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Papers by Thomas Muñoz
Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2021
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by ... more Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that they allow looping for a number of steps that is bounded by the matrix dimension. In this paper we extend the matrix query language MATLANG with this type of recursion, and show that this suffices to express classical linear algebra algorithms. We study the expressive power of this language and show that it naturally corresponds to arithmetic circuit families, which are often said to capture linear algebra. Furthermore, we analyze several sub-fragments of our language, and show that their expressive power is closely tied to logical formalisms on semiringannotated relations.
Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2021
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by ... more Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that they allow looping for a number of steps that is bounded by the matrix dimension. In this paper we extend the matrix query language MATLANG with this type of recursion, and show that this suffices to express classical linear algebra algorithms. We study the expressive power of this language and show that it naturally corresponds to arithmetic circuit families, which are often said to capture linear algebra. Furthermore, we analyze several sub-fragments of our language, and show that their expressive power is closely tied to logical formalisms on semiringannotated relations.
En esta página, se presenta un ejemplo interesante que permite al estudiante obtener expresiones ... more En esta página, se presenta un ejemplo interesante que permite al estudiante obtener expresiones para un caso general una vez examinados las dos o tres primeras situaciones. Se trata de un ejercicio de progresiones geométricas, un tema habitual en los cursos de Matemáticas a nivel elemental.
Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2021
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by ... more Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that they allow looping for a number of steps that is bounded by the matrix dimension. In this paper we extend the matrix query language MATLANG with this type of recursion, and show that this suffices to express classical linear algebra algorithms. We study the expressive power of this language and show that it naturally corresponds to arithmetic circuit families, which are often said to capture linear algebra. Furthermore, we analyze several sub-fragments of our language, and show that their expressive power is closely tied to logical formalisms on semiringannotated relations.
Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2021
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by ... more Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that they allow looping for a number of steps that is bounded by the matrix dimension. In this paper we extend the matrix query language MATLANG with this type of recursion, and show that this suffices to express classical linear algebra algorithms. We study the expressive power of this language and show that it naturally corresponds to arithmetic circuit families, which are often said to capture linear algebra. Furthermore, we analyze several sub-fragments of our language, and show that their expressive power is closely tied to logical formalisms on semiringannotated relations.
En esta página, se presenta un ejemplo interesante que permite al estudiante obtener expresiones ... more En esta página, se presenta un ejemplo interesante que permite al estudiante obtener expresiones para un caso general una vez examinados las dos o tres primeras situaciones. Se trata de un ejercicio de progresiones geométricas, un tema habitual en los cursos de Matemáticas a nivel elemental.