Abstract: In the paper we define grammars on a class of labeled, partially ordered hypergraphs, called distributed systems. A distributed system models both the spatial and the temporal aspects of a real system through the relations of adjacency and causality. Terminal symbols represent the (deterministic, certain) past history of the system while nonterminal symbols model the (possibly nondeterministic, potential) future history of the system. The (context free) productions of a grammar represent the possible stand-alone evolutions of system components. From the productions, we obtain a (possibly infinite) number of rewriting rules, which model the synchronized evolution of adjacent system components. The (terminal) distributed systems derived within a given grammar represent the alternative deterministic, concurrent computations of a single nondeterministic system which is thus completely modeled by the grammar.

Abstract: The constraints imposed on system design by microcomputer hardware and system software are discussed. File structure is described and there is a brief account of the overall system configuration. Indexing is by limited file inversion, with a number of choices of indexing mode. Boolean searching is used together with adjacency and character matching facilities. A number of uses of the system are briefly described.

Abstract: This paper treats the modeling of an important class of databases, i.e., geographic databases, with emphasis on both structural (data definition) and behavioral (data manipulation) aspects. Geometric objects such as polygons, line segments, and points may have different relations among each other (such as order, adjacency, connectivity) and can be represented in a uniform spatial data structure (structure graph). The dynamic behavior is defined by a finite set of consistency-preserving state transitions (productions) where coincidence problems as well as topological properties have to be solved. Moreover, the graph grammar approach can be used to study the synchronization of several concurrent productions (Church-Rosser properties).

Abstract: In this paper, a proof is constructed to show tbat assignment polytope of order n is edge N(n) connected where N(n) is the number of adjacent vertices to any vertex on the assignment polytope. This settles the conjecture made by Balinski and Russakeff on the assignment polytope in its weeker form. Furthermore, the set of N(n) edge-disjoint paths need not consist of a path of length greater than four. The result is extended to all polytopes of diameter two and paths can be constructed there of provided the corresponding adjacency rules are known.

Abstract: Given a formulation of a problem, a compact representation is required both for theoretical purposes -- measuring the complexity of algorithms, and for practical purposes -- data compression. The adjacency lists method for representing graphs is compared to the information theoretic lower bounds, and it is shown to be optimal in many instances. For n-vertex labeled planar graphs the adjacency lists method requires 3nlogn + O(n) bits, a linear algorithm is presented to obtain a 3/2nlogn + O(n) representation while nlogn + O(n) is shown to be the minimum.