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The Boolean satisfiability problem (SAT) is, given a formula, to check whether it is satisfiable. This decision problem is of central importance in many areas of computer science, including theoretical computer science, complexity theory, [3] [4] algorithmics, cryptography [5] [6] and artificial intelligence. [7] [additional citation(s) needed]
There is often only a small difference between a problem in P and an NP-complete problem. For example, the 3-satisfiability problem, a restriction of the Boolean satisfiability problem, remains NP-complete, whereas the slightly more restricted 2-satisfiability problem is in P (specifically, it is NL-complete), but the slightly more general max ...
Boolean satisfiability problem (SAT). [2] [3]: LO1 There are many variations that are also NP-complete. An important variant is where each clause has exactly three literals (3SAT), since it is used in the proof of many other NP-completeness results. [3]: p. 48 Circuit satisfiability problem; Conjunctive Boolean query [3]: SR31
In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete.That is, it is in NP, and any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem.
In 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 P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
A problem related to satisfiability is that of finite satisfiability, which is the question of determining whether a formula admits a finite model that makes it true. For a logic that has the finite model property , the problems of satisfiability and finite satisfiability coincide, as a formula of that logic has a model if and only if it has a ...
For example, it's quite possible to reduce a difficult-to-solve NP-complete problem like the boolean satisfiability problem to a trivial problem, like determining if a number equals zero, by having the reduction machine solve the problem in exponential time and output zero only if there is a solution. However, this does not achieve much ...