@article {IOPORT.00126121,
    author       = {Satyanarayana, M. and Mohanty, Supriya},
    title        = {Limited semaphore codes.},
    year         = {1992},
    journal      = {Semigroup Forum},
    volume       = {45},
    number       = {3},
    issn         = {0037-1912},
    pages        = {364-371},
    publisher    = {Springer-Verlag, New York},
    doi          = {10.1007/BF03025776},
    abstract     = {An alphabet $A$ is a set of symbols called letters. A word over $A$ is a finite catenation of letters. $A\sp*$ denotes a free monoid over $A$ which includes an empty word represented by 1. A subset $X$ of $A\sp +=A\backslash 1$ is called a code over $A$ if $x\sb 1x\sb 2\cdots x\sb n=y\sb 1 y\sb 2\cdots y\sb m$ with $x\sb i,y\sb i\in X$, then $n=m$ and $x\sb i=y\sb i$ for every $i$, $1\le i\le n$. A word in $X$ is called an $X$-word. A code $X$ is called a uniformly synchronous code if for some non-negative integer $d$, $uxv\in X\sp*$ with $x\in X\sp d$, $u,v\in A\sp*$ implies $ux$, $xv\in X\sp*$, where $X\sp*$ is a free monoid over $X$. The smallest $d$ satisfying this property is called the synchronizing delay of $X$ denoted by $\sigma(x)$. A code $X$ is right complete if, for any $u\in A\sp*$ there exists a $t$ such that $ut\in X\sp*$. A code $X$ satisfies the $F-d$ condition if $A\sp + X\sp d A\sp +\cap X=\emptyset$, where $d$ is a natural number. A code $X$ is called a semaphore code iff $A\sp* XA\sp +\cap X=\emptyset$ and $X$ is right complete, equivalently iff $X$ is a right complete prefix code satisfying the $F-1$ condition. A code $X$ is a synchronous code if there exists an $x\in A\sp*$ such that $A\sp* x\subseteq X\sp*$ and $x$ is called a synchronizing word for $X$. A code $X$ is called $d$-synchronous iff $A\sp* X\sp d\subseteq X\sp*$. Let $m$, $n$ be any two non-negative integers such that $m+n\ne 0$. A code $X$ over $A$ is said to be an $(m,n)$-limited code if for any sequence $\{u\sb 0,u\sb 1,\dots,u\sb{m+n}\}$ in $A\sp*,u\sb 0 u\sb 1,u\sb 1 u\sb 2,\dots,u\sb{m+n-1} u\sb{m+n}\in X\sp*$ implies $u\sb m\in X\sp*$. A limited code is an $(m,n)$-limited code for some non-negative integers $m$, $n$ with $m+n\ne 0$. Some conditions are given for when a semaphore code, not necessarily limited, is a synchronous code and vice-versa. It is observed that limited semaphore codes are not only synchronous but also $d$-synchronous. It is shown that 1-synchronous codes are always semaphore codes as well as limited codes and the structure of certain 1- synchronous codes are shown to be exactly (1,0)-limited semaphore codes. It is assumed that no code is a subset of $A$.},
    reviewer     = {I.F.Blake (Waterloo / Ontario)},
    identifier   = {00126121},
}