Maxterm Index Complement Convention Checker
Construct a maxterm from a binary row index and check a proposed most-significant-bit negation mask.
Description
A maxterm is a disjunction false on exactly one binary assignment.
A maxterm is a disjunction false on exactly one binary assignment. Its literal signs are the complement of the minterm signs for the same row.1
The tool returns maxterm, conventionMatches. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Maxterm Index Complement Convention Checker
Use this for the following task: Construct a maxterm from a binary row index and check a proposed most-significant-bit negation mask. Prepare the specified logical encoding before running the check or transformation.
How to use Maxterm Index Complement Convention Checker and understand its results
- Prepare the requested Boolean values, complete truth-table rows, or identifier atoms. An atom is a name such as p or premise_1, not a natural-language sentence.
- Enter variables, index, negated according to the field table, then run the tool.
- Read maxterm, conventionMatches. Use the matching rule, assignment order or nonempty-class assumptions below to interpret the result.
- For a false check, inspect the supplied encoding and matching rule. A well-formed false result is different from an input error.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| variables | Distinct variables in most-significant-bit order | list of string; minimum entries 0; maximum entries 52; each entry: maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| index | Maxterm index | integer; minimum 0; maximum 9007199254740991 | Required |
| negated | Proposed negation mask | list of boolean; minimum entries 0; maximum entries 52 | Required |
Provide distinct variables in most-significant-bit order, an in-range index and one proposed negation flag per variable. Render the maxterm and test whether every flag equals its row bit.
row bit 1 → negated literal; row bit 0 → positive literal The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| maxterm | Maxterm formula | string (propositional-formula) |
| conventionMatches | Negation convention matches | boolean |
{
"input": {
"variables": [
"p",
"q"
],
"index": 1,
"negated": [
false,
true
]
},
"output": {
"maxterm": "p || !q",
"conventionMatches": true
}
}Limitations and assumptions
At most 52 variables are accepted. Zero variables give the maxterm "false" at index zero. conventionMatches checks the mask, not an arbitrary expression.
The supplied encodings must represent the intended propositions or classes. No natural-language parsing or assessment of empirical premise truth is performed. Malformed input gives a tool error rather than a logical false result.
Alternative or Complementary methods
Choose Minterm Index Binary Assignment Decoder when you need its operation: Decode a minterm index into fixed-width binary bits and the corresponding conjunction of identifier literals. Choose Full CNF Clause Set Builder from Truth Table for the complementary operation: Build equivalent canonical CNF clauses from every false truth-table row without auxiliary variables.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- Minterm Index Binary Assignment Decoder
Decode a minterm index into fixed-width binary bits and the corresponding conjunction of identifier literals.
- Full CNF Clause Set Builder from Truth Table
Build equivalent canonical CNF clauses from every false truth-table row without auxiliary variables.