Autonomous Units and Their Semantics — The Sequential Case

Abstract

Abstract. In this paper, we introduce the notion of a community of autonomous units as a rule-based and graph-transformational device to model processes that run interactively but independently of each other in a common environment. The emphasis of the approach is laid on the study of the formal semantics of a community as a whole and of each of its member units separately. We concentrate on the sequential case where only one unit can act at a time and the rule applications of the involved units are interleaved with each other.

Graph Transformation Units – An Overview

“…In this sense, a graph transformation unit is a centralized computational entity. The concept of autonomuous units (see, e.g., [26][27][28]) is a generalization to a decentralized processing of graphs. The autonomuous units in a community act, interact, and communicate in a common environment, with each of them controling its own activities autonomuously.…”

Autonomous Units and Their Semantics - The Parallel Case

“…In this paper, we have supplemented the sequential-process semantics of autonomous units in [1] by a parallel-process semantics which allows the units of a community to act and interact simultaneously in a common environment. Moreover, we have studied the relationship of autonomous units to three other modeling frameworks that provide notions of parallelism: Petri nets, cellular automata, and multiagent systems.…”

“…In [1] we have shown that autonomous units with sequential process semantics generalize our former modeling concept of graph transformation units (see, e.g., [14]). While the latter apply their rules without any interference from the outside, an autonomous unit works in a dynamic environment which may change because of the activities of other units in the community.…”

“…is a regular graph of type k subject to the condition: for each v ∈ V, there is a sequence of edges e(v) 1 …”

Autonomous Units for Communication-based Dynamic Scheduling

“…The changes of the environment happen in a well-defined way as application of graph transformation rules on the environment graph, yielding a rigorous formal operational semantics not only for a single autonomous unit but also for the community as a whole. The sequential semantics as discussed in (Hölscher et al 2006b) is used if exactly one unit is performing an action at any given point of time. The parallel semantics, where a number of actions take place in parallel at the same time is investigated in (Kreowski and Kuske 2006).…”