Description
List automaton states with a graph path to a supplied accepting state.
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.
List automaton states with a graph path to a supplied accepting state.
When to use this tool
Use coaccessibility to identify every declared state from which some accepting state can be reached.
How to use the tool and how it works
- Enter transitionsJson, states, alphabet, accepting 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.states, using the stated boundary, ordering, sign and absence conventions.
Validate the deterministic partial table and accepting-state membership. Reverse-traverse from accepting states, including those accepting states themselves, to list every state with a path to acceptance.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. |
| accepting | Explicit literal accepting-state IDs; full automaton operations require membership in states. | 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.states | State trace or state inventory in the precise initial-state/discovery/bank order described above. |
{
"input": {
"transitionsJson": "[{\"from\": \"a\", \"symbol\": \"x\", \"to\": \"b\"}, {\"from\": \"b\", \"symbol\": \"x\", \"to\": \"b\"}]",
"states": [
"a",
"b",
"c"
],
"alphabet": [
"x"
],
"accepting": [
"b"
]
},
"output": {
"result": {
"states": [
"b",
"a"
]
}
}
}Limitations and assumptions
- The inventory uses reverse breadth-first discovery with supplied accepting seed order and original transition order. An empty accepting set yields an empty inventory.
- 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 Dead State Partitioner
Partition declared states into states with a path to acceptance and dead states without such a path.
- DFA Reachable State Inventory
List automaton states reachable from an explicit start in breadth-first discovery order.