Chapter 5: Two Dimensions and Beyond

Section 6: Multiway Systems

History [of multiway systems]

Versions of multiway systems have been invented many times in a variety of contexts. In mathematics specific examples of them arose in formal group theory (see below) around the end of the 1800s. Axel Thue considered versions with two-way rules (analogous to semigroups, as discussed below) in 1912, leading to the name semi-Thue systems sometimes being used for general multiway systems. Other names for multiway systems have included string and term rewrite systems, production systems and associative calculi. From the early 1900s various generalizations of multiway systems were used as idealizations of mathematical proofs (see page 1150); multiway systems with explicit pattern variables (such as s_) were studied under the name canonical systems by Emil Post starting in the 1920s. Since the 1950s, multiway systems have been widely used as generators of formal languages (see below). Simple analogs of multiway systems have also been used in genetic analysis in biology and in models for particle showers and other branching processes in physics and elsewhere.

From Stephen Wolfram: A New Kind of Science [citation]