1,794 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
A Language-centered Approach to support environmental modeling with Cellular Automata
Die Anwendung von Methodiken und Technologien aus dem Bereich der Softwaretechnik auf den Bereich der Umweltmodellierung ist eine gemeinhin akzeptierte Vorgehensweise. Im Rahmen der "modellgetriebenen Entwicklung"(MDE, model-driven engineering) werden Technologien entwickelt, die darauf abzielen, Softwaresysteme vorwiegend auf Basis von im Vergleich zu Programmquelltexten relativ abstrakten Modellen zu entwickeln. Ein wesentlicher Bestandteil von MDE sind Techniken zur effizienten Entwicklung von "domänenspezifischen Sprachen"( DSL, domain-specific language), die auf Sprachmetamodellen beruhen. Die vorliegende Arbeit zeigt, wie modellgetriebene Entwicklung, und insbesondere die metamodellbasierte Beschreibung von DSLs, darüber hinaus Aspekte der Pragmatik unterstützen kann, deren Relevanz im erkenntnistheoretischen und kognitiven Hintergrund wissenschaftlichen Forschens begründet wird. Hierzu wird vor dem Hintergrund der Erkenntnisse des "modellbasierten Forschens"(model-based science und model-based reasoning) gezeigt, wie insbesondere durch Metamodelle beschriebene DSLs Möglichkeiten bieten, entsprechende pragmatische Aspekte besonders zu berücksichtigen, indem sie als Werkzeug zur Erkenntnisgewinnung aufgefasst werden. Dies ist v.a. im Kontext großer Unsicherheiten, wie sie für weite Teile der Umweltmodellierung charakterisierend sind, von grundsätzlicher Bedeutung. Die Formulierung eines sprachzentrierten Ansatzes (LCA, language-centered approach) für die Werkzeugunterstützung konkretisiert die genannten Aspekte und bildet die Basis für eine beispielhafte Implementierung eines Werkzeuges mit einer DSL für die Beschreibung von Zellulären Automaten (ZA) für die Umweltmodellierung. Anwendungsfälle belegen die Verwendbarkeit von ECAL und der entsprechenden metamodellbasierten Werkzeugimplementierung.The application of methods and technologies of software engineering to environmental modeling and simulation (EMS) is common, since both areas share basic issues of software development and digital simulation. Recent developments within the context of "Model-driven Engineering" (MDE) aim at supporting the development of software systems at the base of relatively abstract models as opposed to programming language code. A basic ingredient of MDE is the development of methods that allow the efficient development of "domain-specific languages" (DSL), in particular at the base of language metamodels. This thesis shows how MDE and language metamodeling in particular, may support pragmatic aspects that reflect epistemic and cognitive aspects of scientific investigations. For this, DSLs and language metamodeling in particular are set into the context of "model-based science" and "model-based reasoning". It is shown that the specific properties of metamodel-based DSLs may be used to support those properties, in particular transparency, which are of particular relevance against the background of uncertainty, that is a characterizing property of EMS. The findings are the base for the formulation of an corresponding specific metamodel- based approach for the provision of modeling tools for EMS (Language-centered Approach, LCA), which has been implemented (modeling tool ECA-EMS), including a new DSL for CA modeling for EMS (ECAL). At the base of this implementation, the applicability of this approach is shown
On the Computational Complexity of MapReduce
In this paper we study MapReduce computations from a complexity-theoretic
perspective. First, we formulate a uniform version of the MRC model of Karloff
et al. (2010). We then show that the class of regular languages, and moreover
all of sublogarithmic space, lies in constant round MRC. This result also
applies to the MPC model of Andoni et al. (2014). In addition, we prove that,
conditioned on a variant of the Exponential Time Hypothesis, there are strict
hierarchies within MRC so that increasing the number of rounds or the amount of
time per processor increases the power of MRC. To the best of our knowledge we
are the first to approach the MapReduce model with complexity-theoretic
techniques, and our work lays the foundation for further analysis relating
MapReduce to established complexity classes
Covering and separation for logical fragments with modular predicates
For every class of word languages, one may associate a decision
problem called -separation. Given two regular languages, it asks
whether there exists a third language in containing the first
language, while being disjoint from the second one. Usually, finding an
algorithm deciding -separation yields a deep insight on
.
We consider classes defined by fragments of first-order logic. Given such a
fragment, one may often build a larger class by adding more predicates to its
signature. In the paper, we investigate the operation of enriching signatures
with modular predicates. Our main theorem is a generic transfer result for this
construction. Informally, we show that when a logical fragment is equipped with
a signature containing the successor predicate, separation for the stronger
logic enriched with modular predicates reduces to separation for the original
logic. This result actually applies to a more general decision problem, called
the covering problem
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