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## Análise operatória de ferramentas computacionais de uso individual e cooperativo; Operatory analysis of computational tools for individual and cooperative use

Fonte: Universidade Federal do Rio Grande do Sul
Publicador: Universidade Federal do Rio Grande do Sul

Tipo: Tese de Doutorado
Formato: application/pdf

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#Logical-operatory#Informática#Educação#Computational tools#Lógica operatória#Cooperative environments#Computer science in education#Educação e informática

Esta tese de doutoramento trata da integração da teoria piagetiana com a Ciência da Computação, mais especificamente, a análise de ferramentas computacionais do ponto de vista da lógica operatória. Para isso, foi preciso investigar, em primeiro lugar, a teoria do sujeito individual, no que se refere a função simbólica e reinterpretar estes conceitos no objeto. Neste caso, o objeto e a ferramenta computacional de uso individual. Portanto, somente a partir deste estudo foi possível construir o modelo geral de interação de um sujeito qualquer com uma ferramenta computacional, para depois analisá-la operatoriamente. Em um segundo momento, introduziu-se a teoria do sujeito coletivo que, para caracterizá-lo, foi necessária a compreensão de alguns conceitos relevantes da teoria em questão envolvidos nas noções de interação interindividual e cooperação. A partir de então, foram construídos os modelos interativos mais simples de um sujeito coletivo com três tipos de ferramentas computacionais de uso cooperativo. Para isso, foram abordados alguns aspectos relativos a Computação Cooperativa ou CSCW - Computer Supported Cooperative Work. Da mesma forma que ocorre no nível individual, foram analisadas operatoriamente ferramentas computacionais de uso cooperativo.; This thesis integrates the piagetian theory with Computer Science...

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## On the practically interesting instances of MAXCUT

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/05/2012
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The complexity of a computational problem is traditionally quantified based
on the hardness of its worst case. This approach has many advantages and has
led to a deep and beautiful theory. However, from the practical perspective,
this leaves much to be desired. In application areas, practically interesting
instances very often occupy just a tiny part of an algorithm's space of
instances, and the vast majority of instances are simply irrelevant. Addressing
these issues is a major challenge for theoretical computer science which may
make theory more relevant to the practice of computer science.
Following Bilu and Linial, we apply this perspective to MAXCUT, viewed as a
clustering problem. Using a variety of techniques, we investigate practically
interesting instances of this problem. Specifically, we show how to solve in
polynomial time distinguished, metric, expanding and dense instances of MAXCUT
under mild stability assumptions. In particular, $(1+\epsilon)$-stability
(which is optimal) suffices for metric and dense MAXCUT. We also show how to
solve in polynomial time $\Omega(\sqrt{n})$-stable instances of MAXCUT,
substantially improving the best previously known result.

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## Formal Theories for Linear Algebra

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We introduce two-sorted theories in the style of [CN10] for the complexity
classes \oplusL and DET, whose complete problems include determinants over Z2
and Z, respectively. We then describe interpretations of Soltys' linear algebra
theory LAp over arbitrary integral domains, into each of our new theories. The
result shows equivalences of standard theorems of linear algebra over Z2 and Z
can be proved in the corresponding theory, but leaves open the interesting
question of whether the theorems themselves can be proved.; Comment: This is a revised journal version of the paper "Formal Theories for
Linear Algebra" (Computer Science Logic) for the journal Logical Methods in
Computer Science

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## Theories for TC0 and Other Small Complexity Classes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We present a general method for introducing finitely axiomatizable "minimal"
two-sorted theories for various subclasses of P (problems solvable in
polynomial time). The two sorts are natural numbers and finite sets of natural
numbers. The latter are essentially the finite binary strings, which provide a
natural domain for defining the functions and sets in small complexity classes.
We concentrate on the complexity class TC^0, whose problems are defined by
uniform polynomial-size families of bounded-depth Boolean circuits with
majority gates. We present an elegant theory VTC^0 in which the provably-total
functions are those associated with TC^0, and then prove that VTC^0 is
"isomorphic" to a different-looking single-sorted theory introduced by
Johannsen and Pollet. The most technical part of the isomorphism proof is
defining binary number multiplication in terms a bit-counting function, and
showing how to formalize the proofs of its algebraic properties.; Comment: 40 pages, Logical Methods in Computer Science

