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Topic: Descriptive complexity

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Computational complexity theory

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	Complexity
		Complexity is one of those terms for which it is difficult to give a precise definition.
		Complexity is often used to describe single sytems made of multiple interacting parts.
		This complexity is measured as the total complexity of encoding the realisation into a descriptive code and decoding it back into a realisation of that code.
	www.iscid.org /encyclopedia/Complexity (237 words)

	Aspects of Complexity in Life and Science
		For instance, internalist theories conclude that complexity increase is driven by inherent properties of either complex systems generally (Herbert Spencer's Law of Evolution from 1890, and his principle of the "instability of the homogeneous" is an early example) or of organisms in particular.
		Salthe (1993) deepened the original notion of complexity as susceptibility to alternative descriptions by his concept of intensional complexity, which is a particular sort of descriptive complexity where the different descriptions relate to particular integrative levels that are levels of generality in a `specification hierarchy' (versus the `scalar hierarchy').
		Complexity does not denote any essentially common or generic phenomenon, as a term it may be viewed as denoting a diverse set of concepts with certain family similarities (e.g., Brandts 1997).
	www.nbi.dk /~emmeche/cePubl/97g.complisci.html (7103 words)

	Rice Algorithms & Complexity Group (Site not responding. Last check: 2007-08-09)
		The computational complexity of a problem is the amount of resources, such as time or space, required by a machine that solves the problem.
		A more recent branch of complexity theory focuses on the descriptive complexity of problems, which is the complexity of describing problems in some logical formalism.
		This equivalence of questions in computational and descriptive complexity is one of the major features of the connection between the two branches of complexity theory.
	www.cs.rice.edu /CS/Algorithms/complexity_theory.html (235 words)

	Descriptive Complexity (Site not responding. Last check: 2007-08-09)
		Computational complexity was originally defined in terms of the natural entities of time and space, and the term complexity was used to denote the time or space used in the computation.
		Begun in 1974 by Fagin, descriptive complexity has characterized all major notions of complexity in terms of the richness of logical languages needed to describe problems.
		Descriptive complexity is part of finite model theory, and it ties together logic and computer science.
	www.cs.umass.edu /~immerman/book/descriptiveComplexity.html (188 words)

	Complexity - NECSIWiki (Site not responding. Last check: 2007-08-09)
		Complexity is sometimes used to refer to the general concept of complex systems.
		The length of a description is measured in units of information (for a given resolution).
		The Algorithmic complexity is the length of the shortest computer program (in the sense of Turing) that generates the string.
	necsi.org /community/wiki/index.php/Complexity (216 words)

	HYLE 6-2 (2000): Biogeochemical Models in the Environmental Sciences
		Complexity thus is a function of the chosen description; systems that can not be described by a single theory or discipline are regarded as complex (Kornwachs and Lucadou 1984).
		In this view, complexity is ontologically conceived and the impossibility of condensing the essence of an ecosystem into a dynamical system is attributed to practical observational and computational (and not principal) limitations.
		Modeling can be a way of coping with different types of complexity: the complexity of integrating and synthesizing (reductionist) statements and of gluing analytically isolated components; the descriptive complexity that allows for numerous, non-equivalent system descriptions, depending upon standpoint; the communicative complexity, both inter- and trans-scientific, arising from nonequivalent descriptions of complex systems.
	www.hyle.org /journal/issues/6/haag.htm (9201 words)

	[No title] (Site not responding. Last check: 2007-08-09)
		The descriptive complexity of a problem is the complexity of describing the problem in some logical formalism.
		This connection was first discovered by the speaker, who showed that the complexity class NP coincides with the class of properties of finite structures expressible in existential second-order logic (where we are allowed to existentially quantify over not just points, as in first-order logic, but also over relations).
		The equivalence of questions in computational and descriptive complexity holds the promise that techniques from one domain can be brought to bear on questions in the other domain.
	math.ucsd.edu /~asl99/abstracts/fagin.txt (444 words)

