Undecidable Cfl Problems, But why finiteness property is decidable inspite having .

Undecidable Cfl Problems, Undecidable problems about CFL's Deepak D'Souza Department of Computer Science and Automation Indian Institute of Science, Bangalore. To do this, we will use Greibach's theorem: . , Later we'll develop a theory that allows us to prove rigorously that there are problems that cannot be solved by any algorithm that can be implemented as a computer program. Recursive Languages2. Which of the following problems is undecidable ? Q4. Problem 3: describe algorithms to test whether an arbitrary string is an element of a context free language, (i. I understand that: Deciding whether a CFG $G$ is ambiguous is undecidable. It is decidable whether a context-free grammar G generates (or a PDA N accepts) any strings at all, that is, whether L (G) = /0 (or L (N) = It is a well-known fact that the following problem is undecidable: Question: Is $L (D) = L (G)$? This question is undecidable even when it is promised that $L (D) = \Sigma^\star$ when $|\Sigma| \ge 2$. 'CFL' implies Context free language. The question here is ambiguous. If we consider a DCFL like a^n b^2n / n>=1, here we Undecidable Problems About CFLs In this lecture we show that a very simple problem about CFLs is undecid able, namely the problem of deciding whether a given CFG generates all strings. 3 If L1 = L2 then L1 $\cap$ L2' = $\phi$ So the above problem can be written as CFL $\cap$ RL = $\phi$ or CFL = $\phi$ which is decidable. I know that generation of a particular string by a given CFG is a decidable Determining whether the complement of a context-free grammar is also context-free is a non-trivial problem. But here you can simply reduce from halting problem and assume it is known as undecidable. Otherwise, identity L1 L2 = L1 L2 ∩ ∪ would imply CFLs are closed under intersection, which is a contradiction. Undecidable Problems about Context-Free Languages You are given two CFGs G and G′. L = { <G1, G2> | G1 & G2 are regular grammar and L (G1) ⊆ L (G2)} True. Recursively Enumerable Languages3. In order to prove that a decision problem is undecidable for a certain model, we typically need to use a special technique known as a reduction, which we will study in greater depth later. 6 of the not decidable. Subset problem is decidable for regular grammars. Hence it is proved that the regularity of CFL is undecidable. So obviously we can CSL and Recursive languages also which Undecidable Problems About CFLs In this lecture we show that a very simple problem about CFLs is undecid able, namely the problem of deciding whether a given CFG generates all strings. Based upon this property, problems are classified as Decidable Here we show all closure properties of all language classes in the theory of computation class (regular, CFL, decidable, recognizable) as well as all decidability and undecidability results (A_X Decidable and undecidable problems on context free grammars. The PC Problem input: two sets of n strings: A = w 1, w 2, CFG here stands for context-free grammar. 2 & 5. Given an instance M of FIN, construct a CFG G such that L(G) = :VALCOMPSt M. 22 November 2016 1 Some Decidable/Undecidable problems Undecidable Problems about Context-Free Languages You are given two CFGs G and G′. If the problem is L (G1)∩L (G2)= Empty , then if G1 and G2 are both cfl's then is it decidable ? According to me it should be decidable since if the intersection is regular then we can DCFL and Non-deterministic CFL both are not closed under intersection, and thus makes the problem undecidable. 19 November 2015 1 Some Decidable/Undecidable problems Regularity of the language generated by a CFG The proof that regularity of the language generated by a CFG is undecidable is very similar to the proof that universality of the I am trying to prove the fact that every CFL is decidable, however I can't come to terms with what the statement exactly means. It may or may not be. I read that it is decidable for DCFL and undecidable for CFL. i said you're asking decidability of 'non emptiness of CFL' We know emptiness for CFL is decidable and non-emptiness is Usually, the "reason" problems become undecidable is that there is some underlying infinite configuration space. The majority of arithmetic expressions are produced using Context How can a CFL be given? If it is given as the language generated by a CFG, then the problem is undecidable. 25 November 2021 1 Some Decidable/Undecidable problems Preview text UNIT- Undecidable Problems: A problem is undecidable if there is no Turing machine which will always halt in finite amount of time to give answer as Which of the following problems is undecidable? Membership problem for CFGs Ambiguity problem problem for FSAs Equivalence problem for FSAs But no such algorithm exists that given a CFL whether it is ambiguous or not. However, if L is a CFL, and L′ is In mathematics, the convergence condition by Courant–Friedrichs–Lewy (CFL) is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) Abstract If a Turing machine can solve any problem that can be solved by algorithms, then we can exploit TMs to explore the boundaries of what This question is undecidable. Specifically, we need to check if the 21. You can use the method in (2) and (3) to prove Undecidable problems about CFL's Deepak D'Souza Department of Computer Science and Automation Indian Institute of Science, Bangalore. Problem can be reduced to checking if L (G) ∩ ( L (R))' = phi. 22 November 2018 1 Some Decidable/Undecidable problems Unlike the RL, many questions about the CFL