Although it might take a staggeringly long time, m will eventually accept or reject w. Decidable and undecidable problems 237 problems f through 1 are undecidable. 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 following. Sat type problems using both universal and existential quantifiers. We prove that checking joint observability of a regular language w. The posts correspondence problem is undecidable when the alphabet has at least two elements. Undecidability, problem reduction, and rices theorem 12. Because of this, it is traditional to define the decision problem equivalently as. Posts correspondence problem but were still stuck with problems about turing machines only. Are there languages that are not decidable by any turing machine tm. A decision problem is decidable undecidable we focus on decision problems. For another survey of undecidable problems, see dav77. Decidable and semidecidable department of computer. Decidable and undecidable languages wellesley college.
Posts correspondence problem pcp is an example of a problem that does not mention tms in its statement, yet is undecidable. It seems that the pcp is still vary useful when considering undecidability for linear grammars. Or, given a string of zeros and ones, is it a palindrome. Let l be any language with property p, and let m l be a tm that accepts l. A undecidable problem is a decision problemthat are not decidable a decision problem is any arbitrary yesorno question on an infinite set of inputs. Are there problems that cannot be if there is some turing machine that accepts every string in l and rejects every. Decidable and undecidable problems on context free grammars.
Lets formalize the proof technique weve been using so far. An undecidable problem is a question that cannot be resolved with the use of one algorithm. H are cfgs and lg lhg context free grammars are not closed under complementation or intersection, and so we cannot use lg \lh lh \lg as was done for eq dfa. Decidable languages a language l is called decidable iff there is a decider m such that. Given m and x, describe 2 pdas that accept computations of the form. Prerequisite turing machine a problem is said to be decidable if we can always construct a corresponding algorithm that can answer the problem correctly. A problem is nphard if an oracle for it would make solving npcomplete problems easy i. A language is called decidable or recursive if there is a turing machine which accepts and halts on every input string w. Decidable and undecidable problems about quantum automata article pdf available in siam journal on computing 346. Undecidable problems a problem is undecidable if no program can solve it. 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. Decidable and undecidable secondorder unification problems by jordi levy get pdf 254 kb.
A problem is decidable if there is an algorithm to solve it an algorithm is a turing machine that halts on all inputs accepts or rejects therefore, an algorithm must always halt problems that are not decidable are called undecidable also called semi decidable, turingrecognizable, or. More decidable undecidable problems problem j is it decidable whether a given turing machine accepts a regular set. What is the difference between decidable and undecidable. Thus in section 1 we will consider the basic intersection problem for. A problem that cannot be solved for all cases by any algorithm whatsoeverequivalently, whose associated language cannot be recognized by a. Problems about automata we can formulate this question as a language.
In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. To prove the undecidability of a problem x, it su ces to choose a suitable lossiness relation l and reduce the structural termination problem for lossy counter. Given a new problem new, want to determine if it is easy or hard right now, easy typically means decidable right now, hard typically means undecidable one option. Decidable and undecidable languages the halting problem and the return of diagonalization friday, november 11 and tuesday, november 15, 2011 reading. Definition of undecidable problem, possibly with links to more information and implementations. We can intuitively understand decidable problems by considering a simple example. Undecidable problems for contextfree grammars liacs. Decidable and undecidable problems computer action team. Undecidable problems about cfls csa iisc bangalore. While i am not sure if this is completely correct, or even how to prove this if it is correct, i am thinking a decidable problem could be reduced to a recognizable, undecidable problem because a polynomial time.
My initial intuition is that this is not the case, and that there are decidable problems that are reducible to undecidable problems. Need to show that union of 2 decidable ls is also decidable let m1 be a decider for l1 and m2 a decider for l2 a decider m for l1. A decision problem is decidable if and only if there exists an algorithm that produces the correct output for the problem for every input. Decidable and undecidable problems in theory of computation. Decidable and undecidable secondorder unification problems. We introduce a decentralized observation problem, where the system under observation is modeled as a regular language l over a finite alphabet. Closure properties of decidable languages decidable languages are closed under. Decidable and undecidable languages recursively enumerable. Learn about the existence of undecidable problems in computer science, like the halting problem, in this article aligned to the ap computer science principles standards. Theory of computation decidable and undecidable problems. Michael sipser 2 turingunrecognizability if and is not trecognizable, then is not turingrecognizable by mappingreducibility to unrecognizable language. Given m and x, build a new machine m0that behaves as follows. Undecidable problems of decentralized observation and. Pdf this work is a survey on decidable and undecidable problems in matrix theory.
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. Undecidable problems in unreliable computations core. And some of the problems we consider turn out to be decidable or to have unknown decidability status. Goedel k on formally undecidable propositions of principia. Decidable and undecidable problems turing machine pdf bitbin. Computer science stack exchange is a question and answer site for students, researchers and practitioners of computer science. To show this, we show that the ability to decide anyone of these problems could be used to decide the halting problem. Relation between semi decidable, undecidable and countable sets. Are there problems that cannot be solved by any algorithm. On formally undecidablf propostions principia mathematica and systems kurt godel in 1931, a young austrian rnathrnatician published an epochm. In fact, we can show that any nontrivial property of the inputoutput behavior of. Blondel, emmanuel jeandel, pascal koiran, and natacha portier abstract. Cisc462, fall 2018, decidability and undecidability 1 decidability and undecidability decidable problems from language theory for simple machine models, such as nite automata or pushdown automata, many decision problems are solvable.
L pfa undecidable undecidable undecidable undecidable qfa undecidable decidable undecidable decidable in this contribution, we consider the problem of determining for a quantum au tomaton a and threshold. There are many well known examples of undecidable problems. Two notions of undecidability there are two common settings in which one speaks of undecidability. If you assume like i did that the input can be any number, then the problem is undecidable. Suppose we are asked to compute all the prime numbers in the range of to 2000. For the love of physics walter lewin may 16, 2011 duration. The problems studied are simply formulated, however most of them are. A proven undecidable problem the idea of the proof is to feed output, reversed, back into the input example. These problems may be partially decidable but they will never be decidable. Undecidable problems about polynomials around hilberts 10th problem anton sadovnikov. 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. Pdf decidable and undecidable problems about quantum.
A problem is said to be decidable if we can always construct a corresponding algorithm that can answer the problem correctly. If you assume that the inputs can only be natural numbers then your solution works and the problem is decidable. Decidability and undecidability stanford university. Some decidable undecidable problems about cfls problems about cfls problem d is it decidable whether the intersection of two given cfgs is nonempty. Decide whether or not these questions are decidable and. Researchers with an interest in turing machines, for example, have tackled the issue of the halting problem, looking at when computer programs stop. A decision problem is a problem which calls for an answer of yes or no, given some input. An undecidable problem for context free languages the following language problem is not decidable.
The halting problem and other non decidable problems the problems in the set nph are called nphard e. Three problems on the decidability and complexity of stability. From pcp, we can prove many other nontm problems undecidable. Given a decider m, you can learn whether or not a string w. Relationship between nphard and undecidable problems. This is a subject of interest in mathematics and computer programming, where the undecidable problem has significant implications. More formally, an undecidable problem is a problem whose language is not a. An nphard is a problem that is at least as hard as any npcomplete problem therefore an undecidable problem can be nphard.
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