The central notion of a rough set is indiscernibility based on equivalence relation. Since equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between upper and lower approximations is lost. We here introduce two different equivalence relations, the one for upper approximation, and the other for lower approximation, and construct co...

Many compilation problems require computing the control dependence equivalence relation which divides nodes in a control ow graph into equivalence classes such that nodes are in the same class if and only if they have the same set of control dependences. In this paper, we show that this relation can be computed in O(E) time by reducing it to a naturally stated graph problem: in a strongly conne...

82 Abstract—This article proposes a cache pattern with multiqueries and describes the multi-query optimization with scheduling, caching and pipelining A set of cache patterns is derived from a set of class of multiqueries that are loaded into the cache. Each cache pattern represents a unique equivalence class in the set of patterns. The multi-query optimization with scheduling, caching and pipe...

The discrete-time dynamics of small neural networks is studied empirically, with emphasis laid on non-trivial bifurcation scenarios. For particular two- and three-neuron networks interesting dynamical properties like periodic, quasi-periodic and chaotic attractors are observed, many of them co-existing for one and the same set of parameters. An appropriate equivalence class of networks is defin...

The equivalence of leaf languages of tree adjoining grammars and monadic linear context-free grammars was shown about a decade ago. This paper presents a proof of the strong equivalence of these grammar formalisms. Non-strict tree adjoining grammars and monadic linear context-free grammars define the same class of tree languages. We also present a logical characterisation of this tree language ...

The formulation of gravity in 3 + 1 dimensions in which the spin connection is the basic field (ω-frame) leads to a theory with first and second class constraints. Here, the Dirac brackets for the second class constraints are evaluated and the Dirac algebra of first class constraints is found to be the usual algebra associated to space-time reparametrizations and tangent space rotations. This e...