Parallel Complexity of Iterated Morphisms and the Arithmetic of Small Numbers
نویسندگان
چکیده
We improve several upper bounds to the complexity of the membership problem for languages deened by iterated morphisms (D0L systems). The complexity bounds are expressed in terms of DLOGT IME-uniform circuit families. We prove: 1) For polynomially growing D0L systems the membership problem is contained in AC 0. 2) For arbitrary D0L systems the membership problem is contained in NC 1. 3) The latter can be improved to T C 0 if and only if upper bounds to a number of natural arithmetic problems can be improved to T C 0. 4) The general D0L membership problem (the D0L system is part of the input) is contained in Cook's class DET .
منابع مشابه
Low Complexity Converter for the Moduli Set {2^n+1,2^n-1,2^n} in Two-Part Residue Number System
Residue Number System is a kind of numerical systems that uses the remainder of division in several different moduli. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers will increase the speed of the arithmetic operations in this system. However, the main factor that affects performance of system is hardware complexity of reverse converter. Reverse co...
متن کاملInteger Division Is in Nc 1
An NC 1 circuit for division of binary numbers is presented. By results of Beame, Cook and Hoover this also shows that iterated product and powering are in NC 1 , and by a result of Borodin all three operations are in log-space. This settles an open issue in parallel and space bounded arithmetic complexity.
متن کاملEfficient Reverse Converter for Three Modules Set {2^n-1,2^(n+1)-1,2^n} in Multi-Part RNS
Residue Number System is a numerical system which arithmetic operations are performed parallelly. One of the main factors that affects the system’s performance is the complexity of reverse converter. It should be noted that the complexity of this part should not affect the earned speed of parallelly performed arithmetic unit. Therefore in this paper a high speed converter for moduli set {2n-1, ...
متن کاملEfficient Reverse Converter for Three Modules Set {2^n-1,2^(n+1)-1,2^n} in Multi-Part RNS
Residue Number System is a numerical system which arithmetic operations are performed parallelly. One of the main factors that affects the system’s performance is the complexity of reverse converter. It should be noted that the complexity of this part should not affect the earned speed of parallelly performed arithmetic unit. Therefore in this paper a high speed converter for moduli set {2n-1, ...
متن کاملOverflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1}
Residue Number System (RNS) is a non-weighted number system for integer number arithmetic, which is based on the residues of a number to a certain set of numbers called module set. The main characteristics and advantage of residue number system is reducing carry propagation in calculations. The elimination of carry propagation leads to the possibility of maximizing parallel processing and reduc...
متن کامل