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 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.
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Constant-depth arithmetic circuits have been defined and studied in [AAD97, ABL98]; these circuits yield the function classes #AC and GapAC. These function classes in turn provide new characterizations of the computational power of threshold circuits, and provide a link between the circuit classes AC (where many lower bounds are known) and TC (where essentially no lower bounds are known). In th...
متن کاملBounded arithmetic theory for the counting functions and Toda’s theorem
In this paper we give a two sort bounded arithmetic whose provably total functions coincide with the class FP . Our first aim is to show that the theory proves Toda’s theorem in the sense that any formula in Σ∞ is provably equivalent to a Σ B 0 formula in the language of FP . We also argue about some problems concerning logical theories for counting classes.
متن کاملOn the de-randomization of space-bounded approximate counting problems
It was recently shown that SVD and matrix inversion can be approximated in quantum log-space [1] for well formed matrices. This can be interpreted as a fully logarithmic quantum approximation scheme for both problems. We show that if prBQL = prBPL then every fully logarithmic quantum approximation scheme can be replaced by a probabilistic one. Hence, if classical algorithms cannot approximate t...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2007
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1191333850