The RAM equivalent of P vs. RP

One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic polynomial time (P). However, this question is only open for Turing Machines, not for Random Access Machines (RAMs). Simon (1981) was able to show that for a sufficiently equipped Random Access Machine, the ability to switch states nondeterministically does not entail any computational advantage. However, in the same paper, Simon describes a different (and arguably more natural) scenario for stochasticity under the RAM model. According to Simon's proposal, instead of receiving a new random bit at each execution step, the RAM program is able to execute the pseudofunction $\textit{RAND}(y)$, which returns a uniformly distributed random integer in the range $[0,y)$. Whether the ability to allot a random integer in this fashion is more powerful than the ability to allot a random bit remained an open question for the last 30 years. In this paper, we close Simon's open problem, by fully characterising the class of languages recognisable in polynomial time by each of the RAMs regarding which the question was posed. We show that for some of these, stochasticity entails no advantage, but, more interestingly, we show that for others it does.Comment: 23 page

NASA Tech Briefs, November 2005

Topics covered include: Laser System for Precise, Unambiguous Range Measurements; Flexible Cryogenic Temperature and Liquid-Level Probes; Precision Cryogenic Dilatometer; Stroboscopic Interferometer for Measuring Mirror Vibrations; Some Improvements in H-PDLCs; Multiple-Bit Differential Detection of OQPSK; Absolute Position Encoders With Vertical Image Binning; Flexible, Carbon-Based Ohmic Contacts for Organic Transistors; GaAs QWIP Array Containing More Than a Million Pixels; AutoChem; Virtual Machine Language; Two-Dimensional Ffowcs Williams/Hawkings Equation Solver; Full Multigrid Flow Solver; Doclet To Synthesize UML; Computing Thermal Effects of Cavitation in Cryogenic Liquids; GUI for Computational Simulation of a Propellant Mixer; Control Program for an Optical-Calibration Robot; SQL-RAMS; Distributing Data from Desktop to Hand-Held Computers; Best-Fit Conic Approximation of Spacecraft Trajectory; Improved Charge-Transfer Fluorescent Dyes; Stability-Augmentation Devices for Miniature Aircraft; Tool Measures Depths of Defects on a Case Tang Joint; Two Heat-Transfer Improvements for Gas Liquefiers; Controlling Force and Depth in Friction Stir Welding; Spill-Resistant Alkali-Metal-Vapor Dispenser; A Methodology for Quantifying Certain Design Requirements During the Design Phase; Measuring Two Key Parameters of H3 Color Centers in Diamond; Improved Compression of Wavelet-Transformed Images; NASA Interactive Forms Type Interface - NIFTI; Predicting Numbers of Problems in Development of Software; Hot-Electron Photon Counters for Detecting Terahertz Photons; Magnetic Variations Associated With Solar Flares; and Artificial Intelligence for Controlling Robotic Aircraft

Spartan Daily, September 23, 1975

Volume 65, Issue 9https://scholarworks.sjsu.edu/spartandaily/5995/thumbnail.jp