eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2006-11-20
1
39
10.4230/DagSemProc.06111.3
article
A Generic Time Hierarchy for Semantic Models With One Bit of Advice
van Melkebeek, Dieter
Pervyshev, Konstantin
We show that for any reasonable semantic model of computation and for any positive integer $a$ and rationals $1 leq c < d$, there exists a language computable in time $n^d$ with $a$ bits of advice but not in time $n^c$ with $a$ bits of advice. A semantic model is one for which there exists a computable enumeration that contains all machines in the model but may also contain others. We call such a model reasonable if it has an efficient universal machine that can be complemented within the model in exponential time and if it is efficiently closed under deterministic transducers. Our result implies the first such hierarchy theorem for randomized machines with zero-sided error, quantum machines with one- or zero-sided error, unambiguous machines, symmetric alternation, Arthur-Merlin games of any signature, interactive proof protocols with one or multiple provers, etc.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol06111/DagSemProc.06111.3/DagSemProc.06111.3.pdf
Time hierarchy
non-uniformity
one bit of advice
probabilistic algorithms