Approximate counting by hashing in bounded arithmetic
نویسنده
چکیده
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.
منابع مشابه
Approximate counting in bounded arithmetic
We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV )), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP , APP , MA, AM ) in PV1 + dWPHP(PV ).
متن کاملHashing-Based Approximate Probabilistic Inference in Hybrid Domains: An Abridged Report
In recent years, there has been considerable progress on fast randomized algorithms that approximate probabilistic inference with tight tolerance and confidence guarantees. The idea here is to formulate inference as a counting task over an annotated propositional theory, called weighted model counting (WMC), which can be partitioned into smaller tasks using universal hashing. An inherent limita...
متن کاملHashing-Based Approximate Probabilistic Inference in Hybrid Domains
In recent years, there has been considerable progress on fast randomized algorithms that approximate probabilistic inference with tight tolerance and confidence guarantees. The idea here is to formulate inference as a counting task over an annotated propositional theory, called weighted model counting (WMC), which can be partitioned into smaller tasks using universal hashing. An inherent limita...
متن کاملAlgorithmic Improvements in Approximate Counting for Probabilistic Inference: From Linear to Logarithmic SAT Calls
Probabilistic inference via model counting has emerged as a scalable technique with strong formal guarantees, thanks to recent advances in hashing-based approximate counting. State-of-theart hashing-based counting algorithms use an NP oracle (SAT solver in practice), such that the number of oracle invocations grows linearly in the number of variables n in the input constraint. We present a new ...
متن کاملA The Ordering Principle in a Fragment of Approximate Counting
The ordering principle states that every finite linear order has a least element. We show that, in the relativized setting, the surjective weak pigeonhole principle for polynomial time functions does not prove a Herbrandized version of the ordering principle over T 2 . This answers an open question raised in [Buss, Ko lodziejczyk and Thapen, 2012] and completes their program to compare the stre...
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. Symb. Log.
دوره 74 شماره
صفحات -
تاریخ انتشار 2009