Description
Check acceptance of a supplied word only when every step is defined and its final state is accepting.
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.
Check acceptance of a supplied word only when every step is defined and its final state is accepting.
When to use this tool
Use word acceptance when the question concerns one explicit symbol sequence and accepting-state set.
How to use the tool and how it works
- Enter transitionsJson, start, symbols, 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.accepted, result.undefinedAt, result.finalState, using the stated boundary, ordering, sign and absence conventions.
Trace the supplied symbols with unique transition keys. Accept only if the trace consumes all symbols and the final reached state belongs to accepting.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. |
| 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.accepted | True exactly when input is fully consumed and finalState belongs to accepting. |
| result.undefinedAt | First input-symbol index with no transition, or null when all symbols were consumed. |
| result.finalState | Last successfully reached state, even when a later requested step is undefined. |
{
"input": {
"transitionsJson": "[{\"from\": \"a\", \"symbol\": \"x\", \"to\": \"b\"}, {\"from\": \"b\", \"symbol\": \"x\", \"to\": \"b\"}]",
"start": "a",
"symbols": [
"x",
"x"
],
"accepting": [
"b"
]
},
"output": {
"result": {
"accepted": true,
"undefinedAt": null,
"finalState": "b"
}
}
}Limitations and assumptions
- An undefined step always makes accepted false, even if the last reached state is accepting. Empty input accepts exactly when start is accepting; this tool has no separate declared-state-bank validation.
- 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.