Consider the problem of maintaining a family F of dynamic sets subject to insertions, deletions, and set-intersection reporting queries: given S, S′ ∈ F , report every member of S ∩S′ in any order. We show that in the word RAM model, where w is the word size, given a cap d on the maximum size of any set, we can support set intersection queries in O( d w/ log2 w ) expected time, and updates in O...

Set constraints are inclusions between expressions denoting sets of trees. The eficiency of their satisfiabili ty test is a central issue in set-based program analysis, their main application domain. W e introduce the class of set constraints with intersection (the only operators forming the expressions are constructors and intersection) and show that i ts satisfiability problem as DEXPTIME-com...

A recent result of J. Damon’s [4] relates the Ae-versal unfoldings of a map-germ f with the KD(G)-versal unfoldings of an associated map germ which induces f from a stable map G. We extend this result to the case where the source is a complete intersection with an isolated singularity. In a similar vein, we also relate the bifurcation theoretic versal deformation of a bifurcation problem (map-g...

Abstract: The 3-SAT problem is one of the most important and interesting NP-complete problems with many applications in different areas. In several previous papers we showed the use of ternary vectors and set-theoretic considerations as well as binary codings and bit-parallel vector operations in order to solve this problem. Lists of orthogonal ternary vectors have been the main data structure,...

An Euler diagram C = {c1, c2, . . . , cn} is a collection of n simple closed curves (i.e., Jordan curves) that partition the plane into connected subsets, called regions, each of which is enclosed by a unique combination of curves. Typically, Euler diagrams are used to visualize the distribution of discrete characteristics across a sample population; in this case, each curve represents a charac...

The permutation representation theory of groups has been extended, through quasigroups, to one-sided left (or right) quasigroups. The current paper establishes a link with the theory of ordered sets, introducing the concept of a Burnside order that generalizes the poset of conjugacy classes of subgroups of a finite group. Use of the Burnside order leads to a simplification in the proof of key p...