Hierarchies of turing machines with restricted tape alphabet size

It is shown that for any real constants b>a≥0, multitape Turing machines operating in space L1(n)=[bnr] can accept more sets than those operating in space L2(n)=[anr] provided the number of work tapes and tape alphabet size are held fixed. It is also shown that Turing machines with k+1 work tapes are more powerful than those with k work tapes if the tape alphabet size and the amount of work space are held constant

Computing Hough Transforms on Hypercube Multicomputers

Efficient algorithms to compute the Hough transform on MIMD and SIMD hypercube multicomputers are developed. Our algorithms can compute p angles of the Hough transform of an N x N image, p ≤ N, in 0(p + log N) time on both MIMD and SIMD hypercubes. These algorithms require 0(N2) processors. We also consider the computation of the Hough transform on MIMD hypercubes with a fixed number of processors. Experimental results on an NCUBE/7 hypercube are presented

Finite automata with multiplication

AbstractA finite automaton with multiplication (FAM) is a finite automaton with a register which is capable of holding any positive rational number. The register can be multiplied by any of a fixed number of rationals and can be tested for value 1. Closure properties and decision problems for various types of FAM's (e.g. two-way, one-way, nondeterministic, deterministic) are investigated. In particular, it is shown that the languages recognized by two-way deterministic FAM's are of tape complexity log n and time complexity n3. Some decision problems related to vector addition systems are also studied

Randomized routing, selection, and sorting on the otis-mesh

The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. In this paper we present efficient algorithms for packet routing, sorting, and selection on the OTIS-Mesh. The diameter of an N 2-processor OTIS-Mesh is 4 √ N − 3. We present an algorithm for routing any partial permutation in 4 √ N +o ( √ N) time. Our selection algorithm runs in time 6 √ N + o ( √ N) and our sorting algorithm runs in 8 √ N + o ( √ N) time. All these algorithms are randomized and the stated time bounds hold with high probability. Also, the queue size needed for these algorithms is O(1) with high probability

Some Related Problems from Network Flows, Game Theory and Integer Programming

We consider several important problems for which no polynomially time bounded algorithm is known. These problems are shown to be related in that a polynomial algorithm for one implies a polynomial algorrithm for the others