Enter transitions, render a diagram, and compute analysis tables. You can model deterministic machines or probabilistic Markov chains using the same input.
- Supports labels and optional probabilities per transition.
- Computes adjacency and transition matrices, degrees, reachability, SCC count, absorbing states.
- Downloads CSV summary and a PDF snapshot for sharing.
Rendered state transition diagram
Example data table
This sample shows how transition records look after parsing.
| # | From | To | Label | Probability |
|---|---|---|---|---|
| 1 | S0 | S1 | go | 0.60 |
| 2 | S0 | S2 | alt | 0.40 |
| 3 | S1 | S3 | next | — |
| 4 | S2 | S2 | loop | 1.00 |
Formula used
How to use this calculator
- Type transitions as comma-separated fields: from,to,label,prob.
- Leave states empty to auto-detect them from transitions.
- Choose a mode: deterministic, Markov, or auto.
- Press Submit to see results below the header.
- Download CSV/PDF for sharing and documentation.
State inventory and naming discipline
Clear state naming reduces ambiguity in proofs and debugging. Use stable identifiers (S0, S1, …) for formal work, then map to operational labels in documentation. When states are inferred, confirm that every transition endpoint is present and that no spelling variants create duplicate nodes in the diagram.
Transition records as measurable events
Each transition line is treated as an event describing direction, optional label, and optional probability. Deterministic workflows often omit probabilities, while stochastic models include them to represent uncertainty. Repeated edges count toward adjacency intensity, helping you spot hotspots where many actions converge across the system.
Adjacency matrix and degree metrics
The adjacency matrix A summarizes structure as counts. Outdegree indicates how many choices leave a state; indegree indicates how many ways a state can be entered. High outdegree can signal complex branching, while high indegree can signal a bottleneck or an important aggregator for multiple paths.
Row‑stochastic transition matrix for Markov analysis
In Markov mode, outgoing probabilities are normalized so each row sums to 1. This creates a transition matrix P suitable for multi‑step reasoning, where P^k describes movement after k steps. If a row’s probabilities do not sum to 1, the tool reports normalization so comparisons remain consistent.
Reachability, components, and stability checks
Reachability answers whether a path exists from one state to another. Strongly connected components highlight clusters with mutual reachability, useful for detecting cycles and reversible behavior. Absorbing states retain probability mass, indicating terminal conditions or traps. Use the start state reachability list to validate expected coverage and locate dead ends.
Reporting outputs for review and governance
The CSV export preserves transitions, degrees, and matrix values for audit trails and regression tests. The PDF snapshot packages the diagram and a compact summary for stakeholders. For change control, keep versioned exports, compare degree shifts, and verify that new transitions do not introduce unintended cycles, unreachable states, or probability imbalance. Pair exports with a review checklist: confirm start reachability, confirm absorbing states are intentional, and verify each label matches a rule. Use the plots to communicate complexity, because rising outdegree and concentrated heatmap cells typically correlate with higher testing effort and stronger validation requirements before deploying to production or publishing results.
FAQs
What input format should I use for transitions?
Use one line per transition: from, to, label, probability. Label and probability are optional. Commas separate fields, and extra spaces are ignored during parsing.
When should I choose Markov mode?
Choose it when probabilities represent uncertain movement between states. The tool normalizes each state’s outgoing probabilities so every row sums to one, enabling multi-step transition analysis.
How does the tool detect absorbing states?
A state is absorbing when its transition row keeps probability one on itself and zero elsewhere. In Markov mode, states with no outgoing transitions are treated as self-looping.
What does the SCC count tell me?
Strongly connected components group states that can reach each other through directed paths. Many components suggest one-way flows, while fewer components indicate cycles and reversible behavior.
Why did I get a normalization warning?
If a state’s provided outgoing probabilities do not sum to one, the tool rescales them to maintain consistency. This keeps comparisons stable across exports and plots.
Can I export the diagram for reports?
Yes. Use the CSV export for tables and matrices, the PDF export for a snapshot summary, and the PNG button for a clean diagram image suitable for documents.