Abstract
Promises are a standard way to formalize partial algorithms; and advice quantifies nonuniformity. For decision problems, the latter is captured in common complexity classes such as \(\mathcal{P}/\operatorname{poly}\), that is, with advice growing in size with that of the input. We advertise constant-size advice and explore its theoretical impact on the complexity of classification problems – a natural generalization of promise problems – and on real functions and operators. Specifically we exhibit problems that, without any advice, are decidable/computable but of high complexity while, with (each increase in the permitted size of) advice, (gradually) drop down to polynomial-time.
Supported in part by the Marie Curie International Research Staff Exchange Scheme Fellowship 294962 within the 7th European Community Framework Programme and by the German Research Foundation (DFG) with project Zi 1009/4-1. We acknowledge seminal discussions with Vassilis Gregoriades, Thorsten Kräling, and Hermann K.-G. Walter.
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Ambos-Spies, K., Brandt, U., Ziegler, M. (2013). Real Benefit of Promises and Advice. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_1
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