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Unit propagation (UP) or boolean constraint propagation (BCP) or the one-literal rule (OLR) is a procedure of automated theorem proving that can simplify a set of (usually propositional) clauses. Definition
In digital logic, a don't-care term [1] [2] (abbreviated DC, historically also known as redundancies, [2] irrelevancies, [2] optional entries, [3] [4] invalid combinations, [5] [4] [6] vacuous combinations, [7] [4] forbidden combinations, [8] [2] unused states or logical remainders [9]) for a function is an input-sequence (a series of bits) for which the function output does not matter.
A clause is a disjunction of literals (or a single literal). A clause is called a Horn clause if it contains at most one positive literal. A formula is in conjunctive normal form (CNF) if it is a conjunction of clauses (or a single clause). For example, x 1 is a positive literal, ¬x 2 is a negative literal, and x 1 ∨ ¬x 2 is a clause.
A law of Boolean algebra is an identity such as x ∨ (y ∨ z) = (x ∨ y) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...
propositional logic, Boolean algebra, Heyting algebra: is false when A is true and B is false but true otherwise. may mean the same as (the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols).
The basic backtracking algorithm runs by choosing a literal, assigning a truth value to it, simplifying the formula and then recursively checking if the simplified formula is satisfiable; if this is the case, the original formula is satisfiable; otherwise, the same recursive check is done assuming the opposite truth value.
By Patricia Zengerle. WASHINGTON (Reuters) - Days before he retires as chairman of the influential U.S. Senate Foreign Relations Committee, Democrat Ben Cardin acknowledged worries about human ...
Each element of the Boolean algebra is a combination of finitely many of the generating propositions, with two such elements deemed identical if they are logically equivalent. Another way to see why the free Boolean algebra on an n-element set has 2 2 n {\displaystyle 2^{2^{n}}} elements is to note that each element is a function from n bits to ...