Decidability Table in Theory of Computation Last Updated : 11 Jul, 2025 Comments Improve Suggest changes 8 Likes Like Report Prerequisite - Undecidability, Decidable and undecidable problems Identifying languages (or problems*) as decidable, undecidable or partially decidable is a very common question in GATE. With correct knowledge and ample experience, this question becomes very easy to solve. A language is undecidable if it is not decidable. An undecidable language maybe a partially decidable language or something else but not decidable. If a language is not even partially decidable , then there exists no Turing machine for that language. In this topic you will see Decidability table and shortcut to learn them. Intersection of 2 recursively enumerable languages is recursively enumerable, so it is decidable. ProblemsRLDCFLCFLCSLRec.LRELDoes 'w' belongs to language L? (i.e, membership problem, where 'w' is any string)DDDDDUDIs L= null? (i.e, emptiness problem)DDDUDUDUDIs L= E* ? (i.e, completeness problem.where, E* is set of all languages possible over given alphabet)DDUDUDUDUDIs L1= L2 ? (i.e, equality problem. L1 and L2 are languages of same type.)DDUDUDUDUDIs L1 subset of L2 ? (i.e, subset problem)DUDUDUDUDUDIs L1 intersection of L2= null?DUDUDUDUDUDIs 'L' finite or not? (i.e, finiteness problem)DDDUDUDUDIs complement of 'L' a language of same type or not?DDUDDDUDIs intersection of two languages of same type or not?DUDUDDDDIs 'L' regular language or not? ('L' is any language.)DDUDUDUDUD In the above table, 'RL' implies Regular language. 'CFL' implies Context free language. 'DCFL' implies deterministic context free language. 'CSL' implies Context sensitive language. 'REC.L' implies Recursive language. 'REL' implies Recursive enumerable language. 'D' implies that the problem is decidable. 'UD' implies that the problem is undecidable. Note: Regular language: It Decidable for all problems.CFL: It is decidable for emptiness problem, finiteness problem, and membership problem.CSL and REC.L: Both are decidable for membership problem, Is complement of 'L' a language of same type or not?, and (Is intersection of two languages of same type or not?.REL: It is decidable for (Is intersection of two languages of same type or not?)DCFL It is decidable for everything decidable in CFL plus (Is complement of 'L' a language of same type or not?), (Is 'L' regular language?). Create Quiz 49. Decidability Chart in TOC Visit Course Comment N nidhi1352singh Follow 8 Improve N nidhi1352singh Follow 8 Improve Article Tags : 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 ; 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