{"id":1165,"date":"2025-05-19T08:04:20","date_gmt":"2025-05-19T08:04:20","guid":{"rendered":"https:\/\/ekomartantoh.net\/artikel\/?p=1165"},"modified":"2025-05-19T08:26:38","modified_gmt":"2025-05-19T08:26:38","slug":"ndfa-dengan-%ce%b5-move","status":"publish","type":"post","link":"https:\/\/ekomartantoh.net\/artikel\/2025\/05\/19\/ndfa-dengan-%ce%b5-move\/","title":{"rendered":"NDFA dengan \u03b5-Move"},"content":{"rendered":"\n

Pada materi ini kita akan membahas tentang \u03b5-closure dan ekivalensi. \u03b5 disini bisa dianggap sebagai empty. Pada NDFA dengan \u03b5-move (transisi \u03b5) diperbolehkan merubah state tanpa membaca input. Disebut dengan transisi \u03b5 karena tidak tergantung pada input ketika melakukan transisi.<\/p>\n\n\n\n

Mesin NFA dengan \u03b5-move Contoh 1<\/h2>\n\n\n\n
\"\"
Gambar 1<\/figcaption><\/figure>\n\n\n\n

q0 tanpa input ke q1
q1 tanpa input ke q2
q4 tanpa input ke q1<\/p>\n\n\n\n

Salah satu kegunaan transisi \u03b5 ini memudahkan kita mengkombinasaikan finite state automata.<\/p>\n\n\n\n

\u03b5-closure untuk suatu NDFA dengan \u03b5-move<\/h3>\n\n\n\n

\u03b5-closure adalah himpunan state-state yang dapat dicapai dari satu state tanpa membaca input.<\/p>\n\n\n\n

Misalnya saja \u03b5-closure (q0) = himpunan state-state yang dapat dicapai state q0 tanpa membaca input maka dengan melihat gambar 1. \u03b5-closure (q0) = {q0,q1,q2}, artinya dari state q0 tanpa membaca input dapat mencapai state q0, q1 dan q2.<\/p>\n\n\n\n

\u03b5-closure untuk state lainnya bisa dilihat sebagai berikut:<\/p>\n\n\n\n

\u03b5-closure (q1) = {q1,q2}
\u03b5-closure (q2) = {q2}
\u03b5-closure (q3) = {q3}
\u03b5-closure (q4) = {q1,q2,q4}<\/p>\n\n\n\n

<\/p>\n\n\n\n

Mesin NFA dengan \u03b5-move Contoh 2<\/h2>\n\n\n\n
\"\"
Gambar 2<\/figcaption><\/figure>\n\n\n\n

\u03b5-closure untuk state lainnya bisa dilihat sebagai berikut:<\/p>\n\n\n\n

\u03b5-closure (q0) = {q0,q1,q3}
\u03b5-closure (q1) = {q1,q3}
\u03b5-closure (q2) = {q2,q4}
\u03b5-closure (q3) = {q3}
\u03b5-closure (q4) = {q4}<\/p>\n\n\n\n

Note: Pada state yang tidak memiliki transisi \u03b5, maka \u03b5-closurenya adalah state itu sendiri.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Ekivalensi NDFA dengan \u03b5-move ke NDFA tanpa \u03b5-move<\/h2>\n\n\n\n
\"\"
Gambar 3. NDFA dengan \u03b5-move<\/figcaption><\/figure>\n\n\n\n
\"\"
Gambar 4. NFA tanpa \u03b5-move ekivalen<\/figcaption><\/figure>\n\n\n\n

Beberapa tahapan untuk mendapatkan perubahan NDFA \u03b5-move ke NDFA tanpa \u03b5-move<\/p>\n\n\n\n

    \n
  1. Buat table transisi NDFA \u03b5-move semula<\/li>\n\n\n\n
  2. Tentukan \u03b5-closure untuk setiap state<\/li>\n\n\n\n
  3. Carilah setiap fungsi transisi hasil perubahan dari NDFA \u03b5-move ke NDFA tanpa \u03b5-move rumusnya
    \u03b4'(state,input) = \u03b5-closure (\u03b4(\u03b5-closure (state),input))<\/strong><\/li>\n\n\n\n
  4. Berdasarkan hasil no(3) kita dapat membuat tabel transisi dan diagram transisi dari NDFA \u03b5-move yang ekivalen dengan NDFA \u03b5-move tersebut.<\/li>\n\n\n\n
  5. Tentukan state-state akhir untuk NDFA tanpa \u03b5-move tersebut yaitu state-state akhir semula ditambah dengan state-state yang \u03b5-closure nya menuju ke salah satu dari state akhir semula.<\/li>\n<\/ol>\n\n\n\n

    Kita coba lakukan:<\/strong><\/p>\n\n\n\n

    Langkah 1:<\/strong><\/p>\n\n\n

    \n
    \"\"
    Gambar 3. NFA dengan \u03b5-move<\/figcaption><\/figure>\n<\/div>\n\n\n

