A Majority Lemma for Randomised Query Complexity

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We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

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Logic resynthesis is the problem of finding a dependency function to re-express a given Boolean function in terms of a given set of divisor functions. In this paper, we study logic resynthesis of majority-based circuits, which is motivated by the increasin ...

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We propose a flow for automated quantum compila- tion. Our flow takes a Boolean function implemented in Python as input and translates it into a format appropriate for reversible logic synthesis. We focus on two quantum compilation tasks: uniform state pre ...

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Typical operators for the decomposition of Boolean functions in state-of-the-art algorithms are AND, exclusive-OR (XOR), and the 2-to-1 multiplexer (MUX). We propose a logic decomposition algorithm that uses the majority-of-three (MAJ) operation. Such a de ...

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Suppose we have randomized decision trees for an outer function f and an inner function g. The natural approach for obtaining a randomized decision tree for the composed function (f∘ gⁿ)(x¹,…,xⁿ) = f(g(x¹),…,g(xⁿ)) involves amplifying the success probabili ...

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The study of the complexity of Boolean functions has recently found applications in logic synthesis and optimization algorithms, as for instance in logic rewriting. Previous works have focused on the minimum length of Boolean chains for functions up to 5 i ...

Recent studies show that majority-based logic synthesis is beneficial for both traditional and nanotechnology digital designs. However, most of the existing synthesis algorithms for majority logic generate majority-of-three (M-3) networks. The optimization ...

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A Majority Lemma for Randomised Query Complexity

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Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

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Logic Resynthesis of Majority-Based Circuits by Top-Down Decomposition

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Exact Synthesis of Boolean Functions in Majority-of-five Forms

SAT-Based Exact Synthesis for Multi-Level Logic Networks