	Descriptive Complexity
		On Size versus Number of Variables, for the slides of three survey talks on descriptive complexity and its applications.
		Natural complexity classes tend to have natural descriptive characterizations.
		This last equality is different, but included as a descriptive characterization of the top class in our diagram, and a characterization that is quite analogous to the others.
	www.cs.umass.edu /~immerman/descriptive_complexity.html (991 words)

	Descriptive complexity - Wikipedia, the free encyclopedia
		Descriptive complexity is a branch of finite model theory, a subfield of computational complexity theory and mathematical logic, which seeks to characterize complexity classes by the type of logic needed to express the languages in them.
		For example, PH is precisely the class of languages expressible by statements of second-order logic.
		This connection between complexity and logic allows results to be transferred easily from one area to the other, facilitating new proof methods and providing additional evidence that the main complexity classes are somehow "natural" and not tied to the specific abstract machines used to define them.
	en.wikipedia.org /wiki/Descriptive_complexity (367 words)

	Kolmogorov complexity - Wikipedia, the free encyclopedia
		In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object.
		Strings whose Kolmogorov complexity is small relative to the string's size are not considered to be complex.
		The notion of Kolmogorov complexity is surprisingly deep and can be used to state and prove impossibility results akin to Gödel's incompleteness theorem and Turing's halting problem.
	en.wikipedia.org /wiki/Kolmogorov_complexity (2039 words)

	On Descriptive Complexity, Language Complexity, and GB
		On Descriptive Complexity, Language Complexity, and GB Institute for Research in Cognitive Science
		On Descriptive Complexity, Language Complexity, and GB James Rogers, University of Pennsylvania
		This provides a flexible approach to establishing language-theoretic complexity results for formalisms that are based on systems of well-formedness constraints on trees.
	repository.upenn.edu /ircs_reports/128 (243 words)

	Brainstorms: Richard Johns: Dynamical Complexity and Regularity
		The irregularity of an object is defined, and then I try to show that the dynamical complexity of an object s, with respect to a regular law, always exceeds the irregularity of s.
		As he himself notes in the conclusion, establishing that irregularity (static complexity) supplies a lower bound for dynamic complexity can be demonstrated only on the basis of assumptions that design critics are not likely to grant (his Global Blindness of Natural Laws principle, much less his symmetry principle).
		They produce irregular DNA with very high salience (low dynamical complexity), which seems to contradict your thesis that dynamical complexity is always greater than the irregularity.
	www.iscid.org /boards/ubb-get_topic-f-6-t-000131.html (1511 words)

	Seminar by Neil Immerman (Site not responding. Last check: 2007-08-09)
		Classical Complexity Classes such as NC, P, and NP are defined in terms of the complexity of checking whether the input satisfies a certain property.
		For many applications a more appropriate complexity measure involves modeling the process as a dynamic one: there is a fairly large object being worked on over a period of time.
		Descriptive complexity offers a clean approach to understanding dynamic problems.
	www.cs.brandeis.edu /~mairson/CS-seminar/immerman.html (224 words)

	Descriptive Complexity Theory for Constraint Databases - Gr, Kreutzer (ResearchIndex)
		We consider the data complexity of various logics on two important classes of constraint databases: dense order and linear constraint databases.
		For dense order databases, we present a general result allowing us to lift results on logics capturing complexity classes from the class of finite ordered databases to dense order constraint databases.
		Considering linear constraints, we show that there is a significant gap between the data complexity of first-order queries on linear constraint...
	citeseer.ist.psu.edu /230369.html (521 words)

	Complexity - Wikipedia, the free encyclopedia
		The use of the term complex is often confused with the term complicated.
		On the other hand, a complex structure uses interwoven components that introduce mutual dependencies and produce more than a sum of the parts.
		Complex systems tend to be high-dimensional, non-linear and hard to model.
	en.wikipedia.org /wiki/complexity (1286 words)

