Describing proofs by short tautologies
نویسندگان
چکیده
منابع مشابه
Describing proofs by short tautologies
Herbrand’s theorem is one of the most fundamental results about first-order logic. In the context of proof analysis, Herbrand-disjunctions are used for describing the constructive content of cut-free proofs. However, given a proof with cuts, the computation of an Herbrand-disjunction is of significant computational complexity, as the cuts in the proof have to be eliminated first. In this paper ...
متن کاملShort Proofs of Tautologies Using the Schema of Equivalence
It is shown how the schema of equivalence can be used to obtain short proofs of tautologies A, where the depth of proofs is linear in the number of variables in A. Eq (A, B, C arbitrary formulas) is the propositional pendant of the schema of identity. It can be argued that, apart form the usual propositional tautologies and inference schemas which are given as axiomatizations of propositional l...
متن کاملTseitin's Tautologies and Lower Bounds for Nullstellensatz Proofs
We use the known linear lower bound for Tseitin's tautologies for establishing linear lower bounds on the degree of Nullstellensatz proofs (in the usual boolean setting) for explicitly constructed systems of polyno-mials of a constant (in our construction 6) degree. It holds over any eld of characteristic distinct from 2. Previously, a linear lower bound was proved 14] for an explicitly constru...
متن کاملShort Discreet Proofs
We show how to produce short proofs of theorems such that a distrusting Verifier can be convinced that the theorem is true yet obtains no information about the proof itself. The proofs are non-interactive provided that the quadratic residuosity bit commitment scheme is available to the Prover and Verifier. For typical applications, the proofs are short enough to fit on a floppy disk.
متن کاملVery Short Primality Proofs
It is shown that every prime p has a proof of its primality of length 0(logp) multiplications modulo p.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2009
ISSN: 0168-0072
DOI: 10.1016/j.apal.2008.10.010