I think the post correspondence problem is a very good example of a simple undecideable problem that is also relatively unknown given a finite set of string tuples a, bba x ab, aa y bba, bb z the problem is to determine if there is a finite sequence of these tuples, allowing for repetition, such that the concatenation of the first half is equal to the concatenation of second. See also undecidable problem, np, npcomplete, solvable, tractable, computable. Decidable and undecidable problems turing machine pdf bitbin. Consider the problem of testing whether a turing machine accepts a given input. 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. More undecidable problems rices theorem posts correspondence problem some real problems. B deciding regularity of a context free language is undecidable. Consider a silly variant of pcp called spcp where corresponding strings in both lists are restricted to have the same length. In this section, we will discuss all the undecidable problems regarding turing machine.
A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. 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. Undecidable problems for contextfree grammars liacs. Decidability and undecidability stanford university.
This means there are problems and possibly, or probably, an infinite number of problems that are undecidable, and not related to the halting. Decidable and undecidable languages computer science. 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. These problems may be partially decidable but they will never be decidable.
In other words, if a tm was decidable, then every turingrecognizable language would also be decidable. Decidability and undecidability decidable problems from language theory for simple machine models, such as nite automata or pushdown automata, many decision problems are solvable. 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. 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. Decidable and undecidable problems computer action team. By inspecting the dfas transitions to see if there is any path to a final state. An example of an easy to understand undecidable problem. Pdf decidable and undecidable problems in schedulability. Can you guys list the problems that you are aware that are decidable for context free language and for deterministic context free languages.
Problems about automata we can formulate this question as a language. Pcp, undecidable problems in language theory and more. This is decidable as emptiness of contextfree languages is decidable and cfl. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. Partially decidable problems and any other problems that are not decidable are referred to as undecidable. In fact, the following proof effectively shows that the complement of a context free language may not even be recursive i. Decidable problem article about decidable problem by the.
Totality for pdas is undecidable we now prove our earlier claim that totality for context free languages is undecidable. Well soon see examples of languages that are in re but. 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. To show this, we show that the ability to decide anyone of these problems could be used to decide the halting problem. We check if lcfg contains any string with length between n and 2n. Pdf decidable and undecidable problems about quantum. An undecidable problem is a question that cannot be resolved with the use of one algorithm.
Undecidable problem about turing machine javatpoint. If you can figure out a systematic way an algorithm to answer the question correctly. Are problems in quantum information theory undecidable. Partially decidable semidecidable and totally not decidable. Decidable and undecidable problems on context free grammars. In this section we will encounter several computationally unsolvable problems. 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. For emphasis, the equivalent term totally decidable problem is sometimes used. What is the difference between decidable and undecidable. In this section, we will understand the concept of reduction first and then we will see an important theorem in this regard. Then there would exist a machine m b that recognized but did not decide b. Imagine a class of problems nph that are at least as hard as np problems. Proof idea iwe construct a turing machine s to decide the problem.
We prove that this problem is decidable or undecidable depending on. Decidable and undecidable problems 237 problems f through 1 are undecidable. Given a decider m, you can learn whether or not a string w. Spinellis 10 showed that a lengthbounded version of cohens problem is decidable and npcomplete. Two notions of undecidability there are two common settings in which one speaks of undecidability. That is there will always be a condition that will lead the turing machine into an infinite loop without providing an answer. 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. Logic godels incompleteness theorems godsl provided undecidable statements in sense 1 for a wide variety of axiom systems. Not all properties of programs are functional some properties of programs are decidable because they are not about the function the. Given a deterministic tm m, one can build a deterministic pda that accepts the following language. If g is in cnf, then it takes at most 2n 1 steps to generate w. 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. I chose to speak about undecidable problems because we are within a year of the. 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.
Undecidable languages are not recursive languages, but sometimes, they may be. Grammar undecidable problems west chester university. The problems for which we cant construct an algorithm that can answer the problem correctly in finite time are termed as undecidable problems. Decidable problems for context free languages theorem a cfg is decidable, where a cfg fhg. Or, given a string of zeros and ones, is it a palindrome. Decidable and undecidable secondorder unification problems article pdf available in lecture notes in computer science february 1998 with 37 reads how we measure reads. A valuable collection both for original source material as well as historical formulations of current problems. A decision problem is decidable if there exists a decision algorithm for it. Decidable and undecidable problems about quantum automata article pdf available in siam journal on computing 346. 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. We could clearly construct a decider for bby running m a tm on hm b.
In fact, for all squarefree d there is a solution, which is why the. And some of the problems we consider turn out to be decidable or to have unknown decidability status. A language is called decidable or recursive if there is a turing machine which accepts and halts on every input string w. By accepting churchs thesis we are able to prove that certain problems are unsolvable undecidable by any computer. Pdf decidable and undecidable secondorder unification. We discuss some basic undecidable problems for contextfree lan. 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. For another survey of undecidable problems, see dav77 2. Alan turing, turing machines and stronger next, decidable problems and undecidable problems in pdas and vpas are explained. We need the fact that a pda can decide whether one con. 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. The reduction is used to prove whether given language is desirable or not.
The associated language is called a decidable language. Decidable and undecidable problems in schedulability analysis using timed automata. Researchers with an interest in turing machines, for example, have tackled the issue of the halting problem, looking at when. Is it decidable whether a given turing machine a has at least 481 states. A problem is semidecidable if there is an algorithm that says yes. For another survey of undecidable problems, see dav77.
Also known as totally decidable problem, algorithmically solvable, recursively solvable. Here again we have an algorithm, and a decidable problem. Decidable and undecidable problems for probabilistic and quantum automata. Tm was decidable, but that some other undecidable language bwas turingrecognizable. Decidable undecidable complexity theory np completeness toc theory of computation part3.
C equality problem is undecidable for all languages except in case of finite automata i. Although it might take a staggeringly long time, m will eventually accept or reject w. Here we will learn techniques for proving unsolvability. The decidable problems are those that lie within turing degree 0. Here are some examples of decision problems involving turing machines. Since we know that the halting problem is undecidable, these problems must be undecidable too. 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. Decidable and undecidable problems in theory of computation.
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