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Natural proof

Index Natural proof

In computational complexity theory, a natural proof is a certain kind of proof establishing that one complexity class differs from another one. [1]

16 relations: AC0, Alexander Razborov, Boolean function, Boolean satisfiability problem, Circuit complexity, Complexity class, Computational complexity theory, Elliptic-curve cryptography, Gödel Prize, Naor–Reingold pseudorandom function, P versus NP problem, P/poly, Pseudorandom function family, Steven Rudich, TC0, Truth table.

AC0

AC0 is a complexity class used in circuit complexity.

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Alexander Razborov

Aleksandr Aleksandrovich Razborov (Алекса́ндр Алекса́ндрович Разбо́ров; born February 16, 1963), sometimes known as Sasha Razborov, is a Soviet and Russian mathematician and computational theorist.

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Boolean function

In mathematics and logic, a (finitary) Boolean function (or switching function) is a function of the form ƒ: Bk → B, where B.

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Boolean satisfiability problem

In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.

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Circuit complexity

In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of Boolean circuits that compute them.

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Complexity class

In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.

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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Elliptic-curve cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.

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Gödel Prize

The Gödel Prize is an annual prize for outstanding papers in the area of theoretical computer science, given jointly by European Association for Theoretical Computer Science (EATCS) and the Association for Computing Machinery Special Interest Group on Algorithms and Computational Theory (ACM SIGACT).

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Naor–Reingold pseudorandom function

In 1997, Moni Naor and Omer Reingold described efficient constructions for various cryptographic primitives in private key as well as public-key cryptography.

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P versus NP problem

The P versus NP problem is a major unsolved problem in computer science.

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P/poly

In computational complexity theory, P/poly is the complexity class of languages recognized by a polynomial-time Turing machine with a polynomial-bounded advice function.

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Pseudorandom function family

In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the PRF family and a random oracle (a function whose outputs are fixed completely at random).

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Steven Rudich

Steven Rudich (born October 4, 1961) is a professor in the Carnegie Mellon School of Computer Science.

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TC0

TC0 is a complexity class used in circuit complexity.

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Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).

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Natural proofs.

References

[1] https://en.wikipedia.org/wiki/Natural_proof

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