For an undecidable language, there is no turing machine which accepts the language and makes a decision for every input string w tm can make decision for some input string though. Here we will learn techniques for proving unsolvability. What is the difference between decidable and undecidable. We could clearly construct a decider for bby running m a tm on hm b. Rices theorem can be used to show that whether the language accepted by a turing machine is context free, regular, or even finite, are undecidable problems. Decidable and undecidable problems turing machine pdf bitbin. Pdf decidable and undecidable secondorder unification. Is it decidable whether a given turing machine a has at least 481 states.
In this section, we will understand the concept of reduction first and then we will see an important theorem in this regard. Undecidable problems creating web pages in your account. Can you guys list the problems that you are aware that are decidable for context free language and for deterministic context free languages. If g is in cnf, then it takes at most 2n 1 steps to generate w. Decidable and undecidable problems table toc january 29, 2018 anup patel resources, toc table to check decidable and undecidable property of all grammar regular, cfl, dcfl, csl, recursive, recursive enumerable. Decidable and undecidable problems for probabilistic and quantum automata. Since we know that the halting problem is undecidable, these problems must be undecidable too. Not all properties of programs are functional some properties of programs are decidable because they are not about the function the. Tm was decidable, but that some other undecidable language bwas turingrecognizable.
Alan turing, turing machines and stronger next, decidable problems and undecidable problems in pdas and vpas are explained. In fact, the following proof effectively shows that the complement of a context free language may not even be recursive i. A decision problem p is decidable if the language l of all yes instances to p is decidable for a decidable language, for each input string, the tm halts either at the accept or the reject state as depicted in the. This means there are problems and possibly, or probably, an infinite number of problems that are undecidable, and not related to the halting. We discuss some basic undecidable problems for contextfree lan. Undecidable problems for contextfree grammars liacs. Partially decidable problems and any other problems that are not decidable are referred to as undecidable. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. Decidable problems for context free languages theorem a cfg is decidable, where a cfg fhg. The decidable problems are those that lie within turing degree 0. We need the fact that a pda can decide whether one con.
In fact, for all squarefree d there is a solution, which is why the. Pdf decidable and undecidable problems about quantum. Researchers with an interest in turing machines, for example, have tackled the issue of the halting problem, looking at when. This is a subject of interest in mathematics and computer programming, where the undecidable problem has significant implications.
By inspecting the dfas transitions to see if there is any path to a final state. Now talking about decidability in terms of a turing machine, a problem is said to be a decidable problem if there exists a corresponding turing machine which. Although it might take a staggeringly long time, m will eventually accept or reject w. Given a deterministic tm m, one can build a deterministic pda that accepts the following language. Consider a silly variant of pcp called spcp where corresponding strings in both lists are restricted to have the same length. The reduction is used to prove whether given language is desirable or not.
Undecidable languages are not recursive languages, but sometimes, they may be. More undecidable problems rices theorem posts correspondence problem some real problems. A language is called decidable or recursive if there is a turing machine which accepts and halts on every input string w. A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. C equality problem is undecidable for all languages except in case of finite automata i. Some are decidable, some not if every problem in np can be reduced to a problem x i such as, say, sat, then x are in nph other problems, not necessarily in np, are at least as hard as np problems and would also belong in nph, e.
We prove that this problem is decidable or undecidable depending on. In this section we will encounter several computationally unsolvable problems. Here again we have an algorithm, and a decidable problem. Decidability and undecidability stanford university. Also known as totally decidable problem, algorithmically solvable, recursively solvable.
Proving undecidability 22 next class examples of some problems we actually care about that are undecidable are there any problems that we dont know if they are decidable or undecidable. A valuable collection both for original source material as well as historical formulations of current problems. Imagine a class of problems nph that are at least as hard as np problems. For another survey of undecidable problems, see dav77 2. We check if lcfg contains any string with length between n and 2n. Decidable and undecidable problems in schedulability analysis using timed automata. For another survey of undecidable problems, see dav77. To show this, we show that the ability to decide anyone of these problems could be used to decide the halting problem.
