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Minimizzazione di automi

Minimizzazione di automi. Stati equivalenti: ~, ~ Pn. x~y  *: (,x =>*,x’  ,y =>*,y’ s.t. x’~y’). x~ Pn y  a: (a,x =>*,x’  a,y =>*,y’ s.t. x’~ P y’). Algoritmo di minimizzazione. Operatori:. refine A ( P= {P1,…,Pk})={Q1,…,Qh} s.t: i[1..h]:  j [1..k]: Qi=Pj

daniel-mullen
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Minimizzazione di automi

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  1. Minimizzazione di automi Stati equivalenti: ~, ~Pn x~y  *: (,x =>*,x’  ,y =>*,y’ s.t. x’~y’) x~Pny  a: (a,x =>*,x’  a,y =>*,y’ s.t. x’~Py’) Algoritmo di minimizzazione Operatori: • refineA(P={P1,…,Pk})={Q1,…,Qh} s.t: • i[1..h]: •  j [1..k]: Qi=Pj •  j [1..k], Qi Pj and • x,y Qi, z  Pj\Qi : x~Pny and x~Pnz • Input: A=<S, , move, s, F> • Output: MA=<PS, , move|Ps, s|Ps, F|Ps > • P= {S\F, F}; • Pn = refineA(P); • while P ≠ Pn do{ • P = Pn; • Pn = refineA(P)} • PS = P • Partizione di S: PS ={P1,…,Pk} • copertura: S =  j[1..k] Pj • equivalenza: Pii≠j[1..k]Pj • Rappresentanti S|Ps su S: PS={P1,…,Pk} • rappresentante: [Pi]  Pi - x  Pi , [x]=[Pi] • S|Ps = {[x]|x S} • move|Ps = {<<[s],a>,U|Ps> |<<s,a>U> move}

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