This paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as many similar variants can be reassembled. This process is formalized by tiling grammars. Our core contribution is an approach for simplifying tiling grammars such that we obtain phys...

Succinct representations of trees are an elegant solution to make large trees fit in main memory while still supporting navigational operations in constant time. However, their construction time remains a bottleneck. We introduce a practical parallel algorithm that improves the state of the art in succinct tree construction. Given a tree on n nodes stored as a sequence of balanced parentheses, ...

Systems of k-ary operations, k > 2, generalizing orthogonal sets are considered. These systems have the following property: every k successive k-ary operations of the system are orthogonal. We call these systems successively orthogonal, establish some properties, give examples and methods of construction of these systems.

In this paper we address the explicit construction of complex update programs from basic update operations like insert tuple and delete tuple The main contribution is the de nition of a semantics that is based on sets of deferred update requests We propose a logic in which besides the concurrent and sequential composition of update operations also set oriented updates can be expressed

By a result of H. Cartan (cf. 5]), the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this paper, we provide a general approach to the construction of Cartan operations in the context of simplicial algebras over an operad.

By formally defining the relevant mathematical spaces and models we show that the operations of addition and multiplication, and the concepts that depend on these operations, are not applicable on ordinal, cardinal, and expected utility. Furthermore, expected utility’s scale construction rule is self-contradictory.

We construct Adams operations on higher algebraic K-groups induced by operations such as symmetric powers on any suitable exact category, by constructing an explicit map of spaces, combinatorially deened. The map uses the S-construction of Waldhausen, and deloops (once) earlier constructions of the map.

Fluid Construction Grammar (FCG) is a formalism for defining the inventory of lexical and grammatical conventions that language processing requires and the operations with which this inventory is used to parse and produce sentences. This chapter introduces some of the key ideas and basic design principles behind the development of Fluid Construction Grammar.