Eligibility:

• Decidable language. When you generate all strings from length 0 to n , if the machine accepts any of them then the language is non-empty. answered Apr 11 Sorted by: If a language decidable by a PDA then it is also decidable by a TM. , the class of languages decidable by PDA is a proper subclass of the class of languages decidable by TM. 2. (Since TM halts on all input, we can have a different TM that flip-flops reject/accept. This one is easy. Let a language be any set of strings (or words) over a given finite alphabet. That L ∈ L D(TM) ⇐⇒ L ∈L D(TM). Decidable Language. You actually do not need the diagonalization language to show that there are undecidable problems as this follows already from a combinatorical argument: You can enumerate the set of all Turing machines (sometimes called Gödelization). Some very much important properties of a context-free language is: Regularity- context-free languages are Non-Regular PDA language. Since this is decidable, we know that either w ∈ A w ∈ A or w ∈ B w ∈ B. Share. Anyway, the problem of testing whether a CFG generates all the strings of the language 1∗ 1 ∗ is truly decidable. Wikipedia gives one example here: P is a class of languages, not a class of algorithms. model, it is time to discuss some examples of decidable languages. Using this definition: If L1 and L2 are decidable, then algorithms (or Turing machines) M1 and M2 exist, so that: M1 accepts all Jul 5, 2020 · This seems like a nice way to study decidable languages, and curious to know if this direction is indeed interesting and whether there are articles published regarding these questions Thanks for any help Mar 31, 2022 · Every Turing-decidable language is Turing-acceptable. Comment. The following language is decidable L = fhDijx111y 2L(D) for at least one x;y 2 g Proof. If a language is decidable, then there exists a decider M for it. A Turing Machine decides a language if it rejects every string it doesn’t accept – i. These hypotheses have the drawback that even the membership problem is undecidable. The set R is the set of all decidable A recognizer of a language is a machine that recognizes that language. (Hint: Σ ∗ is decidable. edu Mar 18, 2023 · Learn how to categorize languages based on Turing machines and their complements. DFA is decidable, so is L. A language ‘L’ is said to be recursively enumerable if there exists a TM which accepts and halt for all input in ‘L’. They always halt and decide whether to accept or reject the input. The language of a Turing machine M, denoted L ( M), is the set of all strings that M accepts: Decidable Languages A language L is called decidable iff there is a decider M such that (ℒ M) = L. proof. In the other hand, it is possible and not hard to find some languages that are not recursive or even not recursively-enumerable. –L s iTuring-decidable if there is some TM that decides L. a) Construct the mapping reduction function. Jul 16, 2019 · Whether a language is decidable or a language is decided by a TM is an entirely different although closely related concept. A language is decidable if there is an algorithm (i. We reserve the term algorithm for this class of problems. These are also called theTuring-decidable or decidable languages. Mar 31, 2022 · Every Turing-decidable language is Turing-acceptable. In both cases, there exists an algorithm that, given a word, returns \yes" or \no A language L is decidable if there exists a decider D such that L(D) = L R. The algorithm you are describing shows that the problem of testing whether a CFG generates some string from 1∗ 1 ∗ is decidable (e. See how to solve problems by reducing them to known undecidable problems. Feb 25, 2019 · 1. Any undecidable language, such as the halting problem, cannot be in NP. T decides a language L if T recognizes L, and halts in all inputs. Bottom line: For every \strictly semi-decidable language", its complement cannot be semi-decidable. Let A be a decidable language with A ≠ ∅ and A ≠ ∅. `It should be in the text of your question, explaining why you are doing all that. But may or may not halt for all input, which are not in ‘L’. 2 on input hA;wi 3 If N accepts accept; otherwise reject. We also show that the same languages ARE closed under inverse homomorphism. 1. However, we only know of one TM (M) that does not decide L 3. , have an algorithm) if the language Apr 3, 2013 · Every regular language is Turing-decidable and therefore Turing acceptable / recognisable (but note that Turing acceptable does not imply Turing decidable). pdx/~harry #decidability_and_undecidability#abhilashav#automata Aug 16, 2021 · Here we show that decidable languages are not closed under homomorphism. Why is the set of decidable languages, R, a subset of the set of recognizable languages, RE? A decider for a language is also a recognizer for that language, so every decidable language is also recognizable. You can probably code such an algorithm yourself in your favorite programming language. Let A A and B B be semi decidable languages. • The classes of Turing-recognizable and Turing-decidable languages are different. Microsoft PowerPoint - class17. A language (or problem) is in P if there is some Turing machine that decides it in a polynomial number of