Construct a Turing Machine for language L = {0n1n2n | n≥1} Last Updated : 11 Jul, 2025 Comments Improve Suggest changes 26 Likes Like Report Prerequisite - Turing Machine The language L = {0n1n2n | n≥1} represents a kind of language where we use only 3 character, i.e., 0, 1 and 2. In the beginning language has some number of 0's followed by equal number of 1's and then followed by equal number of 2's. Any such string which falls in this category will be accepted by this language. The beginning and end of string is marked by $ sign. Examples - Input : 0 0 1 1 2 2 Output : Accepted Input : 0 0 0 1 1 1 2 2 2 2 Output : Not accepted Assumption: We will replace 0 by X, 1 by Y and 2 by Z Approach used - First replace a 0 from front by X, then keep moving right till you find a 1 and replace this 1 by Y. Again, keep moving right till you find a 2, replace it by Z and move left. Now keep moving left till you find a X. When you find it, move a right, then follow the same procedure as above. A condition comes when you find a X immediately followed by a Y. At this point we keep moving right and keep on checking that all 1's and 2's have been converted to Y and Z. If not then string is not accepted. If we reach $ then string is accepted. Step-1: Replace 0 by X and move right, Go to state Q1. Step-2: Replace 0 by 0 and move right, Remain on same state Replace Y by Y and move right, Remain on same state Replace 1 by Y and move right, go to state Q2. Step-3: Replace 1 by 1 and move right, Remain on same state Replace Z by Z and move right, Remain on same state Replace 2 by Z and move right, go to state Q3. Step-4: Replace 1 by 1 and move left, Remain on same state Replace 0 by 0 and move left, Remain on same state Replace Z by Z and move left, Remain on same state Replace Y by Y and move left, Remain on same state Replace X by X and move right, go to state Q0. Step-5: If symbol is Y replace it by Y and move right and Go to state Q4 Else go to step 1 Step-6: Replace Z by Z and move right, Remain on same state Replace Y by Y and move right, Remain on same state If symbol is $ replace it by $ and move left, STRING IS ACCEPTED, GO TO FINAL STATE Q5 Create Quiz Comment R RishabhMalik Follow 26 Improve R RishabhMalik Follow 26 Improve Article Tags : Misc GATE CS Theory of Computation Explore Automata _ IntroductionIntroduction to Theory of Computation5 min readChomsky Hierarchy in Theory of Computation2 min readApplications of various Automata4 min readRegular Expression and Finite AutomataIntroduction of Finite Automata3 min readArden's Theorem in Theory of Computation6 min readSolving Automata Using Arden's Theorem6 min readL-graphs and what they represent in TOC4 min readHypothesis (language regularity) and algorithm (L-graph to NFA) in TOC7 min readRegular Expressions, Regular Grammar and Regular Languages7 min readHow to identify if a language is regular or not8 min readDesigning Finite Automata from Regular Expression (Set 1)4 min readStar Height of Regular Expression and Regular Language3 min readGenerating regular expression from Finite Automata3 min readCode Implementation of Deterministic Finite Automata (Set 1)8 min readProgram for Deterministic Finite Automata7 min readDFA for Strings not ending with "THE"12 min readDFA of a string with at least two 0’s and at least two 1’s3 min readDFA for accepting the language L = { anbm | n+m =even }14 min readDFA machines accepting odd number of 0’s or/and even number of 1’s3 min readDFA of a string in which 2nd symbol from RHS is 'a'10 min readUnion Process in DFA4 min readConcatenation Process in DFA3 min readDFA in LEX code which accepts even number of zeros and even number of ones6 min readConversion from NFA to DFA5 min readMinimization of DFA7 min readReversing Deterministic Finite Automata4 min readComplementation process in DFA2 min readKleene's Theorem in TOC | Part-13 min readMealy and Moore Machines in TOC3 min readDifference Between Mealy Machine and Moore Machine4 min readCFGRelationship between grammar and language in Theory of Computation4 min readSimplifying Context Free Grammars6 min readClosure Properties of Context Free Languages11 min readUnion and Intersection of Regular languages with CFL3 min readConverting Context Free Grammar to Chomsky Normal Form5 min readConverting Context Free Grammar to Greibach Normal Form6 min readPumping Lemma in Theory of Computation4 min readCheck if the language is Context Free or Not4 min readAmbiguity in Context free Grammar and Languages3 min readOperator grammar and precedence parser in TOC6 min readContext-sensitive Grammar (CSG) and Language (CSL)2 min readPDA (Pushdown Automata)Introduction of Pushdown Automata5 min readPushdown Automata Acceptance by Final State4 min readConstruct Pushdown Automata for given languages4 min readConstruct Pushdown Automata for all length palindrome6 min readDetailed Study of PushDown Automata3 min readNPDA for accepting the language L = {anbm cn | m,n>=1}2 min readNPDA for accepting the language L = {an bn cm | m,n>=1}2 min readNPDA for accepting the language L = {anbn | n>=1}2 min readNPDA for accepting the language L = {amb2m| m>=1}2 min readNPDA for accepting the language L = {am bn cp dq | m+n=p+q ; 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