An Algorithm for Minimal Insertion in a Type Lattice 3
نویسنده
چکیده
2 The problem of inserting a new element x into a lattice of types L is addressed in the paper. As the poset L + x obtained by the direct insertion of x in L, is not necessarily a lattice, some set of auxiliary elements should be added to restore the lattice properties. An approach towards the lattice insertion is presented which allows the set of auxiliary elements to be kept minimal. The key idea is to build the nal lattice L + as isomorphic to the Dedekind-McNeille completion of the order L + x. Our strategy is based on a global deenition of the set of auxiliary elements and their location in L +. Each auxiliary is related to a speciic element of L, an odd, which represents GLB (LUB) of some elements in L superior (inferior) to x. An appropriate computation scheme for the auxiliary types is given preserving the sub-typing in the lattice L +. The insertion strategy presented is more general than the existing ones, since it deals with general kind lattices and makes no hypothesis on the location of x in L. An algorithm computing L + from L and x of time complexity O(jLjjJ (L)j! 3 (L)) is provided.
منابع مشابه
An Algorithm for Minimal Insertion in a Type Lattice
We consider the insertion of a new element x in a lattice of types L. As the poset L + x obtained by the direct insertion of x in L, is not necessarily a lattice, a set of auxiliary elements should be added in order to restore the lattice properties. We describe an approach towards the lattice insertion based on a global deenition of the set of necessary auxiliary elements and their location in...
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