McGill University School of Computer Science Ph.D. Student in the Modelling, Simulation and Design Lab Eugene Syriani Hans Vangheluwe

McGill UniversitySchool of Computer Science

Ph.D. Student in the Modelling, Simulation and Design Lab

Programmed Graph Rewriting with Time for

Simulation-Based Design

Eugene SyrianiHans Vangheluwe

McGill UniversitySchool of Computer Science

Ph.D. Student in the Modelling, Simulation and Design Lab

Programmed Graph Rewriting with Time for

Simulation-Based Design

Eugene SyrianiHans Vangheluwe

Programmed Graph Rewriting with Time for Simulation-Based Design

OVERVIEW

Background

In the context

The Modular Timed Graph Transformation (MoTiF) language

Case Study: Reactive PacMan Game

Modelling, Simulation and Synthesis

Modelling of transformation and its environment

Simulation for optimization

Synthesis of application

Conclusion and Future Work3


IN THE CONTEXT• Model Transformation Graph Transformation

• Controlled Graph Rewriting (rewriting rules)

• Control Primitives :Sequencing, Branching, Looping, Parallelism, Hierarchy

• Time is inherent in our transformation models

Modelling, Simulation and Synthesis4


IN THE CONTEXTModel of System

Model of Environment

Simulation Experiments

Synthesis of Application

5


MoTiF: SEMANTIC DOMAIN• The Discrete Event System Specification [1]

(DEVS) formalism

• Highly compositional simulation framework

• DEVS:– Blocks

– Ports

– Events

• Semantics: Parallel composition of blocks/models

6[1] Zeigler B.P., Multifacetted Modelling and Discrete Event Simulation/ Academic Press, London (1984)


MoTiF: SEMANTIC DOMAIN

Atomic DEVS:– Time Advance– Output Function– Internal Transition– External Transition

ATOMIC

7


MoTiF: SEMANTIC DOMAINCoupled DEVS

8

C1A1

A2

C2


MoTiF [2]• Blocks– Atomic: encapsulate a graph rewriting rule

– Coupled: encapsulate a set of rules (graph grammar)

• Events– Inport: receive the host graph

– Outport(s): send the transformed graph

9[2] Syriani E. and Vangheluwe H.: Programmed Graph Rewriting with DEVS. AGTIVE 2007, LNCS (2008)


MoTiFMODELLING ENVIRONMENT IN AToM3 [3]

10[3] de Lara J., Vangheluwe H., AToM3: A tool for multi-formalism and meta-modelling. FASE, LNCS 2306 (2002), 174-188


MoTiF EXECUTION

COMPILE

GENERATE

IMPORT

SIMULATE

class Pacmaneat: def match(): … def execute(): …

class Kill(ARule): def __init__(self): ARule.__init__(self, name=‘Kill') self.state = ARuleState(Pacdie()) def weightFunction(self): return 1.0

class Pacmanmoveri: def match(): … def execute(): …

class Pacmandie: def match(): … def execute(): …

11


CASE STUDY: REACTIVE PACMAN GAMESimplified PacMan formalism [4]

[4] Heckel R., Graph Transformation in a nutshell. FoVMT, ENTCS 148 (2006), 187-198 12


CASE STUDY: REACTIVE PACMAN GAMEBuild the Graph Rewriting Rules

13

14

2

1

2

5 pacLink

3

ghostLink

3

ghostLink

1: Match[1].score + 1

1

2

3

1

2

35

4

pacLink

foodLink

6

4

pacLink


CASE STUDY: REACTIVE PACMAN GAMEBuild the Graph Rewriting Rules

14

4

1 2

35

gridLeft

ghostLink

1 2

3

4

6

gridLeft

ghostLink

4

1 2

6

gridRight

pacLink

1 2

4

5

gridRight

pacLink

33


15



Model of System



MODELLING OF THE TRANSFORMATION: SYSTEM

• User – Controller – Autonomous loop

• Feed-back to User

• On User interrupt: User Controlled

• Feed-back to User

Autonomous UserControlled

16


MODELLING OF THE TRANSFORMATION: AUTONOMOUS CRule

Priorities

17


MODELLING OF THE TRANSFORMATION: GHOSTMOVE CRule

Decider finds the next move for the ghost

Decider consumes time

18


MODELLING OF TRANSFORMATION: SYSTEM


19


MODELLING OF THE TRANSFORMATION: USERCONTROLLED CRule

Conditional rule execution20


MODELLING OF THE TRANSFORMATION: SYSTEM


21


MODELLING OF ENVIRONMENT: USER CoupledBlock

UserBehavior

UserInteraction

•Customization

•Modularity

22


MODEL OF THE PLAYER: STRATEGY

23

DummyRandom Smart

class Key: up = 'u' down = 'd' left = 'l' right = 'r' keys = [up, down, left, right]

def nextRandom(self): import random return random.Random().choice(Key.keys)


MODELLING OF ENVIRONMENT: USERBEHAVIOR CoupledBlock

Back-tracking

Collector consumes time

24


MODELLING OF ENVIRONMENT: TRYMOVE CRule

4

1 2

5

gridRight

pacLink

1 2

4

6

gridRight

pacLink

33

1

78

ghostLink

25Non-determinism


MODEL OF THE PLAYER: SPEEDPlayer reaction time [5]:– Thinking time

– Motorics time

26

𝑭ሺ𝒙ሻ= 𝒆−𝒆𝒃−𝒙𝒂

[5] Zaitev A.V., Skorik Y.A., Mathematical description of sensorimotor reaction time distribution, Human Psychology 28(4) (2002), 494-497

Slow Normal FastVery Fast


27



Model of System



WHY DO WE NEED SIMULATION?

• A.I. StrategyRandom – Smart – Very Smart

• SpeedToo Slow – … – Too Fast

Fix Strategy: Very Smart

Find optimal speed

We want to build a “playable” game

28


SIMULATION RESULTSFinding the optimal game speed

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30



Model of System



SYNTHESIS OF APPLICATION• Synthesis of a reactive game

• Discard the UserBehavior block

• Runs on a web browser using AJAX and SVG

• Real-time model transformation

31

UserInteractionUser

BehaviorUser

Interaction


SUMMARYMoTiF allows for

• Modelling and Simulation-Based Design– Graph transformation rules

– Timed transformation system

– User

• Synthesis of applications– Reactive

– Real-time

32


Model E

veryth

ing


FUTURE WORK

• Model A.I. behavior: backtracking

• Re-use and parametrisation of transformation models

• MORE COMPLEX EXAMPLES

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Documents

McGill University School of Computer Science Ph.D. Student in the Modelling, Simulation and Design Lab Eugene Syriani Hans Vangheluwe