Real Benefit of Promises and Advice [chapter]

Klaus Ambos-Spies, Ulrike Brandt, Martin Ziegler
2013 Lecture Notes in Computer Science  
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 P/ 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
more » ... advice, are decidable/computable but of high complexity while, with (each increase in the permitted size of) advice, (gradually) drop down to polynomial-time.
doi:10.1007/978-3-642-39053-1_1 fatcat:tqppbmbfi5a5tow6q3k7tjafue