{"id":1187,"date":"2025-05-26T05:34:52","date_gmt":"2025-05-26T05:34:52","guid":{"rendered":"https:\/\/ekomartantoh.net\/artikel\/?p=1187"},"modified":"2025-05-26T05:34:54","modified_gmt":"2025-05-26T05:34:54","slug":"ndfa-dengan-%ce%b5-move-studi-kasus-penggabungan-dan-konkatenasi","status":"publish","type":"post","link":"https:\/\/ekomartantoh.net\/artikel\/2025\/05\/26\/ndfa-dengan-%ce%b5-move-studi-kasus-penggabungan-dan-konkatenasi\/","title":{"rendered":"NDFA dengan \u03b5-move: Studi Kasus, Penggabungan, dan Konkatenasi"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Studi Kasus<\/h2>\n\n\n\n<p>Perhatikan gambar NFA \u03b5-move berikut:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"915\" height=\"385\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-13.png\" alt=\"\" class=\"wp-image-1188\" style=\"width:656px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-13.png 915w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-13-300x126.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-13-768x323.png 768w\" sizes=\"auto, (max-width: 915px) 100vw, 915px\" \/><\/figure>\n\n\n\n<p>Kita akan coba merubah diagram ini ke NDFA tanpa \u03b5-move dengan tahapan yang sudah diberikan pada materi sebelumnya.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Langkah 1<\/h3>\n\n\n\n<p>Menentukan tabel transisi, kebetulan sudah di gambarkan pada gambar diatas<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Langkah 2<\/h3>\n\n\n\n<p>Menentukan \u03b5-closure untuk setiap state:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"141\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-15.png\" alt=\"\" class=\"wp-image-1190\" style=\"width:189px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-15.png 307w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-15-300x138.png 300w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Langkah 3<\/h3>\n\n\n\n<p>Carilah setiap fungsi transisi hasil perubahan dari NDFA \u03b5-move ke NDFA tanpa \u03b5-move rumus:<\/p>\n\n\n\n<p>               <strong>\u03b4'(state,input) = \u03b5-closure (\u03b4(\u03b5-closure (state),input))<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"271\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-16.png\" alt=\"\" class=\"wp-image-1191\" style=\"width:387px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-16.png 450w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-16-300x181.png 300w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"460\" height=\"274\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-17.png\" alt=\"\" class=\"wp-image-1192\" style=\"width:386px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-17.png 460w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-17-300x179.png 300w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"275\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-18.png\" alt=\"\" class=\"wp-image-1193\" style=\"width:384px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-18.png 469w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-18-300x176.png 300w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Langkah 4<\/h3>\n\n\n\n<p>Berdasarkan hasil diatas maka kita bisa membuat tabel transisi untuk NFA tanpa \u03b5-move:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"507\" height=\"201\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-19.png\" alt=\"\" class=\"wp-image-1194\" style=\"width:391px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-19.png 507w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-19-300x119.png 300w\" sizes=\"auto, (max-width: 507px) 100vw, 507px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Langkah 5<\/h3>\n\n\n\n<p>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.<\/p>\n\n\n\n<p>Himpunan state akhir semula adalah q0. State-state yang \u03b5-closure nya menuju q0, kita lihat<\/p>\n\n\n\n<p><strong>\u03b5-cl<\/strong> (q2) = {q0,q1,q2}                  ini yang mengandung q0<\/p>\n\n\n\n<p>Sehingga himpunan state akhirnya adalah {q0,q2).<\/p>\n\n\n\n<p>Berikut gambar hasil NFA tanpa \u03b5-move yang ekivalen:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"986\" height=\"735\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-20.png\" alt=\"\" class=\"wp-image-1195\" style=\"width:486px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-20.png 986w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-20-300x224.