Automata Tutorial Last Updated : 26 Aug, 2025 Comments Improve Suggest changes Like Article Like Report Automata Theory is a branch of the Theory of Computation. It deals with the study of abstract machines and their capacities for computation. An abstract machine is called the automata. It includes the design and analysis of automata, which are mathematical models that can perform computations on strings of symbols according to a set of rules.Why we study Theory of Computation?Regular Expressions (RE) : Used for pattern matching in Linux/Unix command prompt, programming languages and XML/DTD to describe structure.Finite Automata in Modeling Systems : Used in designing and checking models and electronic circuits that operate based on certain rules. Context-Free Grammars (CFG) : Used in Compiler / Programming Language design to describe syntax and natural language processing to describe structure.Mathematical Models : Mathematical understanding of computing devices by mathematically modeling them.Building Block for Quantam Computing: Turing Machines (we study in this subject) are considered a fundamental building block for understanding quantum computation models.Optimizing Algorithm Efficiency : Helps classify problems based (e.g., P, NP, NP-complete, and NP-hard), proving that some problems have no efficient solutions.Understanding Computability : Study of which problems can be solved using algorithms, essentially defining the boundaries of what a computer can calculate.. Problems like the "Halting Problem" which are demonstrably impossible to solve with a general algorithm.Please refer Why we Study Theory of Computation? for details.Automata – IntroductionIntroduction Grammar in Theory of ComputationChomsky HierarchyApplications of various AutomataFinite AutomataFinite Automata Introduction Minimization of DFA Operations on DFA NFA to DFA Conversion Problems on Finite Automata Regular Expressions, Grammar & LanguageRegular Expressions, Grammar & Languages Designing Finite Automata from Regular ExpressionsArden’s TheoremL-graphs and what they representHypothesis (language regularity) and algorithm (L-graph to NFA) How to identify if a language is regular or not Star Height of Regular Expression and Regular LanguageGenerating regular expression from finite automata Kleene’s Theorem Part-1MEALY and MOORE MachinesMealy vs Moore Machine >> Quiz on Regular Languages and Finite AutomataCFG (Context Free Grammar)Relationship between grammar and languageSimplifying Context Free GrammarsClosure Properties of Context Free Languages(CFL)Union & Intersection of Regular languages with CFLConverting Context Free Grammar to Chomsky Normal FormConverting Context Free Grammar to Greibach Normal FormPumping LemmaCheck if the language is Context Free or NotAmbiguity in Context Free GrammarOperator grammar and precedence parserContext-sensitive Grammar (CSG) and Language (CSL)PDA (Pushdown Automata)Pushdown AutomataPushdown Automata Acceptance by Final StateDetailed Study of PushDown AutomataProblems on Pushdown Automata>> Quiz on Context Free Languages and Pushdown AutomataTuring MachineTuring MachineHalting ProblemTheory of Computation | Applications of various AutomataTuring Machine as ComparatorProblems on Turing Machine>> Quiz on Turing Machines and Recursively Enumerable SetsDecidabilityDecidable and undecidable problemsDecidabilityUndecidability and ReducibilityNP-Completeness | Set 1 (Introduction)Proof that Hamiltonian Path is NP-CompleteProof that vertex cover is NP completeComputable and non-computable problems>> Quiz on UndecidabilityQuick Links Last Minute Notes(LMNs)‘Quizzes’ on Theory Of Computation !Recent Articles on Theory Of Computation Comment More infoAdvertise with us K kartik Follow Improve Article Tags : Theory of Computation GateCS2023 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-14 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 ; m,n,p,q>=1}2 min readConstruct Pushdown automata for L = {0n1m2m3n | m,n ≥ 0}3 min readConstruct Pushdown automata for L = {0n1m2n+m | m, n ≥ 0}2 min readNPDA for accepting the language L = {ambncm+n | m,n ≥ 1}2 min readNPDA for accepting the language L = {amb(m+n)cn| m,n ≥ 1}3 min readNPDA for accepting the language L = {a2mb3m|m>=1}2 min readNPDA for accepting the language L = {amb2m+1 | m ≥ 1}2 min readNPDA for accepting the language L = {aibjckdl | i==k or j==l,i>=1,j>=1}3 min readConstruct Pushdown automata for L = {a2mc4ndnbm | m,n ≥ 0}3 min readNPDA for L = {0i1j2k | i==j or j==k ; i , j , k >= 1}2 min readNPDA for accepting the language L = {anb2n| n>=1} U {anbn| n>=1}2 min readNPDA for the language L ={wЄ{a,b}* | w contains equal no. of a's and b's}3 min readTuring MachineTuring Machine in TOC7 min readTuring Machine for addition3 min readTuring machine for subtraction | Set 12 min readTuring machine for multiplication2 min readTuring machine for copying data2 min readConstruct a Turing Machine for language L = {0n1n2n | n≥1}3 min readConstruct a Turing Machine for language L = {wwr | w ∈ {0, 1}}5 min readConstruct a Turing Machine for language L = {ww | w ∈ {0,1}}7 min readConstruct Turing machine for L = {an bm a(n+m) | n,m≥1}3 min readConstruct a Turing machine for L = {aibjck | i*j = k; i, j, k ≥ 1}2 min readTuring machine for 1's and 2’s complement3 min readRecursive and Recursive Enumerable Languages in TOC6 min readTuring Machine for subtraction | Set 22 min readHalting Problem in Theory of Computation4 min readTuring Machine as Comparator3 min readDecidabilityDecidable and Undecidable Problems in Theory of Computation6 min readUndecidability and Reducibility in TOC5 min readComputable and non-computable problems in TOC6 min readTOC Interview preparationLast Minute Notes - Theory of Computation13 min readTOC Quiz and PYQ's in TOCTheory of Computation - GATE CSE Previous Year Questions2 min read Like