Description
Audit missing transition targets and sources independently against an explicit declared state bank.
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.
Audit missing transition targets and sources independently against an explicit declared state bank.
When to use this tool
Use endpoint coverage to inspect incomplete transition records before enforcing a full declared automaton.
How to use the tool and how it works
- Enter transitionsJson, states 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.missing, result.missingSources, using the stated boundary, ordering, sign and absence conventions.
Check each transition endpoint against the distinct supplied state bank and report missing targets and missing sources separately with original transition indexes.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. |
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.missing | Missing endpoint or state/symbol evidence with the original indexes or bank ordering described above. |
| result.missingSources | Transitions whose from state is absent from states, with original transition indexes. |
{
"input": {
"transitionsJson": "[{\"from\": \"a\", \"symbol\": \"x\", \"to\": \"b\"}, {\"from\": \"b\", \"symbol\": \"x\", \"to\": \"b\"}]",
"states": [
"a"
]
},
"output": {
"result": {
"missing": [
{
"index": 0,
"state": "b"
},
{
"index": 1,
"state": "b"
}
],
"missingSources": [
{
"index": 1,
"state": "b"
}
]
}
}
}Limitations and assumptions
- This is an endpoint coverage audit. It does not require deterministic keys, an alphabet declaration or a complete transition table; the state bank may be empty.
- 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 Deterministic Transition Key Audit
Audit repeated deterministic state/symbol transition keys, including identical duplicate records.
- DFA Alphabet Transition Completeness
List missing state/alphabet transition pairs in a declared deterministic automaton.