	CMI-PCMI Undergraduate Program
		The basic object of the theory is a complexity class: the set of problems that can be solved in a particular model under particular resource constraints.
		The most interesting complexity classes are robust, meaning that they can be defined by a number of different constraints in different models.
		One possibility is for the advanced section to view the landscape of complexity classes through the lens of Immerman's "descriptive complexity theory".
	www.admin.ias.edu /ma/2000/ugprogram2000.htm (487 words)

	Bounded Arithmetic and Descriptive Complexity - Blumensath (ResearchIndex) (Site not responding. Last check: 2007-08-09)
		We study definability of languages in arithmetic and the free monoid by bounded versions of fixed-point and transitive-closure logics.
		In particular we give logical characterisations of complexity classes C by showing that a language belongs to C if and only if it is definable in either arithmetic or the free monoid by a formula of a certain logic.
		We investigate in which cases the bounds of fixed-point operators may be omitted.
	citeseer.ist.psu.edu /390185.html (364 words)

	Descriptive Complexity (Site not responding. Last check: 2007-08-09)
		Descriptive complexity studies the relation between formal languages and computational resources (space and time) required to solve problems formulated in those languages.
		Techniques and results of descriptive complexity theory are used in database theory and computer aided verification.
		The aim of the course is to introduce the basics of descriptive complexity theory and prove the theorem (due to Immerman and Vardi) that, on ordered structures, polynomial time queries are exactly those which can be formulated in first order logic plus the least fixed point operator.
	www.cs.nott.ac.uk /~nza/MGS/MGS00 (221 words)

	IBM Research \| Research Areas \| Algorithms & Theory
		Researchers at IBM have a distinguished history in the development of algorithms and the theory of computation in a variety of areas including foundations of complexity theory, combinatorial optimization, randomized algorithms, cryptography, streaming algorithms, search algorithms, queuing theory, online algorithms, quantum computation, communication networks, and algebraic circuit complexity.
		These include polynomial-time complexity (Cobham), algebraic complexity (Winograd), information-theoretic complexity (Chaitin), descriptive complexity (Fagin), alternating complexity (Chandra, Kozen, and Stockmeyer), parallel complexity (Pippenger), and computational complexity on the reals (Shub).
		For example, we have proved that the element distinctness problem - that is, testing whether a database has two identical entries - cannot be solved in linear time under a realistic computational model limited only by working memory that is slightly smaller than the input size.
	www.research.ibm.com /compsci/spotlight/algorithms/index.html (835 words)

	SFU Computing Science - PIMS Distinguished Lecture Series
		Descriptive complexity measures the richness of logical languages that are needed to describe computational tasks.
		Fagin proved that the complexity class NP is exactly the set of problems expressible in second-order existential logic.
		I will survey a few of the high points of descriptive complexity and talk about some current directions including applications to dynamic algorithms, static analysis of programs, and progress in understanding the trade-off between parallel time and amount of computational hardware.
	www.cs.sfu.ca /SeminarsAndEvents/LectureSeries (659 words)

	Descriptive complexity, bounded set theory and Web-like databases (Site not responding. Last check: 2007-08-09)
		Descriptive complexity, bounded set theory and Web-like databases
		This is an overview lecture 1) on descriptive complexity theory via (flat) finite model theory and 2) on extending this approach to the case of (nested) hereditarily-finite sets or hypersets satisfying Aczel's antifoundation axiom.
		Original results of the author will be presented (including, if the time will permit, proof theoretic conservativity and independence results related to BST and "P=NP?").
	www.ii.uib.no /~pinar/seminar/sazonov.html (105 words)

