Dependence relation

Abstract: The order in which the statements of a program are executed can affect the execution time of the program. Optimizing compilers have made use of this fact by reordering code to improve its performance on a machine. Some statement orderings are essential to a program's results, however; these orderings form the basis of a dependence relation among the statements of a program. Dependences can arise in two separate ways within a program: from data considerations, and from control considerations. However, since all control dependences can be converted to data dependences by guarding statements with precise conditions that control their execution, data dependence is the more general concept. Data dependences within loops can arise from two separate effects. The position of statements within the loops may cause a dependence, or iteration of a specific loop may cause a dependence. Characterizing dependence in this manner provides the foundation of extremely effective algorithms for reordering transformations. One very important reordering transformation which is made possible by dependence is vectorization. Vectorization of a program can often be enchanced by loop interchange. Dependence plays an important role in determining when loops should be interchanged. Interchange preventing dependences inhibit a particular interchange; interchange sensitive dependences may make an interchange less profitable in terms of increased vectorization. Dependence for symbolic subscripts is an extremely difficult problem. Nevertheless, some cases can be handled by techniques based on standard dependence tests. One last reordering transformation which is of extreme importance on vector machines is sectioning, or devectorization. Dependence not only determines when a statement can be correctly sectioned but it also can be used to improve the register performance of a sectioned statement.

Abstract: A general method for the identification of the independent subsets in loops with constant dependence vectors is presented. It is shown that the dependence relation remains invariant under a unimodular transformation. Then a unimodular transformation is used to bring the dependence matrix into a form where the independent subsets are obtained by a direct and inexpensive partitioning algorithm. This leads to a procedure for the automatic conversion of a serial loop into a nest of parallel DO-ALL loops. Another unimodular transformation results in an algorithm to label the dependent iterations of an n-fold nested loop in O(n/sup 2/) time. This provides a multithreaded dynamic scheduling scheme requiring only one fork and one join primitive. >

Abstract: In a system of performing automatic translation from natural language into another natural language based on dependence relation among concepts, a thesaurus representing implication among concepts and a co-occurrence dictionary storing co-occurrence relation between a predicate word and an argument concept are utilized to select a suitable translation word when a plurality of candidate words exist corresponding to a predicate concept. Furthermore, knowledge regarding the co-occurrence relation is obtained based on feedback information from a revise operation to translation results, thereby contents of co-occurrence relation dictionary can be more and more complete.

Abstract: A new solution to the star-triangle relation is given, for an Ising type model that involves interacting spins, that contain integer and real valued components. Boltzmann weights of the model are given in terms of the lens elliptic-gamma function, and are based on Yamazaki's recently obtained solution of the star-star relation. The star-triangle given here, implies Seiberg duality for the $4\!-\!d$ $\mathcal{N}=1$ $S_1\times S_3/\mathbb{Z}_r$ index of the $SU(2)$ quiver gauge theory, and the corresponding two component spin case of the star-star relation of Yamazaki. A proof of the star-triangle relation is given, resulting in a new elliptic hypergeometric integral identity. The star-triangle relation in this paper contains the master solution of Bazhanov and Sergeev as a special case. Two other limiting cases are considered one of which gives a new star-triangle relation in terms of ratios of infinite $q$-products, while the other case gives a new way of deriving a star-triangle relation previously obtained by the author.