It seems that the pcp is still vary useful when considering undecidability for linear grammars. Undecidable problems in fractal geometry 425 dence problem pcp and its variants. What is the difference between decidable and undecidable. 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. 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. Researchers with an interest in turing machines, for example, have tackled the issue of the halting problem, looking at when computer programs stop. Decidable and undecidable problems with examples in. In this section, we will discuss all the undecidable problems regarding turing machine. Here we present a short list of undecidable problems, that is, problems which no computer program can solve. 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.
An instance of the post correspondence problem for short, pcp is given by two sequences u u. Why arent recursively enumerable languages undecidable. Is the language accepted by a tm empty, finite, regular, or context free. Given context free grammars g 1, g 2, is lg 1 lg 2. From pcp, we can prove many other nontm problems undecidable. 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. We will call a formula of pm with exactly one free variable of type natural numbers a 175 classsign.
This is known to be undecidable for a set of six or more 3. And some of the problems we consider turn out to be decidable or to have unknown decidability status. Decidable and undecidable problems about quantum automata article pdf available in siam journal on computing 346. Undecidable problems we will now discuss the notion of undecidability. The essence of reducing one problem to another is the existence of a function from one. Decidable and undecidable problems on context free grammars. I am looking for an undecidable problem that i could give as an easy example in a presentation to the general public.
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. Show that atm that could decide halt tm could be used to decide atm which we already proved is undecidable. Pdf on nov 9, 2011, alexei myasnikov and others published strongly. M is a tm and m halts on input w proof is by reduction from atm.
But were still stuck with problems about turing machines only. 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. Some undecidable problems involving elementary functions. In computability theory, an undecidable problem is a type of computational problem that. Npcomplete problems although the general cases of the aforementioned problems are undecidable, it turns out that it is possible to obtain their. By encoding the universal thring machine, we construct two undecidable sets. A valuable collection both for original source material as well as historical formulations of current problems.
A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. In this section, we will understand the concept of reduction first and then we will see an important theorem in this regard. Undecidable languages are not recursive languages, but sometimes, they may be recursively enumerable. 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. 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. Or, given a string of zeros and ones, is it a palindrome. Lg 2 these related problems about pdas are also undecidable. An undecidable problem is a question that cannot be resolved with the use of one algorithm.
Pdf strongly, super, and absolutely undecidable problems. Undecidable problems unsolvable problems decidable languages. Decidable and undecidable problems with examples in telugu. These problems may be partially decidable but they will never be decidable. For simple machine models, such as nite automata or pushdown automata, many decision problems are solvable. 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.
Because this is impossible, tm h must not exist, so atm is undecidable. 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. Thus, problem mentioned in option a is undecidable. Undecidableproblemsforcontextfreegrammars hendrik jan hoogeboom universiteitleiden nl abstract. In a similar way well talk about other decision problems, ultimately talking about some underlying language.
We will assume the classsigns are somehow numbered, call the nth one r n. That is there will always be a condition that will lead the turing machine into an infinite loop without providing an answer. 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. Thus in section 1 we will consider the basic intersection problem for. Before reading this page, you should first read turing machines. 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. Here, context free grammar generates a context free language and set of all context free languages is also a set. A contextfree grammar g is unambiguous iff every string s in. Find a mimimal pda in terms of number of states for a context free language. Finding unsolvable problems we can use the fact that l d. Dec 07, 2015 decidable and undecidable problems on context free grammars.
We have reached a contradiction, so as long as nothing else is questionable our assumption must be wrong. Apr 30, 2020 an undecidable problem is a question that cannot be resolved with the use of one algorithm. Undecidable theory of computation cognitive science. We discuss some basic undecidable problems for context free languages, starting from valid and invalid computations of tms.
We will now construct an undecidable theorem of the system pm, i. Please comment below if you find anything wrong in the above post. Undecidable problem about turing machine javatpoint. Decidable and undecidable problems computer action team. More undecidable problems rices theorem posts correspondence problem some real problems. For the love of physics walter lewin may 16, 2011 duration. 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. 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. The infiniteness property is the set of infinite languages. 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. More formally, an undecidable problem is a problem whose language is not a. This is a subject of interest in mathematics and computer programming, where the undecidable problem has significant implications.
If problem p reduces to problem q, and p is undecidable, then q is 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. In fact, we can show that any nontrivial property of the inputoutput behavior of programs is undecidable. We need the fact that a pda can decide whether one con. Blondel, emmanuel jeandel, pascal koiran, and natacha portier abstract. 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. If you can figure out a systematic way an algorithm to answer the question correctly.
Turing machine m yes accept input decider for a string no reject a computational problem is decidable if the corresponding language is decidable. 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. An example of an easy to understand undecidable problem. However, can anybody give me an example in which both a problem and its complement are undecidable. Thus, a tool that uncovers all triggerbased behavior all the time reduces to the halting problem.
Proving undecidability acceptance language a tm m is a tm description and m accepts input w we proved atm is undecidable last class. Pdf decidable and undecidable problems about quantum. Decidability and undecidability stanford university. 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. The reduction is used to prove whether given language is desirable or not. Other undecidable problems examples of undecidable problems. Reduction proof by contradiction and construction assume mbis a tm that decides lb. For any of these problems, in principle we can compute a speci c ifor which y.
Proving pcp is undecidable well introduce the modified pcp mpcp problem. Two notions of undecidability there are two common settings in which one speaks of undecidability. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. Equivalent language cannot be recognized by a turing machine that halts for all inputs.
Imagine a class of problems nph that are at least as hard as np problems. 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. Decidable and undecidable problems in telugu with examples simple and quick learning by raja sekhar kummari. 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. Given a deterministic tm m, one can build a deterministic pda that accepts the following language. Convert p 2s input instance to p 1s input instance s. Totality for pdas is undecidable we now prove our earlier claim that totality for context free languages is undecidable.
So must show how a tm that decides halttm can be used to decide atm. A lot of famous undecidable problems are nonetheless at least semidecidable, with their complement being undecidable. For another survey of undecidable problems, see dav77. 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. Examples of undecidable problems about turing machines. One example above all can be the halting problem and its complement. Undecidable problem semidedidable or totally not decidable a problem that cannot be solved for all cases by any algorithm whatsoever. It was one of the first problems to be proved undecidable so the halting problem is historically important. Apr 06, 2016 for the love of physics walter lewin may 16, 2011 duration. Context free n text n sitive sive rsively m erable r.
Posts correspondence problem pcp is an example of a problem that does not mention tms in its statement, yet is undecidable. We shall describe a class i2 of such decision problems and a construction a such that if f is a problem in d. 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. List of undecidable problems wikipedia republished wiki 2. These results allow one to build a simple geometrical model of computation based on ifs which is computa tionally universal. But, ambiguity is not an operation and hence we can never say that cfg is closed under ambiguity. 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. Same as pcp, but the solution must start with the first pair in the list. Show that we can build a tm that uses m as a subroutine in order to recognize l.
Pdf decidable and undecidable problems about quantum automata. 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. On formally undecidable propositions of principia mathematica. Apr 09, 2019 decidable and undecidable problems in telugu with examples simple and quick learning by raja sekhar kummari. Undecidable problems for contextfree grammars liacs. Aug 30, 2016 heres probably the oldest known example.
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