This is a subject of interest in mathematics and computer programming, where the undecidable problem has significant implications. Pdf strongly, super, and absolutely undecidable problems. I am looking for an undecidable problem that i could give as an easy example in a presentation to the general public. Two notions of undecidability there are two common settings in which one speaks of undecidability. Researchers with an interest in turing machines, for example, have tackled the issue of the halting problem, looking at when computer programs stop. For another survey of undecidable problems, see dav77. We will call a formula of pm with exactly one free variable of type natural numbers a 175 classsign. Decidable and undecidable problems in theory of computation. The reduction is used to prove whether given language is desirable or not. It was one of the first problems to be proved undecidable so the halting problem is historically important. Equivalent language cannot be recognized by a turing machine that halts for all inputs. And some of the problems we consider turn out to be decidable or to have unknown decidability status.

In all the undecidable decision problems we present, the source of the undecidability 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. 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. Decidable and undecidable problems with examples in. One example above all can be the halting problem and its complement. In computability theory, an undecidable problem is a type of computational problem that. The infiniteness property is the set of infinite languages. For any of these problems, in principle we can compute a speci c ifor which y. More undecidable problems rices theorem posts correspondence problem some real problems. However, can anybody give me an example in which both a problem and its complement are undecidable. Here, context free grammar generates a context free language and set of all context free languages is also a set. This is known to be undecidable for a set of six or more 3. Undecidable problems in fractal geometry 425 dence problem pcp and its variants.

In this section, we will discuss all the undecidable problems regarding turing machine. We will now construct an undecidable theorem of the system pm, i. A valuable collection both for original source material as well as historical formulations of current problems. Finding unsolvable problems we can use the fact that l d. Undecidable problems we will now discuss the notion of undecidability. Given a deterministic tm m, one can build a deterministic pda that accepts the following language. Context free n text n sitive sive rsively m erable r. In fact, we can show that any nontrivial property of the inputoutput behavior of programs is undecidable. Pdf decidable and undecidable problems about quantum automata. Same as pcp, but the solution must start with the first pair in the list. But were still stuck with problems about turing machines only. For the love of physics walter lewin may 16, 2011 duration. One of the first problems suspected to be undecidable, in the second sense of the term, was the word problem for groups, first posed by max dehn in 1911, which asks if there is a finitely presented group for which no algorithm exists to determine whether two words are equivalent.

List of undecidable problems from wikipedia, the free encyclopedia in computability theory, an undecidable problem is a type of computational problem that requires a yesno answer, but where there cannot possibly be any computer program that always gives the correct answer. But, ambiguity is not an operation and hence we can never say that cfg is closed under ambiguity. 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. Please comment below if you find anything wrong in the above post. M is a tm and m halts on input w proof is by reduction from atm. Undecidable problems for contextfree grammars liacs. A lot of famous undecidable problems are nonetheless at least semidecidable, with their complement being undecidable. Posts correspondence problem pcp is an example of a problem that does not mention tms in its statement, yet is undecidable. Blondel, emmanuel jeandel, pascal koiran, and natacha portier abstract.

Convert p 2s input instance to p 1s input instance s. If problem p reduces to problem q, and p is undecidable, then q is undecidable. Lg 2 these related problems about pdas are also undecidable. Since we know atm is undecidable, we can show a new language b is undecidable if a machine that can decide b could be used to build a machine that can decide atm. Researchers with an interest in turing machines, for example, have tackled the issue of the halting problem, looking at when computer programs stop, versus running infinitely. Examples of undecidable problems about turing machines. 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 problem about turing machine javatpoint.

That is there will always be a condition that will lead the turing machine into an infinite loop without providing an answer. Turing machine m yes accept input decider for a string no reject a computational problem is decidable if the corresponding language is decidable. We shall describe a class i2 of such decision problems and a construction a such that if f is a problem in d. I mean easy in the sense that the mathematics behind it can be described, well, without mathematics, that is with analogies and intuition, avoiding technicalities. Undecidableproblemsforcontextfreegrammars hendrik jan hoogeboom universiteitleiden nl abstract. Find a mimimal pda in terms of number of states for a context free language. A contextfree grammar g is unambiguous iff every string s in. In a similar way well talk about other decision problems, ultimately talking about some underlying language.

A language a is decidable, if there is a turing machine m decider that accepts the language a and halts on every input string decision on halt. Proving undecidability acceptance language a tm m is a tm description and m accepts input w we proved atm is undecidable last class. Torelli, some recursively unsolvable problems relating to isolated cutpoints in probabilistic automata, in proceedings of the 4th international decidable and undecidable quantum automata problems 1473 colloquium on automata, languages and programming, lecture notes in comput. Students may have heard of unsolvable problems such as trisecting an angle constructing an angle a third the size of a given angle or squaring the circle constructing a square with the same area as a given circle, the latter. We need the fact that a pda can decide whether one con. The post correspondence problem due to emil post is another undecidable problem that turns out to be a very helpful tool for proving problems in logic or in formal language theory to be undecidable. An undecidable problem is a question that cannot be resolved with the use of one algorithm. Undecidable theory of computation cognitive science.