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-20-768x572.png 768w\" sizes=\"auto, (max-width: 986px) 100vw, 986px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Penggabungan dan Konkatenasi<\/h2>\n\n\n\n<p>Pada mesin Finite Automata kita dapat melakukan penggabungan, disebut Union serta Konkatenasi.<\/p>\n\n\n\n<p>Misal terdapat 2 mesin sebagai berikut:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"908\" height=\"237\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-21.png\" alt=\"\" class=\"wp-image-1196\" style=\"width:674px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-21.png 908w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-21-300x78.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-21-768x200.png 768w\" sizes=\"auto, (max-width: 908px) 100vw, 908px\" \/><\/figure>\n\n\n\n<p>Bila diketahui:<br>L(M<sub>1<\/sub>) adalah bahasa yang diterima oleh M<sub>1<\/sub>.<br>L(M<sub>2<\/sub>) adalah bahasa yang diterima oleh M<sub>2<\/sub>.<\/p>\n\n\n\n<p>Dilakukan operasi union berikut:<br>L(M<sub>3<\/sub>) = L(M<sub>1<\/sub>) \u222a L(M<sub>2<\/sub>) atau dengan notasi lain:<br>L(M<sub>3<\/sub>) = L(M<sub>1<\/sub>) + L(M<sub>2<\/sub>)<\/p>\n\n\n\n<p>Kita bisa membuat penggabungan atau disini kita sebut mesin M<sub>3 <\/sub>yang menerima bahasa L(M<sub>3<\/sub>) dengan cara:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Tambahkan state awal untuk M<sub>3<\/sub>, hubungkan dengan state awal M<sub>1<\/sub> dan state awal M<sub>2<\/sub> dengan transisi \u03b5.<\/li>\n\n\n\n<li>Tambahkan sate akhir untuk M<sub>3<\/sub> hubungkan dengan state-state akhir M<sub>1<\/sub> dan state-state akhir M<sub>2<\/sub> menggunakan transisi \u03b5.<\/li>\n<\/ul>\n\n\n\n<p>Berikut hasil penggabungan dari M<sub>1<\/sub> dan M<sub>2<\/sub> menjadi M<sub>3<\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"766\" height=\"371\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-22.png\" alt=\"\" class=\"wp-image-1197\" style=\"width:510px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-22.png 766w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-22-300x145.png 300w\" sizes=\"auto, (max-width: 766px) 100vw, 766px\" \/><\/figure>\n\n\n\n<p>Kemudian kita lanjutkan untuk menentukan konkatenasi atau disini disebut L(M<sub>4<\/sub>) = L(M<sub>1<\/sub>) L(M<sub>2<\/sub>) dengan cara:<br>1. State awal M<sub>1<\/sub> menjadi state awal M<sub>4<\/sub><br>2. State akhir M<sub>2<\/sub> menjadi state akhir M<sub>4<\/sub><br>3. Hubungkan state-state akhir M<sub>1<\/sub> dengan sate awl M<sub>2<\/sub> menggunakan transisi \u03b5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"826\" height=\"198\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-23.png\" alt=\"\" class=\"wp-image-1198\" style=\"width:622px;height:auto\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-23.png 826w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-23-300x72.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2025\/05\/image-23-768x184.png 768w\" sizes=\"auto, (max-width: 826px) 100vw, 826px\" \/><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Studi Kasus Perhatikan gambar NFA \u03b5-move berikut: Kita akan coba merubah diagram ini ke NDFA tanpa \u03b5-move dengan tahapan yang sudah diberikan pada materi sebelumnya. Langkah 1 Menentukan tabel transisi, kebetulan sudah di gambarkan pada gambar diatas Langkah 2 Menentukan \u03b5-closure untuk setiap state: Langkah 3 Carilah setiap fungsi transisi hasil perubahan dari NDFA \u03b5-move [&hellip;]<\/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-1187","post","type-post","status-publish","format-standard","hentry","category-teori-bahasa-dan-otomata"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NDFA dengan \u03b5-move: Studi Kasus, Penggabungan, dan Konkatenasi - eko&#039;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=\"https:\/\/ekomartantoh.net\/artikel\/2025\/05\/26\/ndfa-dengan-\u03b5-move-studi-kasus-penggabungan-dan-konkatenasi\/\" \/>\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: Studi Kasus, Penggabungan, dan Konkatenasi - eko&#039;s Article\" \/>\n<meta property=\"og:description\" content=\"Studi Kasus Perhatikan gambar NFA \u03b5-move berikut: Kita akan coba merubah diagram ini ke NDFA tanpa \u03b5-move dengan tahapan yang sudah diberikan pada materi sebelumnya. 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