The word problem for semigroups with two generators

1949 ◽  
Vol 14 (2) ◽  
pp. 115-118 ◽  
Author(s):  
Marshall Hall
Keyword(s):  
Finite Number ◽  
Word Problem ◽  
Thue System

Emil Post has shown that the word problem for Thue systems is unsolvable. A Thue system is a system of strings of letters x1, x2, …, xr, where a string or word is either void or a succession of letters a1a2 … at with each ai some xi. We are given a finite number of pairs of strings Ai, Bii = 1, …, m. Operations in the Thue system consist of the replacements or “productions.”

scholarly journals Solution of the Word Problem for Certain Types of Groups I

1956 ◽  
Vol 3 (1) ◽  
pp. 45-54 ◽  
Author(s):  
J. L. Britton
Keyword(s):  
Finite Number ◽  
Word Problem ◽  
Infinite Number ◽  
Finite System ◽  
Defining Relations ◽  
Number Of Generators ◽  
Infinite Word ◽  
Formed Part ◽  
Free Product Of Groups ◽  
Product Of Groups

The main result of this series of papers is a theorem on the free product of groups (Theorem 1) which formed part of a doctoral thesis. This theorem has an immediate application to the word problem (Theorem 2). Usually the word problem refers to a finite system of generators and a finite number of defining relations, but in this context it is more natural to allow an infinite number of generators and defining relations. This (infinite) word problem is not solvable in general (Example 2).

An Algorithmic Solution for a Word Problem in Group Theory

1964 ◽  
Vol 16 ◽  
pp. 509-516 ◽  
Author(s):  
N. S. Mendelsohn
Keyword(s):  
Group Theory ◽  
Finite Number ◽  
Word Problem ◽  
Finite Index ◽  
Unit Element ◽  
Systematic Procedure ◽  
Algorithmic Solution ◽  
Finite Set ◽  
The Right

This paper describes a systematic procedure which yields in a finite number of steps a solution to the following problem. Let G be a group generated by a finite set of generators g1, g2, g3, . . . , gr and defined by a finite set of relations R1 = R2 = . . . = Rk = I, where I is the unit element of G and R1R2, . . . , Rk are words in the gi and gi-1. Let H be a subgroup of G, known to be of finite index, and generated by a finite set of words, W1, W2, . . . , Wt. Let W be any word in G. Our problem is the following. Can we find a new set of generators for H, together with a set of representatives h1 = 1, h2, . . . , hu of the right cosets of H (i.e. G = H1 + Hh2 + . . . + Hhu) such that W can be expressed in the form W = Uhp, where U is a word in .

scholarly journals A finite thue system with decidable word problem and without equivalent finite canonical system

1985 ◽  
Vol 35 ◽  
pp. 337-344 ◽  
Author(s):  
Deepak Kapur ◽  
Paliath Narendran
Keyword(s):  
Word Problem ◽  
Canonical System ◽  
Thue System

A solution of the uniform word problem for ortholattices

2010 ◽  
Vol 20 (4) ◽  
pp. 625-638 ◽  
Author(s):  
ANDREA MEINANDER
Keyword(s):  
Finite Number ◽  
Word Problem ◽  
Natural Deduction ◽  
Atomic Formula ◽  
Proof Search ◽  
Finite Set ◽  
Finitely Presented

The uniform word problem for finitely presented ortholattices is shown to be solvable through a method of terminating proof search. The axioms of ortholattices are all Harrop formulas, and thus can be expressed in natural deduction style as single succedent rules. A system of natural deduction style rules for orthologic is given as an extension of the system for lattices presented by Negri and von Plato. By considering formal derivations of atomic formulas from a finite number of given atomic formulas, it is shown that proof search is bounded, and thus that the question of derivability of any atomic formula from any finite set of given atomic formulas is decidable.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

PI-D Controller Design with Finite Number of Frequency Responces Model via a Ratio of Fourier Transformations of Input and Output Signals

2019 ◽  
Vol 139 (4) ◽  
pp. 402-408
Author(s):  
Yasushi Kami ◽  
Ryosuke Tanaka ◽  
Yuuichiroh Mitani ◽  
Eitaku Nobuyama
Keyword(s):  
Finite Number ◽  
Controller Design ◽  
Input And Output
Sign in / Sign up

Export Citation Format

Share Document