## AAI – Actor-Actor Interaction. A Toy-Example, No.1

eJournal: uffmm.org, ISSN 2567-6458
13.Dec.2017
Email: info@uffmm.org

Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

#### Contents

1 Problem ….. 3
2 AAI-Check ….. 3
3 Actor-Story (AS) …..  3
3.1 AS as a Text . . . . . . . . . . . . . . . . . .3
3.2 Translation of a Textual AS into a Formal AS …… 4
3.3 AS as a Formal Expression . . . . . . . . . .4
3.4 Translation of a Formal AS into a Pictorial AS… 5
4 Actor-Model (AM) …..  5
4.1 AM for the User as a Text . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . .6
4.2 AM for the System as a Text . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Combined AS and AM as a Text …..  6
5.1 AM as an Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Simulation …..  7
6.1 Simulating the AS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
6.2 Simulating the AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
6.3 Simulating AS with AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7 Appendix: Formalisms ….. 8
7.1 Set of Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
7.2 Predicate Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8 Appendix: The Meaning of Expressions …11
8.1 States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.2 Changes by Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

#### Abstract

Following the general concepts of the paper ’AAI – Actor-Actor Interaction. A Philosophy of Science View’ from 3.Oct.2017 this paper illustrates a simple application where the difference as well as the
interaction between an actor story and several actor models is shown. The details of interface-design as well as the usability-testing are not part of this example.(This example replaces the paper with the title
’AAI – Case Study Actor Story with Actor Model. Simple Grid-Environment’ from 15.Nov.2017). One special point is the meaning of the formal expressions of the actor story.

Attention: This toy example is not yet in fully conformance with the newly published Case-Study-Template

To read the full text see PDF

Clearly, one can debate whether a ‘toy-example’ makes sens, but the complexity of the concepts in this AAI-approach is to great to illustrate these in the beginning  with a realistic example without loosing the idea. The author of the paper has tried many — also very advanced — versions in the last years and this is the first time that he himself has the feeling that at least the idea is now clear enough. And from teaching students it is very clear, if you cannot explain an idea in a toy-example you never will be able to apply it to real big problems…