steps. . Turing decidable means it halts in an accepting state if the input word is in the language, and halts in a rejecting state if the word is not in the language, Turing recognizable means it halts in an accepting state if the word is in the language, and in a rejecting state or fails to halt if the word is not in the language. Although it might take a long time, M will accept or reject w. A decideable language is a language that can be recognized by a Turing machine that always halts. Here we look at the language THREE_DFA, which is the set of all DFAs that accept at most three strings. For the proof, note first that if L L is finite then all its subsets are finite and so decidable. These languages will have a somewhat different character from most of the lan-guages we discussed previously in the course; their definitions are centered on May 30, 2015 · $\begingroup$ Thanks. Languages recognized by a TM are called recognizable. PROOF Note R is already a string!! Convert R to an NFA and use Theorem 4. T's states will be similar to D's. Decidable Language : EQ. Modified 6 years, 1 month ago. Furthermore, if L1 and L2 are decidable languages, then their intersection L1 ∩L2 is decidable, since we can accept if both the Turing machines for L1 and Aug 29, 2016 · E(dfa) is a decidable language. Apr 11, 2017 · Rather, it proves that every decidable language is itself recognizable. Jun 28, 2021 · Identifying languages (or problems*) as decidable, undecidable or partially decidable is a very common question in GATE. In Theorem 3. • Obviously. Viewed 2k times 1 $\begingroup$ May 26, 2021 · Context-Free Language (CFL) is a language which is generated by a context-free grammar or Type 2 grammar (according to Chomsky classification) and gets accepted by a Pushdown Automata. We rst note the following: L 2 is a regular language that can be recognized by a DFA Dec 12, 2018 · Context-free languages are not regular but decidable; on the other hand recursively enumerable languages are not regular and only semi-decidable. That is, a decider T is guaranteed to either accept, or reject, and never fall into an infinite loop. With correct knowledge and ample experience, this question becomes very easy to solve. Alternative: M M accepts a language iff M M halts on w w iff w ∈ L w ∈ L. A set L is called semi-decidable if there exists an algorithm that: { given a word w, { returns \yes" if and only if the word w belongs to the language L. This comparison explains where the term \semi-decidable" (i. A language is decidable if there is a Turing Machine that halts and accepts strings that belong to the language, and halts and rejects strings that do not belong to the language. Reduce undecidable language to decidable language? Ask Question Asked 6 years, 1 month ago. Let B be a language with B ≠ ∅ and B ≠ ∅. Jul 2, 2021 · In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language, a W -index. A theory is a set of formulas, often assumed to be closed under logical consequence. In other words TM are more computationally powerful than PDA, i. we could represent DFA B by its five components: Q, Σ, δ, q0, F. Regular languages are decidable: given any two regular languages A and B, an algorithm can determine whether A and B contain the same strings. May 7, 2018 · The language of all binary representations of prime numbers is decidable since there is an algorithm that decides whether an integer is prime. The set R is the set of all decidable languages. Given a decider M, you can learn whether or not a string w ∈ (ℒ M). Improve this answer. Corollary The complement of HALT is not CE. Although it might take a staggeringly long time, M will eventually accept or reject w. Proof: we know that HALT is CE but not decidable if complement of HALT wereCE, then HALT is CE and co-CE hence decidable. In this way any story can be regarded as a "word". Dec 17, 2004 · decidable problem. ) Language is Turing recognizable if some Turing machine recognizes it •Also called “recursively enumerable” Machine that halts on all inputs is a decider. Between these two types are the recursive non-context-sensitive languages. 2 P = “On input hR;wiwhere R is a regular expression 1 Convert R to an equivalent NFA A, using the Regular Expression-to-NFA procedure 2 Run TM N in Thm 4. You can also easily simulate a PDA on a TM. That is what is needed so that people understand what you are at. , have an algorithm) if the language Decidable languages Atri Rudra May 26 A. Definition: A language is called decidable For example, one may speak of languages decidable on a non-deterministic Turing machine. For a correct proof, need a convincing argument that the Aug 10, 2019 · 2. That means, in particular, that if you choose a language at random, with probability 1 you choose a language not in P or NP. To prove a language is decidable, we can show how to construct a TM that decides it. If we would have printed \(\fbox{Y}\), then halt on an accept state. Also known as totally decidable problem, algorithmically solvable, recursively solvable. 10) Jul 2, 2021 · In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language, a W -index. I want to show that B B is decidable. 