A Graph Transformation System Model of Reliable Dynamic Communication Networks for Location Transparent Mobile Agents M. Kurihara (Hokkaido Univ., Japan) and M. Numazawa (Otaru Univ. Commerce, Japan)

Introduction Distributed software technologies Mobile agent technology Future intelligent telecommunication technologies research practice Mobile agents are software agents that can move around the network.

Introduction (2) mobile agent network Location transparent Static: reliable Dynamic: sound

Structure of this talk 1.Mobile agents & location transparency 2.Proxy networks (Reliablity) 3.Graph transformation system (Soundness)

Mobile Agents Software agents that can move around the network agent stop resume move Host 1 Host 2 location transparent network

Location Transparency The communications will not fail even if agent B has moved to B ’ without any notice to A. A BB' communicating move Can communicate? In the location transparent network, yes.

Approaches to location transparency (system-level implementation) Logging: the agents leave (in the agent server) the trail information containing the next location Brute Force: the system searches for the target agent by sending a query to every agent server Registration: the system keeps the locations of all agents in a unique directory server, updating the information each time an agent makes a move

Proxy Networks (application-level implementation of location transparency) Basic idea: simple communication path for forwarding messages A B'BB" pro xy targe t Problems Reliability: what if a proxy is abnormal? Performance: O(the length of the path) forward

Reliable and more efficient proxy networks Reliable: one abnormal proxy is allowed. Performance: there is a shorter path. Target Special proxy Normal proxies

Formal Representation (graph-theoretical definition of proxy networks) A proxy network is a finite, simple, directed acyclic graph G=(V, E) that satisfy the following three conditions (in the next slide). (The vertexes of V are called agents, and the directed edges of E are called links. By definition, a simple graph contains no parallel edges, which connect the same start and end vertexes; and an acyclic graph contains no circuits.)

Graph-theoretical definition of proxy networks (Contd.): the three conditions 1. There exists a unique agent (called the target) with no outgoing links. (The agents other than the target are called proxies.) 2. There exists a unique proxy (called the special proxy) with exactly one outgoing link. The link should be connected to the target. 3. The remaining proxies (called normal proxies) have exactly two outgoing links.

Theorem 1 (Reliability) For all pairs of distinct proxies v and w, there exists a path from v to the target t without passing through w. vwt

Proof of Theorem 1 Start from v and follow an appropriate path as follows. At normal proxies, follow a link whose end vertex is not w. Repeat this process while you are at a normal proxy. normal proxy w

Proof of Theorem 1 (Contd.) Eventually, you will reach either the special proxy or the target. If you are at the target, you are done. Otherwise, you are at the special proxy. Follow the link connected to the target. special proxy t

Graph Transformation Rule

Graph Transformation System

The initial network G 0 st

Application of graph rewrite rules

Theorem 2 (Soundness) If, then is a proxy network.

Summary 1.Mobile agents & location transparency 2.Proxy networks (Reliablity) 3.Graph transformation system (Soundness)

Future Work Formal theory of more complex mobile agent systems that might allow us (or even agents) to rigorously (or mechanically) reason about the dynamic nature of the networks.