Undecidable problems unsolvable problems decidable languages. List of undecidable problems wikipedia republished wiki 2. If you can figure out a systematic way an algorithm to answer the question correctly. Show that atm that could decide halt tm could be used to decide atm which we already proved is undecidable. An example of an easy to understand undecidable problem. Decidable and undecidable problems in telugu with examples simple and quick learning by raja sekhar kummari. Pdf decidable and undecidable problems about quantum. For simple machine models, such as nite automata or pushdown automata, many decision problems are solvable. Decidability and undecidability stanford university. Reduction proof by contradiction and construction assume mbis a tm that decides lb. Because this is impossible, tm h must not exist, so atm is undecidable. Decidable and undecidable problems on context free grammars.

Other undecidable problems examples of undecidable problems. Imagine a class of problems nph that are at least as hard as np problems. The problems for which we cant construct an algorithm that can answer the problem correctly in finite time are termed as undecidable problems. Thus, a tool that uncovers all triggerbased behavior all the time reduces to the halting problem. Dec 07, 2015 decidable and undecidable problems on context free grammars. These results allow one to build a simple geometrical model of computation based on ifs which is computa tionally universal. Apr 30, 2020 an undecidable problem is a question that cannot be resolved with the use of one algorithm. Apr 09, 2019 decidable and undecidable problems in telugu with examples simple and quick learning by raja sekhar kummari. Here we present a short list of undecidable problems, that is, problems which no computer program can solve. Totality for pdas is undecidable we now prove our earlier claim that totality for context free languages is undecidable. We have reached a contradiction, so as long as nothing else is questionable our assumption must be wrong. In computability theory, an undecidable problem is a type of computational problem that requires a yesno answer, but where there cannot possibly be any computer program that always gives the correct answer.

In this paper we obtain general results for undecidable first order decision problems that is, problems about elements in a particular group, such as the word and conjugacy problems. Is the language accepted by a tm empty, finite, regular, or context free. In this section, we will understand the concept of reduction first and then we will see an important theorem in this regard. Thus in section 1 we will consider the basic intersection problem for.

In each case we take a known undecidable language and reduce it to the unknown one, thereby proving that the unknown one is also undecidable. Pdf on nov 9, 2011, alexei myasnikov and others published strongly. Aug 30, 2016 heres probably the oldest known example. Or, given a string of zeros and ones, is it a palindrome. An instance of the post correspondence problem for short, pcp is given by two sequences u u. Apr 06, 2016 for the love of physics walter lewin may 16, 2011 duration. Statement in terms of decision problems saying that problem a reduces to problem b means that, in some sense, b is equally as general or more general than a, because b can decide for a. Students may have heard of unsolvable problems such as trisecting an angle constructing an angle a third the size of a given angle or squaring the circle constructing a square with the same area as a. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. Undecidable problem semidedidable or totally not decidable a problem that cannot be solved for all cases by any algorithm whatsoever.

By encoding the universal thring machine, we construct two undecidable sets. So must show how a tm that decides halttm can be used to decide atm. Why arent recursively enumerable languages undecidable. Given context free grammars g 1, g 2, is lg 1 lg 2. A decision problem p is called undecidable if the language l of all yes instances to p is not decidable.

Problem reduction in the universal tm halting problem we proved that the halting problem is undecidable, translating this into the question of whether a certain language l is undecidable. Some undecidable problems involving elementary functions. We discuss some basic undecidable problems for context free languages, starting from valid and invalid computations of tms. Decidable and undecidable problems computer action team. Proving pcp is undecidable well introduce the modified pcp mpcp problem. Show that we can build a tm that uses m as a subroutine in order to recognize l. In computability theory, an undecidable problem consists of a family of instances for which a particular yesno answer is required, such that there is no computer program that, given any problem instance as input, terminates and outputs the required answer after a finite number of steps. Before reading this page, you should first read turing machines. Thus, problem mentioned in option a is undecidable. 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 2. Ntms are known to be no more powerful than tms in the sense that the set of problems decidable by ntms is identical to the set of problems decidable by tms, so clearly by this definition there can be no undecidable problems in np. An equivalent definition of np is that it consists of all problems that are decidable not just verifiable in polynomial time by a nondeterministic turing machine. Decidable and undecidable problems with examples in telugu. Undecidable languages are not recursive languages, but sometimes, they may be recursively enumerable.

Some undecidable problems involving elementary functions of a real variable volume 33 issue 4 daniel richardson skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. From pcp, we can prove many other nontm problems undecidable. These problems may be partially decidable but they will never be decidable. More formally, an undecidable problem is a problem whose language is not a. What is the difference between decidable and undecidable. One of the sets is a map of a family of parametrized ifss. This is the definition of decidable from wikipedia. On formally undecidable propositions of principia mathematica. Npcomplete problems although the general cases of the aforementioned problems are undecidable, it turns out that it is possible to obtain their. It seems that the pcp is still vary useful when considering undecidability for linear grammars. Decidable and undecidable problems about quantum automata article pdf available in siam journal on computing 346. We will assume the classsigns are somehow numbered, call the nth one r n. The essence of reducing one problem to another is the existence of a function from one.

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