Sentence examples for length of proof from inspiring English sources

The case of the Speed-up Theorem where the length of proof is measured by the number of symbols was proved by Mostowski in 1952 (Mostowski 1982).

This project exceeded previous mathematical endeavours by its sheer size, in both length of proof and number of researchers.

Gödel measures the length of proofs by the number of formulas; but there are also other possibilities, such as the number of symbols in the proof.

Other publications of the 1930s include those on the decision problem for the predicate calculus, on the length of proofs, and on differential and projective geometry.

The computation time that was previously ignored now appears explicitly as the length of proofs [17] and theories can naturally evolve by the addition and transformation of proofs in the collection, with new concepts emerging by the introduction of cuts and definition inferences.

These games are a useful device for showing upper and lower bounds on the lengths of proofs in various proof systems.

Over the years several related proofs were published, but the first full proof of Gödel's original result was given only in 1994 by Sam Buss in his 'On Gödel's theorems on lengths of proofs I: Number of lines and speedups for arithmetic.' (Buss 1994).

Though both measures may be equally natural candidates for measuring the length of a proof, proving the theorem for length measured by the number of symbols avoids a technical complication introduced by the other measure: there are only finitely many proofs with a given number of symbols, whereas there are infinitely many proofs with a given number of formulas.

Because of increased competition in the lupus field, this patient population will be increasingly difficult to recruit - as a result, the expected length of the proof-of-concept study may be upwards of 2 years or more.

This method is proven to be asymptotically optimal among brute-force strategies in terms of proof length, space and time [4].

Cover the front of the fan completely with a length of fine, insect-proof, metal mesh.