Defining Effectiveness Using Finite Sets A Study on Computability

AbstractThis paper studies effectiveness in the domain of computability. In the context of model-theoretical approaches to effectiveness, where a function is considered effective if there is a model containing a representation of such function, our definition relies on a model provided by functions between finite sets and uses category theory as its mathematical foundations. The model relies on the fact that every function between finite sets is computable, and that the finite composition of such functions is also computable. Our approach is an alternative to the traditional model-theoretical based works which rely on (ZFC) set theory as a mathematical foundation, and our approach is also novel when compared to the already existing works using category theory to approach computability results. Moreover, we show how to encode Turing machine computations in the model, thus concluding the model expresses at least the desired computational behavior. We also provide details on what instances of the model would indeed be computable by a Turing machine

Validades Existenciais e Enigmas Relacionados

A lógica não contém teoremas puramente existenciais: as únicas sentenças existenciaisválidas são aquelas com análogas universais válidas. Aqui, mostramos que istorealmente é assim quando corretamente interpretado: toda validade ex- istencial possuiuma análoga universal simples, que também é válida. Também caracterizamos validadesuniversais e existenciais em termos de tautologias.Logic does not have purely existential theorems: the only existentialsentences that are valid are those with valid universal analogues. Here, we showindeed this is so, when properly interpreted: every existential validity has asimple universal analogue, which is also valid. We also characterize existentialand universal validities in terms of tautologies

Bio-Strings: A Relational Database Data-Type for Dealing with Large Biosequences

DNA sequencers output a large set of very long biological data strings that we should persist in databases rather than basic text file systems. Many different data models and database management systems (DBMS) may deal with both storage and efficiency issues regarding genomic datasets. Specifically, there is a need for handling strings with variable sizes while keeping their biological meaning. Relational database management systems (RDBMS) provide several data types that could be further explored for the genomics context. Besides, they enforce integrity, consistency, and enable good abstractions for more conventional data. We propose the relational text data type to represent and manipulate biological sequences and their derivatives. We present a logical schema for representing the core biological information, which may be inferred from a given biological conceptual data schema and the corresponding function manipulations. We implement and evaluate these stored functions into an actual RDBMS for both efficacy and efficiency. We show that it is possible to enforce basic and complex requirements for the genomic domain. We claim that the well-established relational text data type in RDBMS may appropriately handle the representation and persistency of biological sequences. We base our approach on the idea of domain-specific abstract data types that can store data with semantically defined functions while hiding those details from non-technical end-users