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## Security Policies as Membranes in Systems for Global Computing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Programming Languages#Computer Science - Logic in Computer Science#D.2.4#D.3.1#F.3.2#F.3.3#F.4.3

We propose a simple global computing framework, whose main concern is code
migration. Systems are structured in sites, and each site is divided into two
parts: a computing body, and a membrane, which regulates the interactions
between the computing body and the external environment. More precisely,
membranes are filters which control access to the associated site, and they
also rely on the well-established notion of trust between sites. We develop a
basic theory to express and enforce security policies via membranes. Initially,
these only control the actions incoming agents intend to perform locally. We
then adapt the basic theory to encompass more sophisticated policies, where the
number of actions an agent wants to perform, and also their order, are
considered.; Comment: 23 pages; to appear in Logical Methods in Computer Science

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## A Game-Theoretic approach to Fault Diagnosis of Hybrid Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/06/2011
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#Computer Science - Formal Languages and Automata Theory#Computer Science - Computer Science and Game Theory

Physical systems can fail. For this reason the problem of identifying and
reacting to faults has received a large attention in the control and computer
science communities. In this paper we study the fault diagnosis problem for
hybrid systems from a game-theoretical point of view. A hybrid system is a
system mixing continuous and discrete behaviours that cannot be faithfully
modeled neither by using a formalism with continuous dynamics only nor by a
formalism including only discrete dynamics. We use the well known framework of
hybrid automata for modeling hybrid systems, and we define a Fault Diagnosis
Game on them, using two players: the environment and the diagnoser. The
environment controls the evolution of the system and chooses whether and when a
fault occurs. The diagnoser observes the external behaviour of the system and
announces whether a fault has occurred or not. Existence of a winning strategy
for the diagnoser implies that faults can be detected correctly, while
computing such a winning strategy corresponds to implement a diagnoser for the
system. We will show how to determine the existence of a winning strategy, and
how to compute it, for some decidable classes of hybrid automata like o-minimal
hybrid automata.; Comment: In Proceedings GandALF 2011...

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## RPO, Second-order Contexts, and Lambda-calculus

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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First, we extend Leifer-Milner RPO theory, by giving general conditions to
obtain IPO labelled transition systems (and bisimilarities) with a reduced set
of transitions, and possibly finitely branching. Moreover, we study the weak
variant of Leifer-Milner theory, by giving general conditions under which the
weak bisimilarity is a congruence. Then, we apply such extended RPO technique
to the lambda-calculus, endowed with lazy and call by value reduction
strategies.
We show that, contrary to process calculi, one can deal directly with the
lambda-calculus syntax and apply Leifer-Milner technique to a category of
contexts, provided that we work in the framework of weak bisimilarities.
However, even in the case of the transition system with minimal contexts, the
resulting bisimilarity is infinitely branching, due to the fact that, in
standard context categories, parametric rules such as the beta-rule can be
represented only by infinitely many ground rules.
To overcome this problem, we introduce the general notion of second-order
context category. We show that, by carrying out the RPO construction in this
setting, the lazy observational equivalence can be captured as a weak
bisimilarity equivalence on a finitely branching transition system. This result
is achieved by considering an encoding of lambda-calculus in Combinatory Logic.; Comment: 35 pages...

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## No justified complaints: On fair sharing of multiple resources

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/06/2011
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#Computer Science - Distributed, Parallel, and Cluster Computing#Computer Science - Computer Science and Game Theory

Fair allocation has been studied intensively in both economics and computer
science, and fair sharing of resources has aroused renewed interest with the
advent of virtualization and cloud computing. Prior work has typically focused
on mechanisms for fair sharing of a single resource. We provide a new
definition for the simultaneous fair allocation of multiple
continuously-divisible resources. Roughly speaking, we define fairness as the
situation where every user either gets all the resources he wishes for, or else
gets at least his entitlement on some bottleneck resource, and therefore cannot
complain about not getting more. This definition has the same desirable
properties as the recently suggested dominant resource fairness, and also
handles the case of multiple bottlenecks. We then prove that a fair allocation
according to this definition is guaranteed to exist for any combination of user
requests and entitlements (where a user's relative use of the different
resources is fixed). The proof, which uses tools from the theory of ordinary
differential equations, is constructive and provides a method to compute the
allocations numerically.

