasingly becoming a form of computational biology.
The ability to design and write computer programs is among the most
indispensable skills that a modern researcher can cultivate. Python has become
a popular programming language in the biosciences, largely because (i) its
straightforward semantics and clean syntax make it a readily accessible first
language; (ii) it is expressive and well-suited to object-oriented programming,
as well as other modern paradigms; and (iii) the many available libraries and
third-party toolkits extend the functionality of the core language into
virtually every biological domain (sequence and structure analyses,
phylogenomics, workflow management systems, etc.). This primer offers a basic
introduction to coding, via Python, and it includes concrete examples and
exercises to illustrate the language's usage and capabilities; the main text
culminates with a final project in structural bioinformatics. A suite of
Supplemental Chapters is also provided. Starting with basic concepts, such as
that of a 'variable', the Chapters methodically advance the reader to the point
of writing a graphical user interface to compute the Hamming distance between
two DNA sequences.Comment: 65 pages total, including 45 pages text, 3 figures, 4 tables,
numerous exercises, and 19 pages of Supporting Information; currently in
press at PLOS Computational Biolog
VP-fronting in Czech and Polish : a case study in corpus-oriented grammar research
Fronting of an infinite VP across a finite main verb - akin to German "VP-topicalization" - can be found also in Czech and Polish. The paper discusses evidence from large corpora for this process and some of its properties, both syntactic and information-structural. Based on this case, criteria for more user-friedly searching and retrieval of corpus data in syntactic research are being developed
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