cannot be answered. Conclusion In conclusion, decidable and undecidable problems highlight the boundaries of what computers can and cannot solve. This result highlights the limitations of algorithmic approaches in formal This document discusses closure properties and decision properties of context-free languages. A. C) Now coming to C). This can be done by just adding Problem 2 describe algorithms to test whether the language generated by a CFG is empty. Decidable and Undecidable Problem || Decidability || Undecidability || Theory of computation Intuitively, the problem is that no TM for HALTTM can always reject (<M>, w) when M loops on w. Prove that the following problems are undecidable. Dive into the fascinating world of Context-Free Languages (CFLs) and their decision properties! This video breaks down the crucial concepts of decidable and undecidable COMP-CFL = fG j :G is a CFG and L(G) is a CFLg. 'CSL' implies Context sensitive UndecidableProblemsforContext-freeGrammars Undecidable Problems for Context-free Grammars Hendrik Jan Hoogeboom Universiteit Leiden (NL) Abstract. deciding regular languages and CFL’s Undecidable problems. So HALTTM is semi-decidable+; our first example of such a language. The answer will be Yes or Problem mentioned in option (2) Ambiguity problem for context-free grammar (CFGS) is undecidable. Due to this equality problem is undecidable. But why finiteness property is decidable inspite having Decidability of CFL Equivalence with Fixed Regular Language Ask Question Asked 1 year, 5 months ago Modified 1 year, 4 months ago Although emptiness is decidable for both DCFLs and CFLs, however CFLs are not closed under complementation. Hence our assumption was false. We will see whether these problems are solvable in CFG or not. Interestingly, however, there are some languages which have structures that cannot be captured by CFL’s. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Now L (R)' is regular, so it also CFL and determining Undecidable problems about CFL's Deepak D'Souza Department of Computer Science and Automation Indian Institute of Science, Bangalore. Yes you are correct, a Turing machine cannot decide whether a context-free language is ambiguous or not, and this can be reduced from the post correspondence problem, We know that every $CFL$ has infinite configuration space. Note: TOC: Decidability and UndecidabilityTopics discussed:1. Let us a call a linear language a language recognized by a linear grammar. That does not seem correct. for eg: problem: Is intersection of two CFL is CFL or not? as CFL/DCFL is not closed under intersection. Given a TM M, modify it in a way that it makes atleast 3 moves on every input, without changing the language M accepts. Deciding whether a CFL $L$ is inherently Equality problem is checking if 2 DCFL's or CFL's are producing same language. Is the problem that intersection of two cfl is a cfl or not undecidable? Ask Question Asked 9 years, 5 months ago Modified 9 years, 5 months ago But we know emptyness problem for CSL is undecidable. Decidable Languages4. It falls under the broader class of problems known as language containment Is this problem decidable: "Is the intersection of two context free languages also context free?" Does all questions asking if operation on two languages of same type, not closed under that operation, result It is well known that the equivalence problem is undecidable for general context-free languages. Hence, decidable in case of DCFLs. Explanation:- The ambiguity of grammar is undecidable, Topics Decidability Undecidability Halting Problem Other undecidable Problems Post Correspondence Problem Undecidable Problems for CFL's Reduction Closure Properties of CFL's A Context Free Language (CFL) is a language produced by a Context Free Grammar, according to formal language theory (CFG). We show a reduction FIN m I-CFL. 31 We are given a CFG G, so we can construct a grammar G’ that has all the rules in G. then is this true saying that not following Properties of CFL 1. And this may take infinite time as we exactly know which string is 4. Concept: In this section, we want to prove that every CFL(without e )can be Undecidable problems about CFL's Deepak D'Souza Department of Computer Science and Automation Indian Institute of Science, Bangalore. Undecidable Problems About CFLs In this lecture we show that a very simple problem about CFLs is undecid able, namely the problem of deciding whether a given CFG generates all strings. The catch is to find a string which has two derivation trees. We discuss some basic undecidable problems for context-free lan-guages, starting from Valid and invalid computations of TM’s: a tool for prov-ing CFL problems undecidable, Section 8. , the acceptance problem deal-ing with the context In this chapter, we will cover some interesting decision problems related to Context-Free Grammars (CFGs). e. Undecidable CFL Problems We say a problem that cannot be solved by any Turing machine is undecidable. So the answer should be decidable according to me but my Such problems are called undecidable. It also follows from Rice's theorem of no ,no i don't mean this , it's irrelevant from what i said. That is, there are many undecidable problems about CFL’s. We discuss some basic undecidable CFL Fullness is Undecidable Theorem It is undecidable whether a context-free grammar G generates (or a PDA N accepts) all strings, that is, whether L (G) = Σ∗ (or L (N) = Σ∗) or not. The set of turning machine codes for TM's that accept all inputs that are palindromes (possible along with some other Conclusion The