Tutoriais - Linguagens Formais e AutômatosApresente as possíveis subpalavras da palavra motherboard.
Segundo Ramos (2009), uma palavra α é uma subpalavra de outra palavra β se for possível escrever β como sendo γαδ, admitindo-se a possibilidade de γ ou δ ou ambos serem palavras vazias (ε). Note que prefixos (γ) e sufixos (δ) são casos particulares de subpalavras (α).
A Tabela 01 apresenta as subpalavras (α) da palavra motherboard (β), conforme a definição apresentada por Ramos (2009).
| |γ| | |α| | |δ| | β | γ | α | δ |
|---|---|---|---|---|---|---|
| 0 | 0 | 11 | motherboard | ε | ε | motherboard |
| 0 | 1 | 10 | motherboard | ε | m | otherboard |
| 1 | 1 | 9 | motherboard | m | o | therboard |
| 2 | 1 | 8 | motherboard | mo | t | herboard |
| 3 | 1 | 7 | motherboard | mot | h | erboard |
| 4 | 1 | 6 | motherboard | moth | e | rboard |
| 5 | 1 | 5 | motherboard | mothe | r | board |
| 6 | 1 | 4 | motherboard | mother | b | oard |
| 7 | 1 | 3 | motherboard | motherb | o | ard |
| 8 | 1 | 2 | motherboard | motherbo | a | rd |
| 9 | 1 | 1 | motherboard | motherboa | r | d |
| 10 | 1 | 0 | motherboard | motherboar | d | ε |
| 0 | 2 | 9 | motherboard | ε | mo | therboard |
| 1 | 2 | 8 | motherboard | m | ot | herboard |
| 2 | 2 | 7 | motherboard | mo | th | erboard |
| 3 | 2 | 6 | motherboard | mot | he | rboard |
| 4 | 2 | 5 | motherboard | moth | er | board |
| 5 | 2 | 4 | motherboard | mothe | rb | oard |
| 6 | 2 | 3 | motherboard | mother | bo | ard |
| 7 | 2 | 2 | motherboard | motherb | oa | rd |
| 8 | 2 | 1 | motherboard | motherbo | ar | d |
| 9 | 2 | 0 | motherboard | motherboa | rd | ε |
| 0 | 3 | 8 | motherboard | ε | mot | herboard |
| 1 | 3 | 7 | motherboard | m | oth | erboard |
| 2 | 3 | 6 | motherboard | mo | the | rboard |
| 3 | 3 | 5 | motherboard | mot | her | board |
| 4 | 3 | 4 | motherboard | moth | erb | oard |
| 5 | 3 | 3 | motherboard | mothe | rbo | ard |
| 6 | 3 | 2 | motherboard | mother | boa | rd |
| 7 | 3 | 1 | motherboard | motherb | oar | d |
| 8 | 3 | 0 | motherboard | motherbo | ard | ε |
| 0 | 4 | 7 | motherboard | ε | moth | erboard |
| 1 | 4 | 6 | motherboard | m | othe | rboard |
| 2 | 4 | 5 | motherboard | mo | ther | board |
| 3 | 4 | 4 | motherboard | mot | herb | oard |
| 4 | 4 | 3 | motherboard | moth | erbo | ard |
| 5 | 4 | 2 | motherboard | mothe | rboa | rd |
| 6 | 4 | 1 | motherboard | mother | boar | d |
| 7 | 4 | 0 | motherboard | motherb | oard | ε |
| 0 | 5 | 6 | motherboard | ε | mothe | rboard |
| 1 | 5 | 5 | motherboard | m | other | board |
| 2 | 5 | 4 | motherboard | mo | therb | oard |
| 3 | 5 | 3 | motherboard | mot | herbo | ard |
| 4 | 5 | 2 | motherboard | moth | erboa | rd |
| 5 | 5 | 1 | motherboard | mothe | rboar | d |
| 6 | 5 | 0 | motherboard | mother | board | ε |
| 0 | 6 | 5 | motherboard | ε | mother | board |
| 1 | 6 | 4 | motherboard | m | otherb | oard |
| 2 | 6 | 3 | motherboard | mo | therbo | ard |
| 3 | 6 | 2 | motherboard | mot | herboa | rd |
| 4 | 6 | 1 | motherboard | moth | erboar | d |
| 5 | 6 | 0 | motherboard | mothe | rboard | ε |
| 0 | 7 | 4 | motherboard | ε | motherb | oard |
| 1 | 7 | 3 | motherboard | m | otherbo | ard |
| 2 | 7 | 2 | motherboard | mo | therboa | rd |
| 3 | 7 | 1 | motherboard | mot | herboar | d |
| 4 | 7 | 0 | motherboard | moth | erboard | ε |
| 0 | 8 | 3 | motherboard | ε | motherbo | ard |
| 1 | 8 | 2 | motherboard | m | otherboa | rd |
| 2 | 8 | 1 | motherboard | mo | therboar | d |
| 3 | 8 | 0 | motherboard | mot | herboard | ε |
| 0 | 9 | 2 | motherboard | ε | motherboa | rd |
| 1 | 9 | 1 | motherboard | m | otherboar | d |
| 2 | 9 | 0 | motherboard | mo | therboard | ε |
| 0 | 10 | 1 | motherboard | ε | motherboar | d |
| 1 | 10 | 0 | motherboard | m | otherboard | ε |
| 0 | 11 | 0 | motherboard | ε | motherboard | ε |
Conforme apresentado na Tabela 01, as subpalavras (α) da palavra motherboard (β) são formalmente definidas como:
{ε, a, b, d, e, h, m, o, r, t, ar, bo, er, he, mo, oa, ot, rb, rd, th, ard, boa, erb, her, mot, oar, oth, rbo, the, boar, erbo, herb, moth, oard, othe, rboa, ther, board, erboa, herbo, mothe, other, rboar, therb, erboar, herboa, mother, otherb, rboard, therbo, erboard, herboar, motherb, otherbo, therboa, herboard, motherbo, otherboa, therboar, motherboa, otherboar, therboard, motherboar, otherboard, motherboard}
Ramos, Marcus Vinícius Midena. (2009). Linguagens Formais: teoria, modelagem e implementação. Porto Alegre: Bookman. 656 páginas.
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