1. Turing-acceptable Languages (1) ¶. with infinite tape but in finite time)? This is, are there words, w, in a decidable language for which cannot be determined a bound f(|w|)? Deciding a CSL is independent of whether there are non-terminating LBA: there only has to exist an LBA for it. Dec 18, 2015 · $\begingroup$ Don't know about hangs, that is an unnecessary concept. 21 we showed that a language is Turing-recognizable iff some enumerator enumerates it. , see here at page 21). If you have Turing machines P1 P 1 and P2 P 2 that recognize L1 L 1 and L2 L 2, then you can recognize any language obtained by elementary set operations on L1 L 1 and L2 L 2 by running P1 P 1 and P2 P 2, obtaining their results, and then computing A recursive language is a formal language for which there exists a Turing machine that, when presented with any finite input string, halts and accepts if the string is in the language, and halts and rejects otherwise. A decider of a language is a machine that decides that language. Let me quote the definition in the book introduction to the theory of computation by Michael Sipser. All languages in P and NP are decidable. Therefore, whenever an ambiguity is possible, the synonym used for "recursive language" is Turing-decidable language, rather than simply decidable. However, you were asking about something else. when M receives input, checks whether it properly represents DFA B and string w. • Decidable Languages • decidable problems concerning regular languages • decidable problems concerning context-free languages • The Halting Problem • The diagonalization method • The halting problem is undecidable • A Turing unrecognizable languages Theory of Computation, Feodor F. Σ* is a set of all possible strings. • But the other direction does not hold---there are languages that are Turing-recognizable but not Turing-decidable. A decidable language • To show that a language is decidable, we have to describe an algorithm that decides it ‣We’ll allow informal descriptions as long as we are confident they can in principle be turned into TMs • Consider ADFA = { M,w ⃒M is a DFA that accepts w } • Algorithm: Check that M is a valid encoding; if not reject. 2. Since its a decider, it halts on all inputs. Thus, you have only countable many decidable languages. See alsoundecidable problem, NP, NP-complete Concatenation: if you have deciders for two decidable languages then you can get a decider for the concatenation of those languages by nondeterministically guessing in the first decider when you have read the part of the string from the first language, and then checking whether the remainder is a string in the second language. Proof: A DFA accepts some string iff reaching an accept state from the start state by >traveling along the arrows of the DFA is possible. See full list on cs. 18. I am supposed to identify why closing a Turing Recognizable language under some operation is trickier to prove than when dealing with Turing Decidable languages. Koether Homework Review Closure Properties of Decidable Languages Intersection Union Closure Properties of Recognizable Languages Intersection Union Assignment Homework Review Exercise 3. L ∈ R iff L is decidable May 7, 2018 · The language of all binary representations of prime numbers is decidable since there is an algorithm that decides whether an integer is prime. E DFA will be the foundational piece for proving that other DFA properties are decidable. (Sipser Q. f. Lets start with some definitions:- Decidable language -A decision problem P is said to be decidable (i. How to use decidable in a sentence. Decidability for a theory concerns whether there is an effective procedure that decides whether the formula is a member of the theory or not, given an arbitrary formula in the signature of the theory. • Theorem 2: If L is Turing-decidable then L is Turing-recognizable. Prove that A ≤m B. However not all languages are decidable by PDA. The alphabet could consist of the symbols we normally use for communication, such as the ASCII characters on a keyboard, including spaces and punctuation marks. A Language ‘L’ is decidable if it is a recursive language. A language L is decidable if there exists a TM. Languages decided by a TM are called decidable. 3 Decidable DFA Properties Lemma 3. Here is a more general statement: A language L L has an undecidable subset iff L L is infinite. Regular Languages are Decidable. Undecidability of Universal Languages: The universal language L u is a recursively enumerable language and we have to prove that it is undecidable (non-recursive). T= "On input , where A is a DFA: 1. It also halts on all input, and accepts the complement of A. A language L is decidable if and only if L is CE and L is co-CE. This shows that almost all languages are undecidable, however, it does not give us an explicit undecidable language. DFA. – If w ∉ L, M enters qReject. Construct a DFA C from A and B, where C accepts only those strings accepted by either A or B but not both (symmetric difference) If A and B accept the same language, then C will accept nothing and we can use the previous proof (for EDFA) to check for this. The recursive languages = the set of all languages that are decided by some Turing Machine = all languages described by a non-looping TM. In this lecture we will focus on examples