theory, Selman's theorem is a theorem relating enumeration reducibility with enumerability relative to oracles. It is named after Alan Selman, who proved...

holds that A is also computably enumerable with oracle X. This is Selman's theorem. In addition to enumeration reducibility, there exist strong versions...

first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes...

neural net that is generated from symbolic rules. An example is the Neural Theorem Prover, which constructs a neural network from an AND-OR proof tree generated...

following equivalence theorem shows that these two concepts are equivalent for most functions used in practice: Theorem.: Theorem 2.6  If f {\displaystyle...

f(x)\neq f(y).} Let X be a connected, non-compact Riemann surface. A deep theorem of Heinrich Behnke and Stein (1948) asserts that X is a Stein manifold...

goal state within the given horizon. This concept is similar to Cook's theorem, where Turing machine computations are represented as SAT formulas. To...

set, but it is always a semialgebraic set: this is the Tarski–Seidenberg theorem. Related fields are o-minimal theory and real analytic geometry. Examples:...

systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling...

that in 4 dimensions, the smooth h-cobordism theorem fails. It was named after Turkish mathematician Selman Akbulut. A compact contractible Stein 4-manifold...

possible f-vectors of simplicial complexes is given by the Kruskal–Katona theorem. By using the f-vector of a simplicial d-complex Δ as coefficients of a...

Queerplatonic relationship Romantic friendship Sharing Social connection Theorem on friends and strangers Womance In comparison to older respondents, who...

zero–one law for first-order graph logic; Fagin's proof used the compactness theorem. According to this result, every first-order sentence is either almost...

⁠ We know P ⊆ NP ⊆ EXPTIME ⊆ NEXPTIME and also, by the time hierarchy theorem, that NP ⊊ NEXPTIME If P = NP, then NEXPTIME = EXPTIME (padding argument);...

before it was widely believed they were not (see Immerman–Szelepcsényi theorem). The latter has become less surprising now that we know SL equals L, which...

on to prove a number of fundamental results such as the Time hierarchy theorem. In his own Turing Award lecture, Richard M. Karp remarks that "[I]t is...

weight of the clauses satisfied by that assignment. Henry Kautz and B. Selman (1996). Pushing the envelope: planning, propositional logic, and stochastic...

lower-order terms. It ignores the size of the exponent. The time hierarchy theorem proves the existence of problems in P requiring arbitrarily large exponents...

smooth manifold. This follows from the work of Kervaire and the h-cobordism theorem. Slightly more strongly, every smooth homology 4-sphere is diffeomorphic...

2004 and 2005. Another application that often involves DPLL is automated theorem proving or satisfiability modulo theories (SMT), which is a SAT problem...

space hierarchy theorems form the basis for most separation results of complexity classes. For instance, the time hierarchy theorem establishes that...

Turing machine. The theorem was proven by Ronald Fagin in 1974 (strictly, in 1973 in his doctoral thesis). As a corollary, Jones and Selman showed that a set...

and successfully applied to heuristic search in the field of automated theorem proving by W. Ertel, J. Schumann and C. Suttner in 1989, thus improving...

Edwin E. (1952). "Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung". Annals of Mathematics. 56 (2): 101–121. doi:10.2307/1969769...

American Mathematical Society is founded by Thomas Fiske. Hilbert's basis theorem is first proved by David Hilbert. Francis Galton introduces the concept...

topological manifold has an essentially unique smooth structure (see Moise's theorem), so the monoid of smooth structures on the 3-sphere is trivial. The group...

revolutionized the theories of rings, fields, and algebras. In physics, Noether's theorem explains the fundamental connection between symmetry and conservation laws...

probability and machine learning to solve combinatorial problems and to guide theorem proving. He introduced the anytime algorithm paradigm in AI, where partial...

introduced hyperbolic geometry into the study of knots with the hyperbolization theorem. Many knots were shown to be hyperbolic knots, enabling the use of geometry...

counterexample of the Beal conjecture, a generalization of Fermat's Last Theorem, published in a refereed and respected mathematics publication Becquerel...