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10.1007/s11047-015-9527-0 http://scihub22266oqcxt.onion/10.1007/s11047-015-9527-0 C5012322!5012322!27616944     free     free     free       Nat+Comput 2016 ; 15 (1): 97-113 Nephropedia Template TP {{tp|p=27616944|t=2016. Counter machines and crystallographic structures |pdf=|usr=}}{{27616944}} gab.com Text Counter machines and crystallographic structures JO: Nat Comput http://www.kidney.de/pget.php?&tw=1&pmid=27616944 #FOAvip 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 ???d, 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 ???d An intersection of d languages in ???1 defines ???d. We prove that there is a one-to-one correspondence between sets of walks starting and ending in the same unit of a d-dimensional periodic (di)graph and the class of languages in ???d. The proof uses the following result: given a digraph ? and a group G, there is a unique digraph ? such that G ? Aut ?, G acts freely on the structure, and ?/G ? ?. Twit Text FOAVip Counter machines and crystallographic structures ????Nat Comput http://www.kidney.de/pget.php?&tw=1&pmid=27616944 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=27616944 #FOAvip English Wikipedia <ref>{{Cite pmid|27616944}}</ref> Counter machines and crystallographic structures #MMPMID27616944 Jonoska N; Krajcevski M; McColm G Nat Comput 2016[Mar]; 15 (1): 97-113 PMID27616944show ga 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 ???d, 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 ???d An intersection of d languages in ???1 defines ???d. We prove that there is a one-to-one correspondence between sets of walks starting and ending in the same unit of a d-dimensional periodic (di)graph and the class of languages in ???d. The proof uses the following result: given a digraph ? and a group G, there is a unique digraph ? such that G ? Aut ?, G acts freely on the structure, and ?/G ? ?. äCounter machines and crystallographic structures (epmc).pdf DeepDyve Pubget Overpricing