Concepts inA constructive proof of the Lovász local lemma
Lemma (mathematics)
In mathematics, a lemma (plural lemmata or lemmas) from the Greek ¿¿¿¿¿ (lemma, ¿anything which is received, such as a gift, profit, or a bribe¿) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself. There is no formal distinction between a lemma and a theorem, only one of intention ¿ see Theorem#Terminology.
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Constructive proof
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object with certain properties by creating or providing a method for creating such an object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem) which proves the validity of a proposition without considering an example.
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Well-formed formula
In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word which is part of a formal language. A formal language can be considered to be identical to the set containing all and only its formulas. A formula is a syntactic formal object that can be informally given a semantic meaning.
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Randomized algorithm
A randomized algorithm is an algorithm which employs a degree of randomness as part of its logic. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random bits. Formally, the algorithm's performance will be a random variable determined by the random bits; thus either the running time, or the output (or both) are random variables.
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Search problem
In computational complexity theory and computability theory, a search problem is a type of computational problem represented by a binary relation.
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Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false.
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Boolean satisfiability problem
In computer science, satisfiability (often written in all capitals or abbreviated SAT) is the problem of determining if the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE. Equally important is to determine whether no such assignments exist, which would imply that the function expressed by the formula is identically FALSE for all possible variable assignments.
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Formula
In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language. In science, a specific formula is a concise way of expressing information symbolically as in a mathematical or chemical formula. The plural of formula can be spelled either formulae (like the original Latin) for mathematical or scientific senses, or formulas for more general senses.
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