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## The one-round Voronoi game replayed

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Computational Geometry#Computer Science - Computer Science and Game Theory#F.2.2

We consider the one-round Voronoi game, where player one (``White'', called
``Wilma'') places a set of n points in a rectangular area of aspect ratio r
<=1, followed by the second player (``Black'', called ``Barney''), who places
the same number of points. Each player wins the fraction of the board closest
to one of his points, and the goal is to win more than half of the total area.
This problem has been studied by Cheong et al., who showed that for large
enough $n$ and r=1, Barney has a strategy that guarantees a fraction of 1/2+a,
for some small fixed a.
We resolve a number of open problems raised by that paper. In particular, we
give a precise characterization of the outcome of the game for optimal play: We
show that Barney has a winning strategy for n>2 and r>sqrt{2}/n, and for n=2
and r>sqrt{3}/2. Wilma wins in all remaining cases, i.e., for n>=3 and
r<=sqrt{2}/n, for n=2 and r<=sqrt{3}/2, and for n=1. We also discuss complexity
aspects of the game on more general boards, by proving that for a polygon with
holes, it is NP-hard to maximize the area Barney can win against a given set of
points by Wilma.; Comment: 14 pages, 6 figures, Latex; revised for journal version, to appear in
Computational Geometry: Theory and Applications. Extended abstract version
appeared in Workshop on Algorithms and Data Structures...

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## Distributive Computability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/06/2003
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This thesis presents a series of theoretical results and practical
realisations about the theory of computation in distributive categories.
Distributive categories have been proposed as a foundational tool for Computer
Science in the last years, starting from the papers of R.F.C. Walters. We shall
focus on two major topics: distributive computability, i.e., a generalized
theory of computability based on distributive categories, and the Imp(G)
language, which is a language based on the syntax of distributive categories.
The link between the former and the latter is that the functions computed by
Imp(G) programs are exactly the distributively computable functions.

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## A Two Step Perspective for Kripke Structure Reduction

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/10/2012
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#Computer Science - Formal Languages and Automata Theory#Computer Science - Logic in Computer Science

This paper presents a novel theoretical framework for the state space
reduction of Kripke structures. We define two equivalence relations, Kripke
minimization equivalence (KME) and weak Kripke minimization equivalence (WKME).
We define the quotient system under these relations and show that these
relations are strictly coarser than strong (bi)simulation and
divergence-sensitive stutter (bi)simulation, respectively. We prove that the
quotient system obtained under KME and WKME preserves linear-time and
stutter-insensitive linear-time properties. Finally, we show that KME is
compositional w.r.t. synchronous parallel composition.; Comment: Accepted for Student Research Forum, 39th International Conference on
Current Trends in Theory and Practice of Computer Science (SOFSEM 2013)

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## On Using Matching Theory to Understand P2P Network Design

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/12/2006
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#Computer Science - Networking and Internet Architecture#Computer Science - Computer Science and Game Theory

This paper aims to provide insight into stability of collaboration choices in
P2P networks. We study networks where exchanges between nodes are driven by the
desire to receive the best service available. This is the case for most
existing P2P networks. We explore an evolution model derived from stable
roommates theory that accounts for heterogeneity between nodes. We show that
most P2P applications can be modeled using stable matching theory. This is the
case whenever preference lists can be deduced from the exchange policy. In many
cases, the preferences lists are characterized by an interesting acyclic
property. We show that P2P networks with acyclic preferences possess a unique
stable state with good convergence properties.

