Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe inverse of Ackermann function is computable in linear time
87
0
0.0
(
0
)
Added by
Claude Sureson
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Claude Sureson
Ask ChatGPT about the research
No Arabic abstract
We propose a detailed proof of the fact that the inverse of Ackermann function is computable in linear time.
rate research
Read More
Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize non-linear CA evolutions in the light of Boolean derivatives and Jacobian Matrices. In this paper two different efforts have been made: first we try to systematize non-linear CA evolution in the light of deviant states and non-deviant states. For all the non-deviant states the nearest linear rule matrix is applicable where as for the deviant states we have a set of other matrices. Second using algebraic manipulation, an efficient algorithm is proposed by which every Non-linear Boolean function can be characterized by a sequence of binary matrices.
Mosse proved that primitive morphisms are recognizable. In this paper we give a computable upper bound for the constant of recognizability of such a morphism. This bound can be expressed only using the cardinality of the alphabet and the length of the longest image under the morphism of a letter.
We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree structure. Our main result shows that ${omega cdot k,omega^star cdot k}$ is computably embeddable in ${omega cdot t, omega^star cdot t}$ iff $k$ divides $t$.
We consider the point-to-point message passing model of communication in which there are $k$ processors with individual private inputs, each $n$-bit long. Each processor is located at the node of an underlying undirected graph and has access to private random coins. An edge of the graph is a private channel of communication between its endpoints. The processors have to compute a given function of all their inputs by communicating along these channels. While this model has been widely used in distributed computing, strong lower bounds on the amount of communication needed to compute simple functions have just begun to appear. In this work, we prove a tight lower bound of $Omega(kn)$ on the communication needed for computing the Tribes function, when the underlying graph is a star of $k+1$ nodes that has $k$ leaves with inputs and a center with no input. Lower bound on this topology easily implies comparable bounds for others. Our lower bounds are obtained by building upon the recent information theoretic techniques of Braverman et.al (FOCS13) and combining it with the earlier work of Jayram, Kumar and Sivakumar (STOC03). This approach yields information complexity bounds that is of independent interest.
Given a set of $n$ weighted points on the $x$-$y$ plane, we want to find a step function consisting of $k$ horizontal steps such that the maximum vertical weighted distance from any point to a step is minimized. We solve this problem in $O(n)$ time when $k$ is a constant. Our approach relies on the prune-and-search technique, and can be adapted to design similar linear time algorithms to solve the line-constrained k-center problem and the size-$k$ histogram construction problem as well.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
