This question divides the set of problems into two parts, namely, decidable and undecidable. A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. Decidable and undecidable questions about automata journal of. The problems studied are simply formulated, however most of them are undecidable. If you can figure out a systematic way an algorithm to answer the question correctly. 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. For undecidability in axiomatic mathematics, see list of statements undecidable in zfc. A problem that cannot be solved for all cases by any algorithm whatsoever. In contrast, we also prove three related problems are. Here are some examples of decision problems involving turing machines. In a similar way well talk about other decision problems, ultimately talking about some underlying language. There are some problems in np hard which are not undecidable decidable, and which i guess are np complete.
The 5th postulate states that, given a straight line on a plane and a point on the same plane outside that line, there always. This is a decidable problem, because if the computer is given any values for x or y, it can use an algorithm to answer the question. Blondel, emmanuel jeandel, pascal koiran, and natacha portier abstract. Pdf decidable and undecidable problems about quantum. 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. Partially decidable problems and any other problems that are not decidable are called undecidable. Partially decidable problems and any other problems that are not decidable are referred to as undecidable. And some of the problems we consider turn out to be decidable or to have unknown decidability status. Given a decider m, you can learn whether or not a string w. Alan turing, turing machines and stronger next, decidable problems and undecidable problems in pdas and vpas are explained.
A problem is semidecidable if there is an algorithm that says yes. Relationship between nphard and undecidable problems. Context a problem is decidable if some turing machine decides solves the. Basic papers on undecidable propositions, unsolvable problems and computable functions dover books on mathematics on free shipping on qualified orders. 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. A problem is said to be decidable if we can always construct a corresponding algorithm that can answer the problem correctly. Although it might take a staggeringly long time, m will eventually accept or reject w.
Decidable and undecidable problems in theory of computation. I mean easy in the sense that the mathematics behind it can be described, well, without. An example of an easy to understand undecidable problem. Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable i. This means that there exists an algorithm that halts eventually when the answer is yes. Recursive languages encloses regular,cfl,csl, and few other languages some of which are recursively enumerable as well but for all of this turing machine can output yes or no. Decidable and undecidable problems related to completely 0simple semigroups t. A problem is called partially decidable, semidecidable, solvable, or provable if a is a recursively enumerable set. If there exists an algorithm to solve a problem, the problem is called decidable. Decidable problem article about decidable problem by the. 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. An undecidable problem is a question that cannot be resolved with the use of one algorithm.
Please like and subscribe that is motivational toll for me. 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. Decidable and undecidable problems about quantum automata. So i was thinking about various undecidable problems and it occured to me that all the ones that i could think of were reducible, or in fact proven undecidiable by reducing to the halting problem. Mar 22, 2020 a simple example might be for any real numbers, is x evenly divisible by y. 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. Undecidable free download as powerpoint presentation. This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable in. Rices theorem can be used to show that whether the language accepted by a turing machine is contextfree, regular, or even finite, are undecidable problems. A decision problem a is called decidable or effectively solvable if a is a recursive set. Undecidable problems in unreliable computations core. Decidability and undecidability stanford university.
Four types of balloon automata defined by one or twoway input and deterministic or nondeterministic finite control and closed classes of balloon automata. Many, if not most, undecidable problems in mathematics can be posed as word problems. Two notions of undecidability there are two common settings in which one speaks of undecidability. 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.
I think here youre implicitly assuming that a problem thats undecidable normally would be decidable on a machine with an oracle for the halting problem. Lecture notes on theory of computation module bput. For another survey of undecidable problems, see dav77. Decidable and undecidable problems decidable and undecidable problems cheat sheet decidable and undecidable problems table gate cs. 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. We apply one result to prove the undecidability of a related problem about kautomatic sets of rational numbers. Why arent recursively enumerable languages undecidable. While termination is decidable for lossy counter machines, structural termination termination for every input is undecidable. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. In contrast, we also prove three related problems are decidable. We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds. Only languages which are recursively enumerable but not recursive are semidecidable because turing machine accepts string which is in the language but if it isnt in the. What is the difference between decidable and undecidable. Decidable and undecidable problems on context free grammars.
Decidable languages a language l is called decidable iff there is a decider m such that. In essence, similarly to how all npc problems are related, this whole class of undecidable problems is related. Partially decidable semi decidable and totally not decidable. We have here a proof by reduction of a problem to another one and this is an important way of showing problems to be decidable or to be undecidable. Or, given a string of zeros and ones, is it a palindrome. Are there some problems for which there are no algorithms to solve the problem. I am looking for an undecidable problem that i could give as an easy example in a presentation to the general public. This is a subject of interest in mathematics and computer programming, where the. By inspecting the dfas transitions to see if there is any path to a final state.
Decidable and undecidable problems turing machine pdf bitbin. A problem is said to be decidable if we can always construct a corresponding algorithm that can answer. 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. 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. Pdf decidable and undecidable problems in schedulability. 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. 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. Well, i seem to have come out to a conclusionthat undecidable problems are a subset of np hard problemsthis is based on the following scenario all problems in np are decidable. Decidable and undecidable problems in theory of computation prerequisite turing machine a problem is said to be decidable if we can always construct a corresponding algorithm that can answer the problem correctly.
Tm tm tm a nov 09, 2017 decidable, or prove from scratch that the problem is hard undecidable e. This work is a survey on decidable and undecidable problems in matrix theory. A problem is called partially decidable, semi decidable, solvable, or provable if a is a recursively enumerable set. Definition of undecidable problem, possibly with links to more information and implementations. Buy on formally undecidable propositions of principia mathematica and related systems on free shipping on qualified orders.
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. 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 theory of computation cognitive science. More undecidable problems rices theorem posts correspondence problem some real problems. We can intuitively understand decidable problems by considering a simple example. More complex problems may not be solvable with a single algorithm for all possible values. Is it decidable whether a given turing machine a has at least 481 states. Pdf decidable and undecidable problems in matrix theory. Are problems in quantum information theory undecidable. Pdf decidable and undecidable problems about quantum automata. Decidable and undecidable problems related to completely 0. Aug 30, 2016 heres probably the oldest known example. Partially decidable semidecidable and totally not decidable. Decidable and undecidable problems computer action team.
On formally undecidable propositions of principia mathematica. Recursive languages encloses regular,cfl,csl, and few other languages some of which are recursively enumerable as well but for all of this turing. Trotter january 20, 1996 abstract the undecidable problems of the title are concerned with the question. Halting problem blank tape problem reducibility decidability duration. Other undecidable problems mississippi state university.