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## A Theory and Calculus for Reasoning about Sequential Behavior

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Logic in Computer Science#Computer Science - Discrete Mathematics#F.4.1#D.2.4#G.2.1

Basic results in combinatorial mathematics provide the foundation for a
theory and calculus for reasoning about sequential behavior. A key concept of
the theory is a generalization of Boolean implicant which deals with statements
of the form:
A sequence of Boolean expressions alpha is an implicant of a set of sequences
of Boolean expressions A
This notion of a generalized implicant takes on special significance when
each of the sequences in the set A describes a disallowed pattern of behavior.
That is because a disallowed sequence of Boolean expressions represents a
logical/temporal dependency, and because the implicants of a set of disallowed
Boolean sequences A are themselves disallowed and represent precisely those
dependencies that follow as a logical consequence from the dependencies
represented by A. The main result of the theory is a necessary and sufficient
condition for a sequence of Boolean expressions to be an implicant of a regular
set of sequences of Boolean expressions. This result is the foundation for two
new proof methods. Sequential resolution is a generalization of Boolean
resolution which allows new logical/temporal dependencies to be inferred from
existing dependencies. Normalization starts with a model (system) and a set of
logical/temporal dependencies and determines which of those dependencies are
satisfied by the model.; Comment: 102 double-spaced pages...

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## Multi-dimensional Type Theory: Rules, Categories, and Combinators for Syntax and Semantics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/08/2004
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#Computer Science - Computation and Language#Computer Science - Artificial Intelligence#Computer Science - Logic in Computer Science#I.2.7

We investigate the possibility of modelling the syntax and semantics of
natural language by constraints, or rules, imposed by the multi-dimensional
type theory Nabla. The only multiplicity we explicitly consider is two, namely
one dimension for the syntax and one dimension for the semantics, but the
general perspective is important. For example, issues of pragmatics could be
handled as additional dimensions.
One of the main problems addressed is the rather complicated repertoire of
operations that exists besides the notion of categories in traditional Montague
grammar. For the syntax we use a categorial grammar along the lines of Lambek.
For the semantics we use so-called lexical and logical combinators inspired by
work in natural logic. Nabla provides a concise interpretation and a sequent
calculus as the basis for implementations.; Comment: 20 pages

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## Set-Theoretic Completeness for Epistemic and Conditional Logic

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Artificial Intelligence#Computer Science - Logic in Computer Science#I.2.4#F.4.1

The standard approach to logic in the literature in philosophy and
mathematics, which has also been adopted in computer science, is to define a
language (the syntax), an appropriate class of models together with an
interpretation of formulas in the language (the semantics), a collection of
axioms and rules of inference characterizing reasoning (the proof theory), and
then relate the proof theory to the semantics via soundness and completeness
results. Here we consider an approach that is more common in the economics
literature, which works purely at the semantic, set-theoretic level. We provide
set-theoretic completeness results for a number of epistemic and conditional
logics, and contrast the expressive power of the syntactic and set-theoretic
approaches; Comment: This is an expanded version of a paper that appeared in AI and
Mathematics, 1998

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## Comparing the notions of optimality in CP-nets, strategic games and soft constraints

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Artificial Intelligence#Computer Science - Computer Science and Game Theory#I.2.11#D.3.3

The notion of optimality naturally arises in many areas of applied
mathematics and computer science concerned with decision making. Here we
consider this notion in the context of three formalisms used for different
purposes in reasoning about multi-agent systems: strategic games, CP-nets, and
soft constraints. To relate the notions of optimality in these formalisms we
introduce a natural qualitative modification of the notion of a strategic game.
We show then that the optimal outcomes of a CP-net are exactly the Nash
equilibria of such games. This allows us to use the techniques of game theory
to search for optimal outcomes of CP-nets and vice-versa, to use techniques
developed for CP-nets to search for Nash equilibria of the considered games.
Then, we relate the notion of optimality used in the area of soft constraints
to that used in a generalization of strategic games, called graphical games. In
particular we prove that for a natural class of soft constraints that includes
weighted constraints every optimal solution is both a Nash equilibrium and
Pareto efficient joint strategy. For a natural mapping in the other direction
we show that Pareto efficient joint strategies coincide with the optimal
solutions of soft constraints.; Comment: 39 pages. To appear in Annals of Mathematics and Artificial
Intelligence

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## Discovery of Invariants through Automated Theory Formation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/06/2011
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#Computer Science - Logic in Computer Science#Computer Science - Artificial Intelligence#Computer Science - Software Engineering

