Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Mathematics
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Mathematics and Statistics Faculty Publications
One way to depict a crystallographic structure is by a periodic (di)graph, i.e., a graph whose group of automorphisms has a translational subgroup of finite index acting freely on the structure. We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages DCLd,d=0,1,2,…, within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class DCLd. An intersection of d languages in DCL1 defines DCLd. We prove that there is …