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When all literals of a one-in-three 3-SAT formula are positive, the satisfiability problem is called one-in-three positive 3-SAT. One-in-three 3-SAT, together with its positive case, is listed as NP-complete problem "LO4" in the standard reference Computers and Intractability: A Guide to the Theory of NP-Completeness by Michael R. Garey and ...
Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true. The truth table of p EQ q (also written as p = q, p ↔ q, Epq, p ≡ q, or p == q) is as follows: The Venn diagram of A EQ B (red part is true)
Switch statements come in two main variants: a structured switch, as in Pascal, which takes exactly one branch, and an unstructured switch, as in C, which functions as a type of goto. The main reasons for using a switch include improving clarity, by reducing otherwise repetitive coding, and (if the heuristics permit) also offering the potential ...
In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions.
A language that supports the statement construct typically has rules for one or more of the following aspects: Statement terminator – marks the end of a statement; Statement separator – demarcates the boundary between two statements; need needed for the last statement; Line continuation – escapes a newline to continue a statement on the ...
An atomic formula is a wff consisting of either a sentential letter or an n-place predicate letter followed by n terms. A sentence is a wff in which any variables are bound. An atomic sentence is an atomic formula containing no variables. It follows that an atomic sentence contains no logical connectives, variables, or quantifiers. A sentence ...
The same three letters are transliterated as plain a, i, u when representing short vowels. The Hepburn romanization system of Japanese, for example, tā (たあ) as opposed to ta (た). The Syriac language uses macrons to indicate long vowels in its romanized transliteration: ā for /aː/, ē for /eː/, ū for /uː/ and ō for /ɔː/.
In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.