Refinement is a powerful mechanism for mastering the complexities that arise
when formally modelling systems. Refinement also brings with it additional
proof obligations -- requiring a developer to discover properties relating to
their design decisions. With the goal of reducing this burden, we have
investigated how a general purpose theory formation tool, HR, can be used to
automate the discovery of such properties within the context of Event-B. Here
we develop a heuristic approach to the automatic discovery of invariants and
report upon a series of experiments that we undertook in order to evaluate our
approach. The set of heuristics developed provides systematic guidance in
tailoring HR for a given Event-B development. These heuristics are based upon
proof-failure analysis, and have given rise to some promising results.; Comment: In Proceedings Refine 2011, arXiv:1106.3488

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## Axiomatic Synthesis of Computer Programs and Computability Theorems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/03/2000
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#Computer Science - Logic in Computer Science#D.1.2#D.2.1#F.1.1#F.2.1#F.3.1#F.4.1#H.2.3#H.2.4#H.3.3#I.2.2

We introduce a set of eight universal Rules of Inference by which computer
programs with known properties (axioms) are transformed into new programs with
known properties (theorems). Axioms are presented to formalize a segment of
Number Theory, DataBase retrieval and Computability Theory. The resulting
Program Calculus is used to generate programs to (1) Determine if one number is
a factor of another. (2) List all employees who earn more than their manager.
(3) List the set of programs that halt no on themselves, thus proving that it
is recursively enumerable. The well-known fact that the set of programs that do
not halt yes on themselves is not recursively enumerable is formalized as a
program requirement that has no solution, an Incompleteness Axiom. Thus, any
axioms (programs) which could be used to generate this program are themselves
unattainable. Such proofs are presented to formally generate several additional
theorems, including (4) The halting problem is unsolvable.
Open problems and future research is discussed, including the use of
temporary sort files, programs that calculate statistics (such as counts and
sums), the synthesis of programs to solve other well-known problems from Number
Theory, Logic, DataBase retrieval and Computability Theory...

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## Bounding Rationality by Discounting Time

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/11/2009
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#Computer Science - Computer Science and Game Theory#Computer Science - Computational Complexity#F.1.1

Consider a game where Alice generates an integer and Bob wins if he can
factor that integer. Traditional game theory tells us that Bob will always win
this game even though in practice Alice will win given our usual assumptions
about the hardness of factoring.
We define a new notion of bounded rationality, where the payoffs of players
are discounted by the computation time they take to produce their actions. We
use this notion to give a direct correspondence between the existence of
equilibria where Alice has a winning strategy and the hardness of factoring.
Namely, under a natural assumption on the discount rates, there is an
equilibriumwhere Alice has a winning strategy iff there is a linear-time
samplable distribution with respect to which Factoring is hard on average.
We also give general results for discounted games over countable action
spaces, including showing that any game with bounded and computable payoffs has
an equilibrium in our model, even if each player is allowed a countable number
of actions. It follows, for example, that the Largest Integer game has an
equilibrium in our model though it has no Nash equilibria or epsilon-Nash
equilibria.; Comment: To appear in Proceedings of The First Symposium on Innovations in
Computer Science

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## A Categorical Semantics for Linear Logical Frameworks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/01/2015
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A type theory is presented that combines (intuitionistic) linear types with
type dependency, thus properly generalising both intuitionistic dependent type
theory and full linear logic. A syntax and complete categorical semantics are
developed, the latter in terms of (strict) indexed symmetric monoidal
categories with comprehension. Various optional type formers are treated in a
modular way. In particular, we will see that the historically much-debated
multiplicative quantifiers and identity types arise naturally from categorical
considerations. These new multiplicative connectives are further characterised
by several identities relating them to the usual connectives from dependent
type theory and linear logic. Finally, one important class of models, given by
families with values in some symmetric monoidal category, is investigated in
detail.; Comment: Based on the technical report arXiv:1405.0033 . To appear in the
proceedings of FoSSaCS 2015, in the Advanced Research in Computing and
Software Science (ARCoSS) subline of Springer's Lecture Notes in Computer
Science series

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