%---> 26 states %---> universel automaton of a ``pure-group'' language \begin{VCPicture}{(-7,-11)(7,10)} \PlainState % \StateIF[p]{(-1,7)}{P} \StateIF[s]{(1,7)}{S} \State[q]{(-4.46,8)}{Q} \StateIF[t]{(4.46,8)}{T} \State[r]{(-4.46,6)}{R} \StateIF[u]{(4.46,6)}{U} % \StateIF[pq]{(-4,-2)}{PQ} \StateIF[st]{(4,2)}{ST} \State[qr]{(-2,0)}{QR} \StateIF[tu]{(2,0)}{TU} \StateIF[pr]{(-4,2)}{PR} \StateIF[su]{(4,-2)}{SU} \StateIF[pt]{(2,4)}{PT} \StateIF[pu]{(2,-4)}{PU} \State[qu]{(0,2)}{QU} \State[qs]{(-2,-4)}{QS} \State[rs]{(-2,4)}{RS} \State[rt]{(0,-2)}{RT} % \ChgStateLabelScale{1.3} \LargeState \StateIFX[pqr]{(-6,-6)}{PQR} \StateIF[ptu]{(4,-8)}{PTU} \StateIF[pqu]{(-2,-7)}{PQU} \State[qsu]{(2,-7)}{QSU} \State[qrs]{(-4,-8)}{QRS} \State[rst]{(2,-9)}{RST} \StateIF[prt]{(-2,-9)}{PRT} \StateIFX[stu]{(6,-6)}{STU} % \FixDimEdge{dotted}{.5}{gray}{gray} \DimEdge \EdgeL{P}{PQ}{} \EdgeL{P}{PR}{} \EdgeL{P}{PT}{} \EdgeL{P}{PU}{} \EdgeL{Q}{PQ}{} \EdgeL{Q}{QR}{} \EdgeL{Q}{QS}{} \EdgeL{Q}{QU}{} \EdgeL{R}{PR}{} \EdgeL{R}{QR}{} \EdgeL{R}{RS}{} \EdgeL{R}{RT}{} \EdgeL{S}{QS}{} \EdgeL{S}{RS}{} \EdgeL{S}{ST}{} \EdgeL{S}{SU}{} \EdgeL{T}{PT}{} \EdgeL{T}{RT}{} \EdgeL{T}{ST}{} \EdgeL{T}{TU}{} \EdgeL{U}{PU}{} \EdgeL{U}{QU}{} \EdgeL{U}{SU}{} \EdgeL{U}{TU}{} % \EdgeL{PQ}{PQR}{} \EdgeL{QR}{PQR}{} \EdgeL{PR}{PQR}{} \EdgeL{QR}{QRS}{} \EdgeL{QS}{QRS}{} \EdgeL{RS}{QRS}{} \EdgeL{PR}{PRT}{} \EdgeL{PT}{PRT}{} \EdgeL{RT}{PRT}{} \EdgeL{PQ}{PQU}{} \EdgeL{PU}{PQU}{} \EdgeL{QU}{PQU}{} \EdgeL{ST}{STU}{} \EdgeL{SU}{STU}{} \EdgeL{TU}{STU}{} \EdgeL{PT}{PTU}{} \EdgeL{PU}{PTU}{} \EdgeL{TU}{PTU}{} \EdgeL{QS}{QSU}{} \EdgeL{QU}{QSU}{} \EdgeL{SU}{QSU}{} \EdgeL{RS}{RST}{} \EdgeL{RT}{RST}{} \EdgeL{ST}{RST}{} \RstEdge % \Initial[s]{P} \Final[n]{T} \Final[s]{S} \Final[s]{U} % \Initial{PQ} \Initial{PR} \Initial[s]{PT} \Initial[n]{PU} \Final{ST} \Final[e]{TU} \Final{SU} % \Initial[sw]{PQR} \Initial[n]{PQU} \Initial[s]{PRT} \Initial[s]{PTU} \Final[se]{STU} % \EdgeR{P}{Q}{a} \LoopW{Q}{b} \ArcR{Q}{R}{a} \LoopW{R}{b} \EdgeR{R}{P}{a} \LoopE{T}{b} \EdgeL{S}{T}{a} \LoopE{U}{b} \ArcL{T}{U}{a} \ArcL{P}{S}{b} \EdgeL{U}{S}{a} \ArcL{S}{P}{b} % \EdgeR{PQ}{QR}{a} \EdgeL{PT}{QU}{a} \EdgeR{QR}{PR}{a} \EdgeL{QU}{RS}{a} \EdgeR{PR}{PQ}{a} \EdgeL{RS}{PT}{a} % \EdgeL{PU}{QS}{a} \EdgeR{SU}{ST}{a} \EdgeL{QS}{RT}{a} \EdgeR{ST}{TU}{a} \EdgeL{RT}{PU}{a} \EdgeR{TU}{SU}{a} % \LoopE[.8]{QR}{b} \LoopW[.2]{TU}{b} \LoopN[.8]{RT}{b} \LoopS[.2]{QU}{b} % \ArcL{PQ}{QS}{b} \ArcL{ST}{PT}{b} \ArcL{QS}{PQ}{b} \ArcL{PT}{ST}{b} \ArcL{PU}{SU}{b} \ArcL{RS}{PR}{b} \ArcL{SU}{PU}{b} \ArcL{PR}{RS}{b} % \EdgeR{PQU}{QRS}{a} \EdgeR{QSU}{RST}{a} \EdgeR{QRS}{PRT}{a} \EdgeR{RST}{PTU}{a} \EdgeR{PRT}{PQU}{a} \EdgeR{PTU}{QSU}{a} % \LoopL{135}{PQR}{a} \LoopL{45}{STU}{a} % \ArcL{QRS}{PQR}{b} \ArcL{PQU}{QSU}{b} \ArcL{PQR}{QRS}{b} \ArcL{QSU}{PQU}{b} \ArcL{PTU}{STU}{b} \ArcL{PRT}{RST}{b} \ArcL{STU}{PTU}{b} \ArcL{RST}{PRT}{b} \end{VCPicture}