problem of determining whether two context-free grammars are equivalent is undecidable. Q3. For now, we will Contents Decidable Languages decidable problems concerning regular languages decidable problems concerning context-free languages The Halting Problem The diagonalization method The halting In this lecture we show that a very simple problem about CFLs is undecidable, namely the problem of deciding whether a given CFG generates all strings. However, all proofs of this fact that I am aware of seem to involve some ambiguous context-free But what if language is not closed under the operation. For CFLs we have to look for a Undecidable problems about CFL's Deepak D'Souza Department of Computer Science and Automation Indian Institute of Science, Bangalore. Useful to have an This paper discusses some basic undecidable problems for context-free languages, starting from Valid and invalid computations of TM’s and improves this to linear grammars as an application of the Problem 4. The problems for which we can’t construct an algorithm that can answer the problem correctly in finite time are termed as Undecidable Problems. Some of these CFL problems are decidable, some are not. There is no algorithm that can solve an undecidable problem. For example, in Dutch, it is possible to have this kind of structure, which loosely mirrors the Undecidability Problems for which no algorithm exist is called as undecidable & if algorithm exist is called as decidable. However, there are some exceptions such that we want to delete rules that include A on the left hand In this context hence it is an undecidable issue whether given a language which is a CFL , the complement will also be a CFL. In this lecture we show that a very simple problem about CFLs is undecidable, namely the problem of deciding whether a given CFG generates all strings. 24 November 2014 1 Some Decidable/Undecidable problems #ContextFreeGrammar #TheoryOfComputation #ClosureProperties #TOC #AutomataTheory 1. This is not mathematically accurate, but it's a good intuition. No. This is Decidable Problems Concerning Context-Free Languages Topics Problem 1: describe algorithms to test whether a CFG generates a particular string Problem 2 describe algorithms to test whether the Is L (G) subset of L (R) decidable ? Where G is CFG and R is regular grammar. As in t e previous problem, we can show FIN m COMP-CFL. CFL Fullness is Undecidable Theorem It is undecidable whether a context-free grammar G generates (or a PDA N accepts) all strings, that is, whether L (G) = Σ∗ (or L (N) = Σ∗) or not. Using the notation of the Context-free language and undecidable Ask Question Asked 10 years, 4 months ago Modified 10 years, 4 months ago What about inherent ambiguity of bounded CFLs? I suspect the answer is either "undecidable" or "open problem", since people have developed techniques to show that specific Decision Algorithm for CFL Finiteness The core idea behind deciding if a CFL is finite involves examining the structure of its context-free grammar (CFG). Post-Correspondence Mar 22, 2022 We need a tool to prove some CFL problems are undecidable => the post correspondence (PC) problem. We shall see that several Answer: d Explanation: These properties are termed as decision properties of a CFL and include a set of problems like infiniteness problem, emptiness problem and Concept A problem is said to be Decidable if we can always construct a corresponding algorithm that can answer the problem correctly. Partially Decidable La Are they closed under complement? The answer is no. Some simple decision problems in the realm of CFLs turn out to be undecidable: Is a given CFG ambiguous? Is any CFG for a given CFL necessarily ambiguous? Is Decidability Decidable Languages decidable problems concerning regular languages decidable problems concerning context-free languages The Halting Problem The diagonalization method The Why we always talk about the amibuity of CFL What about the amibuity of CSL, Recursive language and Recursive enurmerable language. Given M and x, describe 2 PDA's that accept computations of the form: c0 # c1 Abstract. 27 November 2013 1 Some Decidable/Undecidable problems Solved MCQs for Unit 3, with PDF download and FREE mock test Decidable and Undecidable Languages The Halting Problem and The Return of Diagonalization Friday, November 11 and Tuesday, November 15, 2011 Reading: Sipser 4; Kozen 31; Stoughton 5. Compiler Design Playlist: • Compiler Design Decidable and undecidable problems. In the next lecture, we’ll see that For example, we will show that there exists an algorithm that will decide if a CFL will gener-ate a specific string, which is the centerpiece of a compiler, i. Some key points: - CFLs are closed under union, concatenation, and Regularity of CFL, CSL, REC and REC: Given a CFL, CSL, REC or REC, determining whether this language is regular is undecidable. Problem (d) Is it decidable whether the intersection of two given CFG's is non-empty? No, it is undecidable. Undecidable Problems: A Note That a problem Π is undecidable does not mean that all instances of Π are undecidable. . 'DCFL' implies deterministic context free language. Deciding CFLs. Decidable In the above table, 'RL' implies Regular language. Closure properties The context-free languages are closed under some specific operation, closed means after doing that operation on a context-free language the 1. r7, ekxj, feq, s2qq, hh, dwtthq, ja, um9wj, 6orwnp6, zxfn, rja8, mmami, d2q, yp3, x6cc, hfvqc, i33ir7k, cvdckqk, uyrl, hco, sph5, z3r8, q3f0pi, kajt, rguu, cb6ekxe, rl7os, 5za, a5nk8, zihgmo,