The workflow supports system analysts in understanding the behaviour of complex computer-based systems modelled as large state transition graphs (tens of thousands of nodes). The analyst interactively selects perspectives — subsets and orderings of state attributes — to perform hierarchical clustering that simultaneously reduces graph complexity and serves as an analysis mechanism. Clustering produces three interrelated data types (hierarchy, metrics, and abstract graph) represented in a single integrated visualisation combining node-link diagrams, bar trees, and arc diagrams. The analyst iteratively takes different perspectives, identifies behavioural patterns, and performs focused analyses to answer questions about system properties such as liveness, symmetry, and deadlock conditions.
The input is a state transition graph G = (V, E) generated from a behavioural specification of a computer-based system (e.g., an industrial wafer stepper). Each state (node) carries multiple typed attributes with discrete, low-cardinality domains: both attributes describing system component contents (e.g., lock contents, robot arm contents) and derived structural attributes (e.g., fan-out). The graph is large (55,043 nodes, 289,443 edges) and cannot be understood through conventional graph drawing.
The analyst selects a subset of state attributes and defines their ordering — this constitutes a "perspective" on the system. They may also cluster domain values of individual attributes to reduce cardinality (e.g., collapsing fan-out values into a binary deadlock/non-deadlock distinction). The system then performs attribute-based hierarchical clustering: the full node set is partitioned by the first attribute's values, each partition is sub-partitioned by the second attribute's values, and so on, producing a tree of p+1 levels for p selected attributes. This simultaneously produces: (a) the clustering hierarchy itself, (b) metric data (cluster sizes at each level), and (c) an abstract transition graph where edges between original nodes are bundled between leaf clusters.
Three representations are combined in a single display: a node-link diagram of the clustering hierarchy (top half, with colour-coded attribute values and cushioned triangles), an arc diagram of the abstract transition graph (centre, with directed arcs interpreted clockwise and thickness encoding bundle size), and a bar tree of cluster sizes (bottom half, with layered bars reflecting hierarchy levels on a logarithmic or linear scale). The analyst can apply focus bands for fisheye magnification, show/hide hierarchy levels in the bar tree, click bars to inspect exact values, and select nodes/edges to trace specific transitions.
The analyst iteratively takes different perspectives to gain insight into system behaviour. From the tray's perspective (selecting fresh-wafer-list and wafers-in-system), they identify deterministic forward progression and exponential complexity growth. From the wafer stage's perspective (prep-stage, proc-stage), they validate safety requirements (e.g., no unprepared wafer can reach the processing stage). From the locks' perspective (lock 1–4), they identify regular nested patterns indicating behavioural symmetry between locks. After each perspective, they assess whether sufficient understanding has been gained or whether a different perspective is needed.
For targeted questions such as deadlock detection, the analyst: (a) clusters on fan-out to isolate deadlock nodes (fan-out = 0), (b) clusters the fan-out domain into binary deadlock/non-deadlock to simplify, (c) combines fan-out with other attributes (tray, robots) to identify conditions leading to deadlock, and (d) uses focus-band zooming to select specific deadlock nodes, inspect their attribute values, highlight incoming edges, and trace these back to originating clusters to identify exact pre-conditions. This focused analysis reveals that deadlock occurs under specific robot-arm configurations and can be prevented by limiting wafers in the system.
The analyst synthesises findings: confirmed liveness properties (forward progression from initial to final state), validated safety requirements (no invalid wafer stage configurations), identified behavioural symmetries (four locks exhibit identical behaviour), detected and explained deadlock (exact pre- and post-conditions identified), and proposed prevention strategies (limiting wafer count).