Canonical normal formIn Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF) or minterm canonical form, and its dual, the canonical conjunctive normal form (CCNF) or maxterm canonical form. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller). Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables.
Algebraic normal formIn Boolean algebra, the algebraic normal form (ANF), ring sum normal form (RSNF or RNF), Zhegalkin normal form, or Reed–Muller expansion is a way of writing propositional logic formulas in one of three subforms: The entire formula is purely true or false: One or more variables are combined into a term by AND (), then one or more terms are combined by XOR () together into ANF. Negations are not permitted: The previous subform with a purely true term: Formulas written in ANF are also known as Zhegalkin polynomials and Positive Polarity (or Parity) Reed–Muller expressions (PPRM).
Clause (logic)In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives. A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term). That is, it is a finite disjunction or conjunction of literals, depending on the context.
Satisfiability modulo theoriesIn computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings. The name is derived from the fact that these expressions are interpreted within ("modulo") a certain formal theory in first-order logic with equality (often disallowing quantifiers).
Disjunctive normal formIn boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if it is a disjunction of one or more conjunctions of one or more literals. A DNF formula is in full disjunctive normal form if each of its variables appears exactly once in every conjunction.
Conjunctive normal formIn Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. As a canonical normal form, it is useful in automated theorem proving and circuit theory. All conjunctions of literals and all disjunctions of literals are in CNF, as they can be seen as conjunctions of one-literal clauses and conjunctions of a single clause, respectively.
BacktrackingBacktracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other.
Data structureIn computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type.
Sigil (computer programming)In computer programming, a sigil (ˈsɪdʒəl) is a symbol affixed to a variable name, showing the variable's datatype or scope, usually a prefix, as in foo,where is the sigil. Sigil, from the Latin sigillum, meaning a "little sign", means a sign or image supposedly having magical power. Sigils can be used to separate and demarcate namespaces that possess different properties or behaviors. The use of sigils was popularized by the BASIC programming language. Literal (computer programming)In computer science, a literal is a notation for representing a fixed value in source code. Almost all programming languages have notations for atomic values such as integers, floating-point numbers, and strings, and usually for booleans and characters; some also have notations for elements of enumerated types and compound values such as arrays, records, and objects. An anonymous function is a literal for the function type. In contrast to literals, variables or constants are symbols that can take on one of a class of fixed values, the constant being constrained not to change.
Constant (computer programming)In computer programming, a constant is a value that should not be altered by the program during normal execution, i.e., the value is constant. When associated with an identifier, a constant is said to be "named," although the terms "constant" and "named constant" are often used interchangeably. This is contrasted with a variable, which is an identifier with a value that can be changed during normal execution, i.e., the value is variable.
Operator (computer programming)In computer programming, operators are constructs defined within programming languages which behave generally like functions, but which differ syntactically or semantically. Common simple examples include arithmetic (e.g. addition with +), comparison (e.g. "greater than" with >), and logical operations (e.g. AND, also written && in some languages). More involved examples include assignment (usually = or :=), field access in a record or object (usually .), and the scope resolution operator (often :: or .).
Persistent data structureIn computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjans' 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified.
Answer set programmingAnswer set programming (ASP) is a form of declarative programming oriented towards difficult (primarily NP-hard) search problems. It is based on the stable model (answer set) semantics of logic programming. In ASP, search problems are reduced to computing stable models, and answer set solvers—programs for generating stable models—are used to perform search. The computational process employed in the design of many answer set solvers is an enhancement of the DPLL algorithm and, in principle, it always terminates (unlike Prolog query evaluation, which may lead to an infinite loop).
Purely functional data structureIn computer science, a purely functional data structure is a data structure that can be directly implemented in a purely functional language. The main difference between an arbitrary data structure and a purely functional one is that the latter is (strongly) immutable. This restriction ensures the data structure possesses the advantages of immutable objects: (full) persistency, quick copy of objects, and thread safety. Efficient purely functional data structures may require the use of lazy evaluation and memoization.
2-satisfiabilityIn computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables. It is a special case of the general Boolean satisfiability problem, which can involve constraints on more than two variables, and of constraint satisfaction problems, which can allow more than two choices for the value of each variable.
Array (data structure)In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called one-dimensional array. For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, .
Logical equivalenceIn logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of and is sometimes expressed as , , , or , depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. In logic, many common logical equivalences exist and are often listed as laws or properties.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Fuzzy setIn mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are now used throughout fuzzy mathematics and have applications in areas such as linguistics , decision-making , and clustering , are special cases of L-relations when L is the unit interval [0, 1].