based on finite automata and context-free grammars. In other words, the machine does not halt if w w is not in L L. To test this condition, we can design a >TM T that uses a marking algorithm similar to that used in Example 3. $\endgroup$ – vzn May 8, 2015 at 17:05 Nov 29, 2021 · Identifying languages (or problems*) as decidable, undecidable or partially decidable is a very common question in GATE. I know you're stuck, but you should at least have a strategy of what you want to do. Conversely, if L L is infinite then it has uncountably many subsets. a Turing Machine decider) to recognize it. posted in Theoretical Computer Science on April 15, 2020 by TheBeard. EQDFA={(A,B)|A and B are DFAs and L(A)=L(B)} Proof idea. I have a language $\qquad\displaystyle L = \{ (R(M_1), R(M_2 Apr 7, 2016 · The question stems from the fact that you can determine whether a regular language is empty by using a Turing machine to count the states n in the given FSM. The problem of decidability arises Apr 8, 2021 · Identifying languages (or problems*) as decidable, undecidable or partially decidable is a very common question in GATE. imagine writing a program to carry out the simulation. A Decider also halts if the string is not in the language. A is a decidable language if there exists a Computational Model (such as Turing Machine) M such that for every string w that belong to Σ*, the following two conditions hold: If w belongs to Every Turing-decidable language is Turing-acceptable. A decider that recognizes language L is said to decide language L Language is Turing decidable, or just decidable, if some Turing machine decides it 2 Example non-halting machine "Theory of Computation"; Portland State University: Prof. Rao, CSE 322 2 Closure Properties of Decidable Languages Decidable languages are closed under ∪, °, *, ∩, and complement Example: Closure under ∪ Need to show that union of 2 decidable L’s is also decidable Let M1 be a decider for L1 and M2 a decider for L2 The meaning of DECIDABLE is capable of being decided; specifically : capable of being decided as following or not following from the axioms of a logical system. (definition) Definition: A decision problem that can be solved by an algorithm that halts on all inputs in a finite number of steps. 3. Decidable languages are closed under ∪ , °, *, ∩ , and complement Example: Closure under ∪ Need to show that union of 2 decidable L’s is also decidable Theorem: ADFA is a decidable language. Mar 30, 2023 · 8. Both types of machine halt in the Accept state on strings that are in the language. What Decidable Means. Built using years of behavioural economics, analytics, natural language generation, insight delivery and storytelling expertise. Rudra, CSE322 3 Please remember… I want to show you the “cool” stuff There are problems that are Jun 14, 2021 · Recursively Enumerable languages −. This is related to the language INFINITE_DFA in that Engineering. Let L 2 = 111 . (2 points) Must L 2 − L 1 be Turing-recognizable? Prove your answer. "-" denotes set subtraction. Dragan, Kent State University 2 Decidability. cs. It is arguable that most languages created to describe everyday problems are context-sensitives. Decidability and Semi-Decidability. e. Nov 20, 2019 · Prerequisite - Undecidability, Decidable and undecidable problems Identifying languages (or problems*) as decidable, undecidable or partially decidable is a very common question in GATE. First, all context-sensitive languages are decidable, since they can be accepted by a LBA (as you said), and a Turing machine is more powerful than a LBA. Every Turing-decidable language is Turing-acceptable. A language is decidable if it's both recognizable and co-recognizable, and a decider is a TM that always halts. Rudra, CSE322 2 Announcements Handouts Sample final List of topics for the finals H/W #8 Remember your lowest H/W grade will be dropped Turn in your H/W #7 Pick up graded H/W #6 at end of class A. Feb 26, 2018 · Show that single-tape TMs that cannot write on the portion of the tape containing the input string recognizes only regular languages. Follow edited Apr 11, 2017 at 9:13. In this paper, we use a different system which allows for naming arbitrary decidable languages, namely programs for characteristic } A language is decidable if and only if it is Turing-recognizable and co-Turing-recognizable Assume language A is decidable. ) Mar 4, 2017 · So in my courses, it was perfectly acceptable to provide an algorithm in a programming language or pseudo code. The associated language is called a decidable language . Run M on w. A Turning Machine which halts and never goes to the infinite loop is called Deciders. Turning Machine - Decidable Language. Computer Science questions and answers. , \half-decidable") comes from. Feb 13, 2022 · 2. Suppose you are given a DFA D such that L = L(D). May 2, 2021 · The negative answer to decidable = non-contracting grammar? suggests the following question: Is there a decidable language that can be recognized only by a space unrestricted Turing Machine (i. Closure properties : Jun 18, 2022 · A few things, It's hard to find what your proof attempt is trying to do. So sadly only knowing about the non-regularity of a language does not help with determining