Description
Report each declared alphabet symbol’s transition indexes and distinct source states, including unused symbols.
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.
Report each declared alphabet symbol’s transition indexes and distinct source states, including unused symbols.
When to use this tool
Use symbol usage to inspect unused alphabet entries and where each symbol has outgoing transitions.
How to use the tool and how it works
- Enter transitionsJson, states, alphabet 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.symbols, using the stated boundary, ordering, sign and absence conventions.
Validate the deterministic partial table. For each declared alphabet symbol, return its original transition indexes and distinct source states in first-occurrence order, even when neither list has entries.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. |
| states | Distinct literal declared state IDs in bank order; full automaton operations require at least one. | Dense list of at most 128 literal strings, each at most 8,192 UTF-16 units. |
| alphabet | Distinct literal alphabet symbols in bank order; an empty alphabet is allowed. | 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.symbols | One usage record per declared alphabet symbol, with transition indexes and distinct source states. |
{
"input": {
"transitionsJson": "[{\"from\": \"a\", \"symbol\": \"x\", \"to\": \"b\"}, {\"from\": \"b\", \"symbol\": \"x\", \"to\": \"b\"}]",
"states": [
"a",
"b",
"c"
],
"alphabet": [
"x"
]
},
"output": {
"result": {
"symbols": [
{
"symbol": "x",
"indexes": [
0,
1
],
"sourceStates": [
"a",
"b"
]
}
]
}
}
}Limitations and assumptions
- This reports declared-symbol usage, not the frequency of symbols in a word. A symbol absent from the transition table remains in the output with empty evidence lists.
- 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 Transition Adjacency Records
List outgoing transition records for every declared deterministic automaton state, including states with no outgoing edges.
- DFA Alphabet Transition Completeness
List missing state/alphabet transition pairs in a declared deterministic automaton.