    Tabel transisi dari gambar 3 sebagai berikut:<\/p>\n\n\n\n

    \u03b4<\/strong><\/td>a<\/strong><\/td>b<\/strong><\/td><\/tr>
    q0<\/td>\u2205<\/td>\u2205<\/td><\/tr>
    q1<\/td>q2<\/td>q3<\/td><\/tr>
    q2<\/td>\u2205<\/td>\u2205<\/td><\/tr>
    q3<\/td>\u2205<\/td>\u2205<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Langkah 2:<\/strong><\/p>\n\n\n\n

    Menentukan \u03b5-<\/strong>closure untuk setiap state (\u03b5-<\/strong>closure bisa kita singkat \u03b5-<\/strong>cl)<\/p>\n\n\n\n

    \u03b5-<\/strong>cl (q0) = {q0,q1}
    \u03b5-<\/strong>cl (q1) = {q1}
    \u03b5-<\/strong>cl (q2) = {q2}
    \u03b5-<\/strong>cl (q3) = {q3}<\/p>\n\n\n\n

    Langkah 3:<\/strong><\/p>\n\n\n\n

    Kemudian kita cari \u03b4’ dengan memanfaatkan tabel transisi dan \u03b5-closure yang kita peroleh sebelumnya sebagai berikut:<\/p>\n\n\n\n

    \u03b4’ (q0,a) = \u03b5-closure (\u03b4(\u03b5-closure(q0,a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q0,q1},a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (q2)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= {q2}<\/p>\n\n\n\n

    \u03b4’ (q0,b) = \u03b5-closure (\u03b4(\u03b5-closure(q0,b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q0,q1},b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (q3)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= {q3}<\/p>\n\n\n\n

    \u03b4’ (q1,a) \u00a0\u00a0\u00a0 = \u03b5-closure (\u03b4(\u03b5-closure(q1,a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q1},a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (q2)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= {q2}<\/p>\n\n\n\n

    \u03b4’ (q1,b) \u00a0\u00a0\u00a0 = \u03b5-closure (\u03b4(\u03b5-closure(q1,b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q1},b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (q3)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= {q3}<\/p>\n\n\n\n

    \u03b4’ (q2,a) \u00a0\u00a0\u00a0 = \u03b5-closure (\u03b4(\u03b5-closure(q2,a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q2},a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u2205)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u2205<\/p>\n\n\n\n

    \u03b4’ (q2,b) \u00a0\u00a0\u00a0 = \u03b5-closure (\u03b4(\u03b5-closure(q2,b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q2},b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u2205)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u2205<\/p>\n\n\n\n

    \u03b4’ (q3,a) \u00a0\u00a0\u00a0 = \u03b5-closure (\u03b4(\u03b5-closure(q3,a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q3},a))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u2205)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u2205<\/p>\n\n\n\n

    \u03b4’ (q3,b) \u00a0\u00a0\u00a0 = \u03b5-closure (\u03b4(\u03b5-closure(q3,b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u03b4({q3},b))
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b5-closure (\u2205)
    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u2205<\/p>\n\n\n\n

    Maka kita akan mendapatkan tabel transisi dari NFA tanpa \u03b5-move dari hasil diatas:<\/p>\n\n\n\n

    \u03b4<\/strong><\/td>a<\/strong><\/td>b<\/strong><\/td><\/tr>
    q0<\/td>q2<\/td>q3<\/td><\/tr>
    q1<\/td>q2<\/td>q3<\/td><\/tr>
    q2<\/td>\u2205<\/td>\u2205<\/td><\/tr>
    q3<\/td>\u2205<\/td>\u2205<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n
    \n
    \"\"
    Gambar NFA tanpa \u03b5-move ekivalen <\/figcaption><\/figure>\n<\/div>\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    Pada materi ini kita akan membahas tentang \u03b5-closure dan ekivalensi. \u03b5 disini bisa dianggap sebagai empty. Pada NDFA dengan \u03b5-move (transisi \u03b5) diperbolehkan merubah state tanpa membaca input. Disebut dengan transisi \u03b5 karena tidak tergantung pada input ketika melakukan transisi. Mesin NFA dengan \u03b5-move Contoh 1 q0 tanpa input ke q1q1 tanpa input ke q2q4 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[101],"tags":[],"class_list":["post-1165","post","type-post","status-publish","format-standard","hentry","category-teori-bahasa-dan-otomata"],"yoast_head":"\nNDFA dengan \u03b5-Move - eko's Article<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/ekomartantoh.net\/artikel\/2025\/05\/19\/ndfa-dengan-\u03b5-move\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NDFA dengan \u03b5-Move - eko's Article\" \/>\n<meta property=\"og:description\" content=\"Pada materi ini kita akan membahas tentang \u03b5-closure dan ekivalensi. \u03b5 disini bisa dianggap sebagai empty. 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Pada NDFA dengan \u03b5-move (transisi \u03b5) diperbolehkan merubah state tanpa membaca input. Disebut dengan transisi \u03b5 karena tidak tergantung pada input ketika melakukan transisi. 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