Showing papers on "Tuple published in 1975"

An algebra of relations for machine computation

Abstract: This paper extends the relational algebra of data bases, presented by Codd [4] and others, in four areas. The first is the use of selector names to remove order dependencies from the columns of a relation. This use of selector names enables us to define a more general class of operations, which include the normal relational operations of union, equi-join etc., as special cases. Thirdly we introduce relations represented algorithmically as well as by a stored set of tuples. Such computed relations cannot always be effectively realised as a finite set of tuples. Finally we consider relational expressions as algorithmic representations of relations and characterize their effectiveness.

On the unambiguity of n-tuple languages

Abstract: Several results concerning the preservation of unambiguity in n-tuple languages are presented here. Furthermore, the notion of n-stratified sets — as appropriate generalization of the straified sets defined by Ginsburg — is introduced and a necessary and sufficient characterisation result for bounded unambiguous n-tuple languages analogous to bounded unambiguous context free languages is given.

Commuting $k$-tuples of self adjoint operators and matrix measures

Abstract: In this note we give a generalization of a spectral representation theorem for self adjoint operators in a Hilbert space recently obtained by the author [1]. Our interest here is to develop corresponding results for a k-tuple (T1, …, Tk) of commuting self adjoint operators.