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DFA Limitations & Turing Machines

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CSCtr 222 Horneu.ork 6 (Due Apr. 22)
1. \\'htit is the trutttber rif otrc-to-one func'tions / fiorn thc set U.2....,n) to the set
{1.2. ..,n} so that there is at niost o1r().T ri,ith./(r:) :.r'l
Givctr ir set ,S. iet /? be thc relatiotr definerl on the po\\cl set P(S) 1;r.AfiB nht:rrevcr
A C B aricl A I B foy A. B C S. Pror,.c rvhethcr cir not fr is leflexivc. sr.mnrt,tric,"
arrtisl'nrrnetric' ol transitir.e.
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4.
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.f , A -+ A lr1' .f rirT u.heno'er the size of rangc {/(r,) | .r: € A} of / is the sanre as
tlre siztr of ratrge {g(r) | .r: € Al o{ q. Plrive t}rat R is rrrr equivalenr.c leltition alcl
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