On Independence of Variants of the Weak Pigeonhole Principle
نویسنده
چکیده
The principle sPHPb (PV (α)) states that no oracle circuit can compute a surjection of a onto b. We show that sPHP P (a)(PV (α)) is independent of PV1(α)+ sPHP π(a) Π(a)(PV (α)) for various choices of the parameters π, Π, %, P . We also improve the known separation of iWPHP(PV ) from S 2 + sWPHP(PV ) under cryptographic assumptions.
منابع مشابه
Circuit principles and weak pigeonhole variants 1
This paper considers the relational versions of the surjective, partial surjective, and multifunction weak pigeonhole principles for PV , Σ1, Π b 1, and B(Σ b 1)-formulas as well as relativizations of these formulas to higher levels of the bounded arithmetic hierarchy. We show that the partial surjective weak pigeonhole principle for Π1 formulas implies that for each k there is a string of leng...
متن کاملCircuit Principles and Weak Pigeonhole Variants
This paper considers the relational versions of the surjective and multifunction weak pigeonhole principles for PV , Σ1 and Θ b 2-formulas. We show that the relational surjective pigeonhole principle for Θ2 formulas in S 1 2 implies a circuit block-recognition principle which in turn implies the surjective weak pigeonhole principle for Σ1 formulas. We introduce a class of predicates correspondi...
متن کاملApproximate counting by hashing in bounded arithmetic
We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.
متن کاملThe weak pigeonhole principle for function classes in S^1_2
It is well known that S1 2 cannot prove the injective weak pigeonhole principle for polynomial time functions unless RSA is insecure. In this note we investigate the provability of the surjective (dual) weak pigeonhole principle in S1 2 for provably weaker function classes. §
متن کامل$P \ne NP$, propositional proof complexity, and resolution lower bounds for the weak pigeonhole principle
Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length Ω(2n ǫ ), (for a constant ǫ = 1/3). One corollary is that certain propositional formulations of the statement P 6= NP do not hav...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Log. Comput.
دوره 17 شماره
صفحات -
تاریخ انتشار 2007