A Generic Time Hierarchy for Semantic Models With One Bit of Advice Preliminary version
نویسندگان
چکیده
We show that for any reasonable semantic model of computation and for any positive integer a and rationals 1 ≤ c < d, there exists a language computable in time n with a bits of advice but not in time n 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 trans-
منابع مشابه
Space Hierarchy Results for Randomized Models
We prove space hierarchy and separation results for randomized and other semantic models of computation with advice. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the following. Let s(n) be any spaceconstructible function that is Ω(log n) and such that s(an) = O(s(n...
متن کاملThe University of Chicago Hierarchy Theorems and Resource Tradeoffs for Semantic Classes a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy Department of Computer Science By
Computational complexity theory studies the minimum resources (time, space, randomness etc.) to solve computational problems. Two fundamental questions in this area are: 1. Can more problems be solved given more of a given resource? A positive answer to this question is known as a hierarchy theorem. 2. Can one resource be traded off with another when solving a given problem? Such a result is kn...
متن کاملTime Hierarchies for Computations with a Bit of Advice
A polynomial time hierarchy for ZPTime with one bit of advice is proved. That is for any constants a and b such that 1 < a < b, ZPTime[n]/1 ( ZPTime[n]/1. The technique introduced in this paper is very general and gives the same hierarchy for NTime∩coNTime, UTime, MATime, AMTime and BQTime. It also significantly simplifies the previously known proofs of hierarchies for BPTime and RPTime with ad...
متن کاملFrom Logarithmic Advice to Single-Bit Advice
Building on Barak’s work (Random’02), Fortnow and Santhanam (FOCS’04) proved a time hierarchy for probabilistic machines with one bit of advice. Their argument is based on an implicit translation technique, which allow to translate separation results for short (say logarithmic) advice (as shown by Barak) into separations for a single-bit advice. In this note, we make this technique explicit, by...
متن کاملOne Bit of Advice
The results in this paper show that coNP is contained in NP with 1 bit of advice (denoted NP/1) if and only if the Polynomial Hierarchy (PH) collapses to D, the second level of the Boolean Hierarchy (BH). Previous work showed that BH ⊆ D =⇒ coNP ⊆ NP/poly. The stronger assumption that PH ⊆ D in the new result allows the length of the advice function to be reduced to a single bit and also makes ...
متن کامل