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A composition theorem for decision tree complexity

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arxiv 1302.4207 v1 pith:BENZHDIA submitted 2013-02-18 cs.CC

Ashley Montanaro This is my paper · ORCID
classification cs.CC
keywords complexitydecisiontreetheorembooleanboolean-valuedcharacterisationcharacterise
verification ladder T0 review T1 audit T2 compute T3 formal
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We completely characterise the complexity in the decision tree model of computing composite relations of the form h = g(f^1,...,f^n), where each relation f^i is boolean-valued. Immediate corollaries include a direct sum theorem for decision tree complexity and a tight characterisation of the decision tree complexity of iterated boolean functions.

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  1. Classical and Quantum Query Complexity of Boolean Functions under Indefinite Causal Order

    quant-ph 2025-06 conditional novelty 7.0 of 10

    Causally indefinite classical processes can compute a constructed Boolean function family with D^0.792 queries instead of D, and indefinite causal order gives an exact three-query quantum algorithm where sequential qu...

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