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