A static dictionary is a data structure for storing subsets of a finite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size Ω(log |U |), and show that for n-element subsets, constant worst case query time can be obtained using B +O(log log |U |) + o(n) bits of storage, where B = dlog2 (|U| n ) e is the minimum number...

We present two masked priming lexical decision experiments in which we examined whether a nonword prime word would activate associative/semantic information from its corresponding addition neighbor (e.g., lght-dark via the addition neighbor light), producing associative/semantic priming. The rationale was the following: If a nonword prime with a missing letter produced a semantic/associative pr...

We consider a probabilistic antimatroid A on the ground set E, where each element e ∈ E may succeed with probability pe . We focus on the expected rank ER(A) of a subset of E as a polynomial in the pe . General formulas hold for arbitrary antimatroids, and simpler expressions are valid for certain well-studied classes, including trees, rooted trees, posets, and finite subsets of the plane. We c...

We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids. We show that for polycyclic monoids of rank 2 or more, such automata accept exactly the context-free languages. For the polycyclic monoid of rank 1 (that is...

Two different constructions are given of a rank 8 arc-transitive graph with 165 vertices and valency 8, whose automorphism group is M11. One involves 3-subsets of an 11-set while the other involves 4-subsets of a 12-set, and the constructions are linked with the Witt designs on 11, 12 and 24 points. Four different constructions are given of a rank 9 arc-transitive graph with 55 vertices and val...

Abstract. The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels. This kernel hierarchy produces a set of tools that provides direct access to computations of interest in probability limit theorems; in particular, f...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

We consider a probabilistic antimatroid A on the ground set E, where each element e ∈ E may succeed with probability pe. We focus on the expected rank ER(A) of a subset of E as a polynomial in the pe. General formulas hold for arbitrary antimatroids, and simpler expressions are valid for certain well-studied classes, including trees, rooted trees, posets, and finite subsets of the plane. We con...

The Dehn function and its higher-dimensional generalizations measure the difficulty of filling a sphere in space by ball. In nonpositively curved spaces, one can construct fillings using geodesics, but become more complicated subsets such as lattices symmetric spaces. this paper, we prove sharp inequalities for (arithmetic) higher rank semisimple Lie groups. When n is less than associated space...

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...