	Department of Computer Science : Algorithms and Complexity Group - Durham University
		Members of this group research in several areas of theoretical computer science including computational complexity, finite model theory, proof complexity, graph algorithms, logic, descriptive complexity and randomised algorithms.
		He has research interests in computational complexity of exact and approximate counting problems; randomised algorithms; Markov Chain Monte Carlo sampling techniques; applications of all of these to problems in phylogenetics.
		Iain Stewart has research interests in computational complexity; finite model theory and descriptive complexity; graph theory and algorithms; interconnection networks for parallel and distributed computing; theoretical aspects of artificial intelligence; group theory; e-Science.
	www.dur.ac.uk /computer.science/research/acid (497 words)

	Abstract of "Some Topics in Descriptive Complexity", Ph. D. thesis authored by Ragnar Nohre, Linköping University, ...
		Abstract of "Some Topics in Descriptive Complexity", Ph.
		With an emphasis on applications in image-coding/analysis, this thesis studies some topics in Descriptive-Complexity and th Minimum Description Length Principle.
		We find that segmentation leads to a coding gain of approximately 0.5 bits/pixel, and that the Gaussian distribution is a fair model for the prediction error in each segment.
	www.bk.isy.liu.se /history/SomeTopicsInDescriptiveComplexity.html (182 words)

	School of Computing, Queen's University (Site not responding. Last check: 2007-08-09)
		Salomaa's research addresses descriptive complexity bounds for automata and related structures, and the specification and use of synchronization constraints for automata and grammars.
		Salomaa's work deals with the nondeterminism degree of pushdown automata which according to our results is more meaningful and useful in practice than the nondeterminism measures considered earlier, for instance, it is more compatible with the complexity of parsing.
		He investigates the tradeoffs between the nondeterminism degree and the state-complexity of pushdown automata, that is, what happens when the amount of nondeterminism used in the computation and the size of the automaton is restricted simultaneously.
	www.cs.queensu.ca /researchreport/faculty/salomaa.html (305 words)

	Bookpool: Descriptive Complexity
		Computational complexity measures how much time or memory is needed as a function of the input problem size.
		Descriptive complexity is concerned with problems which may be described in first-order logic.
		By virtue of the close relationship between logic and relational databses, it turns out that this subject has important applications to databases such as analysing the queries computable in polynomial time, analysing the parallel time needed to compute a query, and the analysis of nondeterministic classes.
	www.bookpool.com /sm/0387986006 (195 words)

	A descriptive complexity approach to the linear hierarchy. (Site not responding. Last check: 2007-08-09)
		A descriptive complexity approach to the linear hierarchy.
		Abstract: This paper gives some new logical characterizations of the class of rudimentary languages in the scope of descriptive complexity.
		These characterizations are based on a logic introduced by Parigot and Pelz to characterize Petri Net languages, and generalized quantifiers of comparison of cardinality.
	www.informatik.uni-hamburg.de /TGI/pnbib/h/hachachi_y1.html (104 words)

	Logic in CS: Descriptive Complexity and Curry-Howard
		In the meantime, look at proof assistants like Coq and languages with dependent types like Epigram.
		Second, logic is useful in complexity theory, via descriptive complexity.
		If you ever find yourself thinking about things like non-finite-state model checking, or knowledge representation, or various other AI-ish topics, then descriptive complexity can serve as a quick cheat sheet for thinking about what the consequences would be if you added a new level of expressiveness or power to your system.
	www.kimbly.com /blog/000451.html (205 words)

	Computer Science 2429H -- Winter 2002 (Site not responding. Last check: 2007-08-09)
		Each of several standard complexity classes, including AC0, LogSpace, Polytime, and PSPACE has a corresponding theory formalizing reasoning using concepts in that class, and corresponding to each theory there is a propositional proof system representing a nonuniform version of the theory.
		Slides for Edinburgh Talk These slides give the gist of the final course lecture, and were presented at the ICMS Workshop "Circuit and Proof Complexity", October, 2001.
		Propositional Translations of V1 Slides for Edinburgh Talk These slides give the gist of the final course lecture, and were presented at the ICMS Workshop "Circuit and Proof Complexity", October, 2001.
	www.cs.toronto.edu /~sacook/csc2429h.02 (334 words)

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