its decidability. Firstly, I would like to know if the following approach works: First, we can check if w ∈ A ∪ B w ∈ A ∪ B. We know that if a language L is decidable, then the complement L¯¯¯¯ is also decidable, since we can simply reverse the accept and reject conditions in the Turing machine deciding L. , have an algorithm) if the language EQDFA is a Decidable Language. Jul 10, 2020 · 5. In this paper, we use a different system which allows for naming arbitrary decidable languages, namely programs for characteristic Jan 5, 2023 · The recursive languages (RL) are ones for which there is a TM that accepts the language, always halting with an accept/reject answer. A language of Turning Machine L (M), is called decidable if there is a Turning machine M, which decides a A language is Turing-decidable, or simply decidable,if some Turing machine decides it. Aug 3, 2023 · Learn the definitions and examples of decidable, undecidable, partially decidable, recursive and recursively enumerable languages in Theory of Computation. Otherwise, the class of problems is said to be unsolvable or undecidable. However, there are arbitrarily inefficient algorithms to determine I am really struggling with determining the decidability of languages and cant figure out whether this problem is decidable or not. It always halt in accept or reject states. Computer Science. So, for example, determining whether a graph is connected is in P, since a TM can determine that efficiently. A homomor a decidable language. Decidability of a theory. Contradiction. One can construct a Turing Machine T that simulates D. An undecidable language ma Decidability is defined as follows: Σ is a set of alphabet and A is a Language such that A is proper subset of Σ*. Since there are only countably many decidable languages, some subset of L L The class of problems which can be answered as 'yes' are called solvable or decidable. Harry Porter; www. Maybe you're confusing two different problems. A decidable language, in computer science, is a language for which there exists some algorithm that can determine, in a finite amount of time, whether a given string belongs to the language or not. Describe an algorithm that decides the language (L1 ∪ L2) − (L1 ∩ L2) using deciders for L1 and L2. Given a decider M, you can learn whether or not a string w ∈ L(M). A language is undecidable if it is not decidable. Since M was a A decidable language in computer science is a language that allows for infinite loops and does not require clear-cut decision-making. The class of all recursive languages is often called R, although this name is also used for the class RP. To prove regularity, it’s most of the time easiest to just provide a regular expression that constructs the language. ” ( LECTURE 15) SLIDES FOR 15-453 Sep 8, 2014 · There are uncountably many languages, but only countably many languages in P and NP. first, examine input <B,w>. A language L is called decidable if there is a decider M such that L( M) = L. May 7, 2015 · $\begingroup$ more general, whether one can recognize a language in a complexity class with advice versus (not with) that same complexity class. Let L 1 be a decidable language, and let L 2 be a language which is Turing-recognizable but not decidable. g. Jul 28, 2015 · Given 3 disjoint Turing-recognizable languages prove that one of them is decidable 2 Does showing a problem and its complement are not Turing-decidable means that the language & its complement are not Turing-recognizable? The existence of undecidable languages follows by a counting argument: The set of all languages is uncountable whereas the set of decidable languages is countable. M such that for all strings w: – If w ∈ L, M enters qAccept. , it never loops. 23. 6, page 160. if not, M rejects. The decision algorithm exploits the fact that set operations can be performed on regular languages, based on transformations of finite automata. Note that any language that is recognisable is also decidable (but not the other way around). Construct a new Turing machine M which is just M but we swapped its accept and reject state. All decidable languages are recursive languages and Decidable and Recognizable Languages Robb T. Question: Let L1 and L2 be decidable languages. Decidable languages are closed under complement. wellesley. Regular Expressions. For a correct proof, need a convincing argument that the First we show that the decidable languages are closed under complement. Jun 14, 2021 · Hence, let us first see what do you mean by decidable language. b) Prove that your function has the mapping reduction property. Turing-decideable: M M accepts a string w w if M M halts on a final state for the input w w, and rejects a string if it halts on a non-final state. 4. Moreover, A ∪ B A ∪ B and A ∩ B A ∩ B are decidable. 1 Proof that $\textit{INFINITE}_{\text{DFA}}$ is decidable. (2 points) Must L 1 − L 2 be Turing-recognizable? Prove your answer. Cite. Jan 26, 2018 · TOC: Decidability and UndecidabilityTopics discussed:1) Recursive Languages2) Recursively Enumerable Languages3) Decidable Languages4) Partially Decidable La 3 was not decidable, no possible Turing machine could decide L 3. These are also known as decidable languages. ss qo me zk fn jv qp pv eb zd