Codes, simplifying words, and open set condition

In formal language theory the concept of simplifying words is considered in connection with the deciphering delay of codes (cf. [BP, Section II.8], [LP]). In this paper we show that transferring a definition from the theory of iterated function systems (IFS) sheds some new light on simplifying words.: Formal languages may be considered as IFS in the Cantor space of infinite strings over a finite alphabet X (cf. [Fe], [S2]). If those IFS satisfy the so-called Open Set Condition (OSC) then the underlying language is a code having simplifying words. Moreover, the simplifying words of a code C are naturally subdivided into nonsubwords (of the set of code messages C) and into simplifying prefixes. It can be shown that the existence of simplifying prefixes for a code C is equivalent to the fulfillment of a strong version of the OSC for the related IFS

Codes, Simplifying Words, and Open Set Condition

A relationship between formal language theory and fractal geometry describing how codes may be used to generate (infinite) iterated function systems fulfilling certain properties is presented