Decidable and undecidable problems about quantum automata article pdf available in siam journal on computing 346. Decidable and undecidable languages computer science. The problems for which we cant construct an algorithm that can answer the problem correctly in finite time are termed as undecidable problems. A problem is semidecidable if there is an algorithm that says yes.
Undecidable problem about turing machine javatpoint. B deciding regularity of a context free language is undecidable. Decidable and undecidable problems about quantum automata. Pcp, undecidable problems in language theory and more guidelines.
Totality for pdas is undecidable we now prove our earlier claim that totality for context free languages is undecidable. Undecidable problems the problems for which we cant construct an algorithm that can answer the problem correctly in finite time are termed as undecidable problems. Given a decider m, you can learn whether or not a string w. Decidable undecidable complexity theory np completeness toc theory of computation part3. Decidable and undecidable problems on context free grammars. Decidable languages a language l is called decidable iff there is a decider m such that. For emphasis, the equivalent term totally decidable problem is sometimes used. Spinellis 10 showed that a lengthbounded version of cohens problem is decidable and npcomplete. Then there would exist a machine m b that recognized but did not decide b. The problems that would be decidable with an oracle for the halting problem would be the turing jump 0. Well soon see examples of languages that are in re but. Here are some examples of decision problems involving turing machines. An undecidable problem is a question that cannot be resolved with the use of one algorithm.
See also undecidable problem, np, npcomplete, solvable, tractable, computable. The 5th postulate states that, given a straight line on a plane and a point on the same plane outside that line, there always exists one and only one straight line passing through that. And some of the problems we consider turn out to be decidable or to have unknown decidability status. Decidability and undecidability decidable problems from language theory for simple machine models, such as nite automata or pushdown automata, many decision problems are solvable. Two notions of undecidability there are two common settings in which one speaks of undecidability. Are problems in quantum information theory undecidable. Logic godels incompleteness theorems godsl provided undecidable statements in sense 1 for a wide variety of axiom systems. I did get some info on list of undecidable problems on stack overflow and wiki, but not related to cfg or dcfg as such in detail. By accepting churchs thesis we are able to prove that certain problems are unsolvable undecidable by any computer. The behavior of all turing machines can be summarized by an infinite 2d table whose rows are turing machines and whose columns are input strings. Proof idea iwe construct a turing machine s to decide the problem. If you can figure out a systematic way an algorithm to answer the question correctly. That is there will always be a condition that will lead the turing machine into an infinite loop without providing an answer. Decidable and undecidable problems computer action team.
Problems about automata we can formulate this question as a language. The associated language is called a decidable language. Pdf we study schedulability problems of timed systems with nonuniformly recurring computation tasks. Pcp, undecidable problems in language theory and more. These problems may be partially decidable but they will never be decidable. Decidable undecidable undecidable undecidable undecidable undecidable lecture 17. Or, given a string of zeros and ones, is it a palindrome. In this section, we will discuss all the undecidable problems regarding turing machine. Partially decidable semidecidable and totally not decidable. Cubitt, david perezgarcia november 24, 2011 abstract this note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable in principle rather than in practice. Npcomplete problems although the general cases of the aforementioned problems are undecidable, it turns out that it is possible to obtain their decidable versions by assuming some bound on the time or memory available to the malware.
Decidable and undecidable secondorder unification problems article pdf available in lecture notes in computer science february 1998 with 37 reads how we measure reads. Pdf decidable and undecidable problems in schedulability. In all the undecidable decision problems we present, the source of the unde cidability can be traced back to a single undecidable decision problem, namely the halting problem, or equivalently the membership problem for listable sets see sections 3. Decidable and undecidable problems 237 problems f through 1 are undecidable. Consider the problem of testing whether a turing machine accepts a given input. Grammar undecidable problems west chester university.
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