Graph Isomorphism is PSPACE-complete

Graph Isomorphism is PSP A CE-complete Matthew Delacorte August 30, 2007 Comb ining the the results of A.R. Meyer and L.J. Sto c kmeye r ”The Equiv alence Problem for Regular Expressions with Squaring Requires Exponential Space”, and K.S. Booth ”Iso- morphism testing f or graphs, semigroups, and finite automata a re p olynomiamlly equiv alent problems” shows that graph isomor phi s m is PSP A CE-complete. 1 Pro of The equiv alenc e problem for regular expressions was sho wn to be PSP A CE-complete by (Mey er and Stockmey er [ 2]). Bo oth [1] has shown that isomorphism of finite automata is equiv alen t to graph isomorphism. T aking these tw o results together with the equiv alence of regular expressions, right-linear grammars, and finite automata see [3] f or example, shows that graph isomorphism is PSP ACE-complet e. References [1] Booth, K.S. Isomorphism testing for graphs, semi groups, and finite aut omata a re poly- nomiamlly equiv alen t problems, SIAM J. Comput. 7, N o 3, (1978) , 273-279. [2] Hopcrof t, J.E., and Ul lman, J. D. (1979), I ntroduction to Auto mata Theo ry , Langu ages and Computation, Addison-W esley , Reading, MA . [3] Mey er, A. R. and Sto c kmey er, L.J. The Equiv alence Problem for Regular Expressions with Squaring Requires Exp onen tial Space, 13th Annual IEEE Symp. on Switch ing and Automata Theory , Oct., 1972,125-129. 1