Description
Count original transition usage along a deterministic symbol trace, stopping at the first undefined step.
A deterministic transition maps a state and one literal alphabet symbol to at most one next state. A partial table may leave some pairs undefined; a complete table defines every state/symbol pair. Tracing one word, exploring all graph paths and changing the accepting set are distinct operations. IDs and symbols use exact string identity.
Count original transition usage along a deterministic symbol trace, stopping at the first undefined step.
When to use this tool
Use transition usage counts to see which original records a specific word actually exercises.
How to use the tool and how it works
- Enter transitionsJson, start, symbols using the definitions below. Serialize JSON text fields in the decoded shape shown below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.counts, result.undefinedAt, using the stated boundary, ordering, sign and absence conventions.
Reject duplicate [from,symbol] transition keys, then follow the supplied symbol sequence from start. Count each original transition index as it is used and stop at the first undefined step.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| transitionsJson | JSON array of {from,symbol,to} literal string records, preserving transition indexes. Determinism is checked or audited as described above. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| start | Literal starting state. Graph operations with a declared state bank require it to be present there. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| symbols | Ordered input symbols to consume, each a literal string. This list is a word, not the declared alphabet. | Dense list of at most 128 literal strings, each at most 8,192 UTF-16 units. |
These decoded structures show the examples inside JSON text fields. Supply their serialized JSON strings as input.
{
"transitionsJson": [
{
"from": "a",
"symbol": "x",
"to": "b"
},
{
"from": "b",
"symbol": "x",
"to": "b"
}
]
}| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.counts | Usage counts aligned with the original transition records, including zeros. |
| result.undefinedAt | First input-symbol index with no transition, or null when all symbols were consumed. |
{
"input": {
"transitionsJson": "[{\"from\": \"a\", \"symbol\": \"x\", \"to\": \"b\"}, {\"from\": \"b\", \"symbol\": \"x\", \"to\": \"b\"}]",
"start": "a",
"symbols": [
"x",
"x"
]
},
"output": {
"result": {
"counts": [
1,
1
],
"undefinedAt": null
}
}
}Limitations and assumptions
- Counts include zero for unused transitions. A missing transition is reported at its input-symbol index; no sink state or later continuation is invented.
- Transition JSON is an array of {from,symbol,to} string records. Tools requiring a declared automaton use a nonempty distinct state bank and distinct alphabet, validate endpoints and symbols, and reject duplicate [from,symbol] keys. Trace-only tools validate keys without inferring a declared universe. No normalization or implicit sink is provided.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric outputs must remain finite and within safe-integer magnitude. Original record indexes and cell coordinates are zero-based; stated half-open ranges exclude their end.
Alternative or Complementary methods
Use endpoint and duplicate-key audits before transformations. Check completeness before complementing an accepting set, and preserve the declared alphabet, start-state convention and acceptance policy with exported tables.
References
Similar or alternative tools
- DFA Symbol Sequence State Trace
Trace a symbol sequence through a partial deterministic transition table with state and transition-index provenance.
- DFA Accepting State Visit Indexes
List every accepting-state visit in a deterministic trace, including the starting state at position zero.