39,404 research outputs found
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing complexity classes and show its
suitability for completeness statements of many non elementary problems. This
hierarchy allows the classification of many decision problems with a
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
Complexity Bounds for Ordinal-Based Termination
`What more than its truth do we know if we have a proof of a theorem in a
given formal system?' We examine Kreisel's question in the particular context
of program termination proofs, with an eye to deriving complexity bounds on
program running times.
Our main tool for this are length function theorems, which provide complexity
bounds on the use of well quasi orders. We illustrate how to prove such
theorems in the simple yet until now untreated case of ordinals. We show how to
apply this new theorem to derive complexity bounds on programs when they are
proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability
Problems (RP 2014, 22-24 September 2014, Oxford
Hierarchical coexistence of universality and diversity controls robustness and multi-functionality in intermediate filament protein networks
Proteins constitute the elementary building blocks of a vast variety of biological materials such as cellular protein networks, spider silk or bone, where they create extremely robust, multi-functional materials by self-organization of structures over many length- and time scales, from nano to macro. Some of the structural features are commonly found in a many different tissues, that is, they are highly conserved. Examples of such universal building blocks include alpha-helices, beta-sheets or tropocollagen molecules. In contrast, other features are highly specific to tissue types, such as particular filament assemblies, beta-sheet nanocrystals in spider silk or tendon fascicles. These examples illustrate that the coexistence of universality and diversity – in the following referred to as the universality-diversity paradigm (UDP) – is an overarching feature in protein materials. This paradigm is a paradox: How can a structure be universal and diverse at the same time? In protein materials, the coexistence of universality and diversity is enabled by utilizing hierarchies, which serve as an additional dimension beyond the 3D or 4D physical space. This may be crucial to understand how their structure and properties are linked, and how these materials are capable of combining seemingly disparate properties such as strength and robustness. Here we illustrate how the UDP enables to unify universal building blocks and highly diversified patterns through formation of hierarchical structures that lead to multi-functional, robust yet highly adapted structures. We illustrate these concepts in an analysis of three types of intermediate filament proteins, including vimentin, lamin and keratin
Complexity Hierarchies and Higher-order Cons-free Term Rewriting
Constructor rewriting systems are said to be cons-free if, roughly,
constructor terms in the right-hand sides of rules are subterms of the
left-hand sides; the computational intuition is that rules cannot build new
data structures. In programming language research, cons-free languages have
been used to characterize hierarchies of computational complexity classes; in
term rewriting, cons-free first-order TRSs have been used to characterize the
class PTIME.
We investigate cons-free higher-order term rewriting systems, the complexity
classes they characterize, and how these depend on the type order of the
systems. We prove that, for every K 1, left-linear cons-free systems
with type order K characterize ETIME if unrestricted evaluation is used
(i.e., the system does not have a fixed reduction strategy).
The main difference with prior work in implicit complexity is that (i) our
results hold for non-orthogonal term rewriting systems with no assumptions on
reduction strategy, (ii) we consequently obtain much larger classes for each
type order (ETIME versus EXPTIME), and (iii) results for cons-free
term rewriting systems have previously only been obtained for K = 1, and with
additional syntactic restrictions besides cons-freeness and left-linearity.
Our results are among the first implicit characterizations of the hierarchy E
= ETIME ETIME ... Our work confirms prior
results that having full non-determinism (via overlapping rules) does not
directly allow for characterization of non-deterministic complexity classes
like NE. We also show that non-determinism makes the classes characterized
highly sensitive to minor syntactic changes like admitting product types or
non-left-linear rules.Comment: extended version of a paper submitted to FSCD 2016. arXiv admin note:
substantial text overlap with arXiv:1604.0893
Ontologies and Information Extraction
This report argues that, even in the simplest cases, IE is an ontology-driven
process. It is not a mere text filtering method based on simple pattern
matching and keywords, because the extracted pieces of texts are interpreted
with respect to a predefined partial domain model. This report shows that
depending on the nature and the depth of the interpretation to be done for
extracting the information, more or less knowledge must be involved. This
report is mainly illustrated in biology, a domain in which there are critical
needs for content-based exploration of the scientific literature and which
becomes a major application domain for IE
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