Decidable problem is also called as totally decidable problem, algorithmically solvable, recursively solvable. Undecidable problems about polynomials around hilberts 10th problem anton sadovnikov saint petersburg state university april 21, 2007 abstract in his tenth problem hilbert asked for an algorithm capable to determine. These problems may be partially decidable but they will never be decidable. In the case of deterministic finite automata, problems like equivalence can be solved. There are some problems in np hard which are not undecidable decidable, and which i guess are np complete. Also known as totally decidable problem, algorithmically solvable, recursively solvable. Aug 30, 2016 heres probably the oldest known example. Pdf decidable and undecidable problems about quantum. Oct, 2019 a problem is decidable, if there is an algorithm that can answer either yes or no.
Although it might take a staggeringly long time, m will eventually accept or reject w. Decidable and undecidable problems on context free grammars. He is of basic importance in the subject because he gave the first precise definition of idealized machines turing machines allowing an exact. A decision problem is a problem that requires a yes or no answer. Spinellis 10 showed that a lengthbounded version of cohens problem is decidable and npcomplete. At least, assuming it was decidable whether a string was in the formal language or not. Practice and sources 1 slide07 universalprogram 2 textbook.
Identifying languages or problems as decidable, undecidable or partially decidable is a very common question in gate. A problem is called partially decidable, semi decidable, solvable, or provable if a is a recursively enumerable set. The undecidable problem in computability theory in computability theory, the halting problem is a decision problem which can be stated as follows. Now we will show some other problems and consider whether they are decidable by algorithm or not. We solved the decision problem for acfg by algorithmically transforming the input into the form needed by another problem for which we could find a deciding tm. Mar 22, 2020 an undecidable problem is a question that cannot be resolved with the use of one algorithm. Some decidable undecidable problems about cfls other undecidable problems about cfls problem e is it decidable whether the intersection of two given cfls is a cfl. No undecidable problem can ever be solved by a computer or computer program of any kind. 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. In general, a semidecidable problem recursively enumerable could be decidable recursive or undecidable nonrecursively enumerable. The associated language is called a decidable language. The undecidability of this problem was proven, even in the case of isolated cut point.
There can be no formal language that describes them all without also describing some undecidable problems. Partially decidable problems and any other problems that are not decidable are called undecidable. 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. 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. It is assumed that basic notions of contextfree grammars and turing ma. Problem f is it decidable whether the complement of a given cfl is a cfl. A decision problem a is called decidable or effectively solvable if a is a recursive set. We prove that this problem is decidable or undecidable depending on whether. Decidable and undecidable problems about quantum automata. With correct knowledge and ample experience, this question becomes very easy to solve. Every string is an encoding of some tm m and string w. Jan 29, 2018 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.
Problems about automata we can formulate this question as a language. Practice and sources 1 slide07 universalprogram 2 textbook page 85 99 3 lab06 from cs 363 at shanghai jiao tong university. Given a description of a program and a finite input, decide whether the program finishes running or. Undecidable definition of undecidable by merriamwebster.
Undecidable definition is not capable of being decided. Is it decidable whether a given turing machine a has at least 481 states. The idea is to show that if b were decidable then a would be too. Decidable languagea decision problem p is said to be decidable i.
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 recursively enumerable. Otherwise, pretend the string decodes to some predetermined group of objects. If the string is a legal encoding, go with that encoding. A decision problem that can be solved by an algorithm that halts on all inputs in a finite number of steps. Pdf decidable and undecidable problems in schedulability. Decidable and undecidable problems turing machine pdf bitbin. Here are some examples of decision problems involving turing machines. An example of an easy to understand undecidable problem. 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. Two notions of undecidability there are two common settings in which one speaks of undecidability. Decidable languages a language l is called decidable iff there is a decider m such that. Theproblemofdeciding whetheragivencfgisambiguousis undecidable.
Reduction proof by contradiction and construction assume mbis a tm that decides lb. Decidable and undecidable languages recursively enumerable. Decidable and undecidable problems in theory of computation. This is a subject of interest in mathematics and computer programming, where the undecidable problem has significant implications. May 09, 2011 partially decidable problems and any other problems that are not decidable are called undecidable. A language for which membership can be decided by an algorithm that halts on all inputs in a finite number of steps. Problem g is it decidable whether a given cfl is a dcfl. If p reduces to q, and q is decidable, then p is decidable. A decision problem is decidable if there exists a decision algorithm for it. Decidability and undecidability in toc geeksforgeeks. It is worth noting that, to the best our knowledge, bounded resetptas and luptas are the only nontrivial sets of syntactic restrictions of ptas making the reachability emptiness problem decidable. This strategy of reducing one problem p to another known problem q is very common.
Decidability and undecidability stanford university. And some of the problems we consider turn out to be decidable or to have unknown decidability status. We have reached a contradiction, so as long as nothing else is questionable our assumption must be wrong. A decommenting program can decomment any text file, including the decommenting program itself. Context a problem is decidable if some turing machine decides solves the. Nov 09, 2017 decidable, or prove from scratch that the problem is hard undecidable e. Undecidable problems for contextfree grammars liacs. This is decidable as emptiness of contextfree languages is decidable and cfl. Pdf we study schedulability problems of timed systems with nonuniformly recurring computation tasks. Reachability and liveness in parametric timed automata. 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. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. A few extensions of this unification problem are still decidable. Pdf decidable and undecidable problems about quantum automata.
Given a decider m, you can learn whether or not a string w. A problem is called partially decidable, semidecidable, solvable, or provable if a is a recursively enumerable set. Decidable and undecidable problems computer action team. A problem that cannot be solved for all cases by any algorithm whatsoeverequivalently, whose associated language cannot be recognized by a turing machine that halts for all inputs. For another survey of undecidable problems, see dav77. 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. Relationship between nphard and undecidable problems. Halting problem is undecidable prove that halting problem is undecidable let a tm m is a tm and accepts w proof technique.
See also undecidable problem, np, npcomplete, solvable, tractable, computable. 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. A decision problem that admits no algorithmic solution is said to be undecidable. Well, i seem to have come out to a conclusionthat undecidable problems are a subset of np hard problems this is based on the following scenario all problems in np are decidable. There are uncountably many undecidable problems, so the list below is necessarily incomplete. Use language to represent various computational problems bcs we have terminology to deal with languages. This is because the set of decidable languages is not recursively enumerable, but any formal language would give a way to enumerate them. This means that there exists an algorithm that halts eventually when the answer is yes but may run for ever if the answer is no.
I know that since s is decidable, but does there exist a subset within s that is undecidable. Though undecidable languages are not recursive languages, they may be subsets. 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. Also note that a problem and its complement could both or just one of them be not even semi decidable nonrecursively enumerable. Decidable and undecidable languages 309 selfreference is not a problem consider the following. Undecidable problems creating web pages in your account. More formally, an undecidable problem is a problem whose language is not a recursive set. I am looking for an undecidable problem that i could give as an easy example in a presentation to the general public.
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