Separation results for the size of constant-depth propositional proofs
نویسندگان
چکیده
منابع مشابه
Separation results for the size of constant-depth propositional proofs
This paper proves exponential separations between depth d -LK and depth (d + 1 2 )-LK for every d ∈ 1 2 N utilizing the order induction principle. As a consequence, we obtain an exponential separation between depth d -LK and depth (d+1)-LK for d ∈ N . We investigate the relationship between the sequence-size, tree-size and height of depth d -LK-derivations for d ∈ 1 2 N , and describe transform...
متن کاملLower Bounds to the Size of Constant-Depth Propositional Proofs
1 LK is a natural modiication of Gentzen sequent calculus for pro-positional logic with connectives : and V ; W (both of unbounded arity). Then for every d 0 and n 2, there is a set T d n of depth d sequents of total size O(n 3+d) which are refutable in LK by depth d + 1 proof of size exp(O(log 2 n)) but such that every depth d refutation must have the size at least exp(n (1)). The sets T d n e...
متن کاملOn Transformations of Constant Depth Propositional Proofs
This paper studies the complexity of constant depth propositional proofs in the cedent and sequent calculus. We discuss the relationships between the size of tree-like proofs, the size of dag-like proofs, and the heights of proofs. The main result is to correct a proof construction in an earlier paper about transformations from proofs with polylogarithmic height and constantly many formulas per...
متن کاملEquational calculi and constant depth propositional proofs
We deene equational calculi for proving equations between functions in the complexity classes ACC(2) and TC 0 , and we show that proofs in these calculi can be simulated by polynomial size, constant depth proofs in Frege systems with counting modulo 2 and threshold connectives respectively.
متن کاملBounded Arithmetic and Constant Depth Frege Proofs
We discuss the Paris-Wilkie translation from bounded arithmetic proofs to bounded depth propositional proofs in both relativized and non-relativized forms. We describe normal forms for proofs in bounded arithmetic, and a definition of Σ -depth for PK-proofs that makes the translation from bounded arithmetic to propositional logic particularly transparent. Using this, we give new proofs of the w...
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: 2005
ISSN: 0168-0072
DOI: 10.1016/j.apal.2005.05.002