/department of mathematics and computer science Visualization of Transition Systems Hannes Pretorius Visualization Group

/department of mathematics and computer science Outline 1.Transition systems 2.Motivation 3.Existing results 4.Process 5.Experiment 1: projection 6.Experiment 2: simulation 7.Experiment 3: clustering 8.General conclusions

/department of mathematics and computer science Transition systems Used to analyze and verify systems Explicit descriptions of system behavior: –All system states –Transitions between these Describe systems whose states evolve over time

/department of mathematics and computer science Transition systems

/department of mathematics and computer science Motivation 1.Facilitate insight: –Tools and techniques to understand systems –Address size and complexity 2.“Gestalt”: –Associate visual form with abstract formalism –Enhances communication

/department of mathematics and computer science Motivation Frank van Ham’s FSMView: –Shows global structure and symmetries New approaches: –FSMView excels at what it was designed for –Investigate techniques with more focus on attributes (data, transition labels, …) –More interaction

/department of mathematics and computer science Process Formal specification LPE LTS Σ ValidateSimulateSpecify Real world

/department of mathematics and computer science Experiment 1: projection Σ Validate Simulate Specify

/department of mathematics and computer science Data communication Data is stored –States: vectors of data values –Multidimensional points Experiment 1: approach [1,1,0,2] [1,1,2,1][2,2,1,0]

/department of mathematics and computer science Experiment 1: approach Data Visual mapping Visual mapping Overview (dims) 2D projection Visual mapping Select subset

/department of mathematics and computer science Experiment 1: overview State Dimension s1s1 s2s2 s3s3 a b c d

/department of mathematics and computer science Experiment 1: projecting to 2D s1s1 s2s2 s3s3

/department of mathematics and computer science Experiment 1: demo

/department of mathematics and computer science Experiment 1: results Identify: –Superfluous variables –Correlations spanning multiple dimensions –States with specific valuations of variables –Phases of behavior Interaction: –Coupling of two views important “Data-centric” view: –Does not reveal enough about behavior

/department of mathematics and computer science Experiment 2: simulation Validate Simulate Specify

/department of mathematics and computer science Experiment 2: approach Simulation: –Quick and incremental checking of specification Text-based output: –Time consuming analysis –Not intuitive –Prone to human error

/department of mathematics and computer science Experiment 2: approach Automated parking garage Custom plug-in: –Maps current system state onto 2D floor plan Visual cues: –Lift position –Status of parking space (free, occupied,…) –Status of shuttles

/department of mathematics and computer science Experiment 2: visual mapping LiftShuttle Occupied Free Conveyor belt

/department of mathematics and computer science Experiment 2: demo

/department of mathematics and computer science Experiment 2: results Efficiency of analysis: –Saves time –Intuitively clear and easy to follow –Identified and corrected serious errors early on Stakeholders: –Convinced colleagues of merit of visualization –Means to communicate abstract ideas to client Shows behavior

/department of mathematics and computer science Experiment 3: clustering Σ Validate Simulate Specify

/department of mathematics and computer science Experiment 3: approach Directed graph: –Reduce size and complexity Associate meaning with states and transitions: –Reduce in meaningful way –Ability to take behavior into account

/department of mathematics and computer science Experiment 3: initial ideas Linear representation: –Predictable –Suggests ordered analysis –Effective way to show patterns Initial clustering: –Ranking (BFS, DFS) –Based on local behavior (fan-in, fan-out of transition labels at every state)

/department of mathematics and computer science Experiment 3: initial ideas

/department of mathematics and computer science Experiment 3: approach Every state is annotated: –Tuple with coordinates –Every coordinate has associated type –Every type has a domain Partition states based on equivalence relation: –Select subset of coordinates –Cluster domain of associated type

/department of mathematics and computer science Experiment 3: approach Define eq. rel. Data Eq. rel Cluster Clustered data Visual mapping Selection info. Vis. Select

/department of mathematics and computer science Experiment 3: approach First partitioning: coordinate i Original transition system

/department of mathematics and computer science Experiment 3: approach Second partitioning: coordinate j Original transition system

/department of mathematics and computer science Experiment 3: approach Allows for clustering based on: –Existing attributes –Derived attributes (structural properties, equivalence classes, …) –Construct hierarchy of clusters

/department of mathematics and computer science Experiment 3: demo

/department of mathematics and computer science Experiment 3: results Definition of equivalence relation on the fly: –Select subset of components –Cluster type domains Assumption: –User associates meaning with components Combination of clusters and hierarchy promising Work in progress: –Interaction –Derived attributes (behavior-related)

/department of mathematics and computer science General conclusions Experiments: –Gap between abstract and real world –Address sub-problems –Better understanding of problem (focus on behavior, clustering more general, …) Looking ahead: –Include insights in current tool –Add more functionality to current tool (annotation, selection, may- and must- transitions)

/department of mathematics and computer science General conclusions Open questions: – How to move from one clustering to the next –Simulation works really well, how to generalize? –User requirements ? ?

/department of mathematics and computer science Questions