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Computability

About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.


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Journal ArticleDOI
01 Sep 1993
TL;DR: The lab component is created for a year long sophomore course in discrete structures, logic, and computability for students majoring in computer science or computer engineering and consists of experiments in declarative programming environments.
Abstract: 19 Overview Many students find it hard to grasp and retai n the ideas presented in courses covering discret e structures, logic, and computability. These subjects provide a foundation for required upper division courses in computer science . Therefore a major effort must be made to improve the learnin g environment for students studying these ideas a t the lower division level . Many of us succeeded academically in spite o f the way we were taught . But how many people hav e not succeeded because of the way material was presented to them? Since people learn in different ways, it makes sense to present students with a va riety of learning experiences . We have created a laboratory component for a year long sophomore course in discrete structures , logic, and computability for students majoring i n computer science or computer engineering . The labs consist of experiments in declarative programming environments . The experiments are designed to reinforce the learning of material o n a daily basis, just like the regular homework assignments . In other words, the lab experiment s are short in duration and relevant to the material covered by each lecture . Short programming labs that correspond t o each lecture should be useful learning tools fo r many traditional courses . The instant feedbac k that students get from wrong assumptions can give them incentive to try something new to experiment and see what happens . The lab component can also encourage the use of laboratory partners, interaction of students, team presenta -

14 citations

Book ChapterDOI
TL;DR: In this paper, the authors show that black-box monitoring of HyperLTL is in general unfeasible, and suggest a gray-box approach to monitor a privacy hyperproperty called distributed data minimality, expressed as a hyperLTL property.
Abstract: Many important system properties, particularly in security and privacy, cannot be verified statically. Therefore, runtime verification is an appealing alternative. Logics for hyperproperties, such as HyperLTL, support a rich set of such properties. We first show that black-box monitoring of HyperLTL is in general unfeasible, and suggest a gray-box approach. Gray-box monitoring implies performing analysis of the system at run-time, which brings new limitations to monitorabiliy (the feasibility of solving the monitoring problem). Thus, as another contribution of this paper we refine the classic notions of monitorability, both for trace properties and hyperproperties, taking into account the computability of the monitor. We then apply our approach to monitor a privacy hyperproperty called distributed data minimality, expressed as a HyperLTL property, by using an SMT-based static verifier at runtime.

14 citations

Proceedings ArticleDOI
TL;DR: In this article, the quantum adiabatic theorem has been employed in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science.
Abstract: We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem enables us to establish a connection between the solution for this class of problems and the asymptotic behavior of solutions of a particular type of time-dependent Schrodinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations.

14 citations

Book
01 Jan 2000
TL;DR: In this paper, Cholak et al. considered the problem of counting the number of Turing degrees in a set and showed that it is NP-hard to find a solution.
Abstract: Randomness in computability theory by K. Ambos-Spies and A. Kucera Open questions about the $n$-c.e. degrees by M. Arslanov The theory of numberings: Open problems by S. Badaev and S. Goncharov $\mathrm{\Pi}^0_1$ classes -- Structure and applications by D. Cenzer and C. G. Jockusch, Jr. The global structure of computably enumerable sets by P. A. Cholak Computability theory in arithmetic: Provability, structure and techniques by C. T. Chong and Y. Yang How many Turing degrees are there? by R. Dougherty and A. S. Kechris Questions in computable algebra and combinatorics by R. Downey and J. B. Remmel Issues and problems in reverse mathematics by H. Friedman and S. G. Simpson Open problems in the theory of constructive algebraic systems by S. Goncharov and B. Khoussainov Independence results from ZFC in computability theory: Some open problems by M. Groszek Problems related to arithmetic by J. F. Knight Embeddings into the computably enumerable degrees by M. Lerman Definability in the c.e. degrees: Questions and results by A. Nies Strong reducibilities, again by P. Odifreddi Finitely axiomatizable theories and Lindenbaum algebras of semantic classes by M. Peretyat'kin Towards an analog of Hilbert's tenth problem for a number field by A. Shlapentokh Natural definability in degree structures by R. A. Shore Recursion theory in set theory by T. A. Slaman Extensions, automorphisms, and definability by R. I. Soare Open problems in the enumeration degrees by A. Sorbi.

14 citations

01 Jan 2012
TL;DR: A new model of property testing that closely minors the active learning model is introduced and testing results in this new model may be used to improve the efficiency of model selection algorithms in learning theory.
Abstract: Given oracle access to some boolean function f, how many queries do we need to test whether f is linear? Or monotone? Or whether its output is completely determined by a small number of the input variables? This thesis studies these and related questions in the framework of property testing introduced by Rubinfeld and Sudan ('96). The results of this thesis are grouped into three main lines of research. I. We determine nearly optimal bounds on the number of queries required to test k-juntas (functions that depend on at most k variables) and k-linearity (functions that return the parity of exactly k of the input bits). These two problems are fundamental in the study of boolean functions and the bounds obtained for these two properties lead to tight or improved bounds on the query complexity for testing many other properties including, for example, testing sparse polynomials, testing low Fourier degree, and testing computability by small-size decision trees. We give a partial characterization of the set of functions for which we can test isomorphism—that is, identity up to permutation of the labels of the variables—with a constant number of queries. This result provides some progress on the question of characterizing the set of properties of boolean functions that can be tested with a constant number of queries. II. We establish new connections between property testing and other areas of computer science. First, we present a new reduction between testing problems and communication problems. We use this reduction to obtain many new lower bounds in property testing from known results in communication complexity. Second, we introduce a new model of property testing that closely minors the active learning model. We show how testing results in this new model may be used to improve the efficiency of model selection algorithms in learning theory. The results presented in this thesis are obtained by applying tools from various mathematical areas, including probability theory, the analysis of boolean functions, orthogonal polynomials, and extremal combinatorics.

14 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202344
2022119
202189
202098
2019111
201897