In a similar way well talk about other decision problems, ultimately talking about some underlying language. Some undecidable problems related to the herbrand theorem. Introduction to theory of computation p, np, and npcompleteness sungjin im university of california, merced 04232015. On an undecidable problem related to difference equations. An introduction to the undecidable and the intractable kindle edition by reiter, edna e. Or, given a string of zeros and ones, is it a palindrome. I am looking for an undecidable problem that i could give as an easy example in a presentation to the general public. Given a decider m, you can learn whether or not a string w. And some of the problems we consider turn out to be decidable or to have unknown decidability status. Grammar undecidable problems west chester university. But my question is has it been proven that all problems which are undecidable can be reduced to another problem which is undecidable.
From pcp, we can prove many other nontm problems undecidable. Decidability and undecidability stanford university. Two notions of undecidability there are two common settings in which one speaks of undecidability. Classical problem becomes undecidable in a quantum setting.
Unsolvable is a less common term which i know mostly to be used synonymous to undecidable. Generic complexity of undecidable problems myasnikov, alexei g. Highly undecidable problems for infinite computations olivier finkel1 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. Undecidability for unrestricted grammars weve shown that unrestricted, type0 grammars are equivalent to tms in the sense that a language l is accepted by a tm if and only if it can be generated by an unrestricted grammar. Cisc462, fall 2018, decidability and undecidability 7 cepts, n accepts. Reductions and undecidability csci 81 spring, 2015 kim bruce undecidable problems the problem view the language view does tm m halt on w.
Finding unsolvable problems we can use the fact that l d. A decision problem that admits no algorithmic solution is said to be undecidable no undecidable problem can ever be solved by a computer or computer program of any kind. Although it might take a staggeringly long time, m will eventually accept or reject w. Reduce the halting problem onto the posts correspondence problem. Decidable and undecidable languages the halting problem and the return of diagonalization friday, november 11 and tuesday, november 15, 2011 reading. With correct knowledge and ample experience, this question becomes very easy to solve.
A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. For another survey of undecidable problems, see dav77. If problem p reduces to problem q, and p is undecidable, then q is undecidable. 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. And, in terms of consistency, that is equivalent to each of a.
We argue that it is beneficial for computer science to go beyond recursive algorithms, making possible to look for exact solutions of intractable problems or even to find solutions of undecidable problems, whereas recursive solutions do not exist. For me, i have been arguing with my friends that undecidable problems are a superset to the np hard problems. Other undecidable problems once we have shown that the halting problem is undecidable, we can show that a large class of other problems about the inputoutput behavior of programs are undecidable. The problems for which we cant construct an algorithm that can answer the problem correctly in finite time are termed as undecidable problems. Whether np hard problems are a subset of undecidable problems, or are they just the same and equal, or is it that they are not comparable. Decidable and undecidable problems on context free grammars. Is it not possible that there exists a undecidable problem which can proved to have no reduction to any other undecidable problem hence to prove the undecidability of such a problem, one cannot use reductions. Nonalgorithmic and approximate solutions to undecidable. Linear difference equations with polynomial coefficients depending on parameters are considered.
Are there languages that are not decidable by any turing machine tm. So decidable undecidable but enumerable nonenumerable is a partition of the class of all problems into three classes, where the middle one is intuitively somthing like the easiest undecidable problems. There are some problems so hard they are beyond even the nonelementary class, and which are effectively undecidable outside of the class of decision. It is proved that the problem of existence of numerical values of parameters for which the given equation has a polynomial solution alternatively, a solution given by a rational function is undecidable similar to the undecidability of the same problem in the differential. Pages in category undecidable problems the following 15 pages are in this category, out of 15 total. Decidable problems represent problem using language language decidable problem decidable dfa th. If you can figure out a systematic way an algorithm to answer the question correctly. For the love of physics walter lewin may 16, 2011 duration. Partially decidable semidecidable and totally not decidable. This undecidability result has farreaching consequences. Undecidable extensions of skolem arithmetic bes, alexis and richard, denis, journal of symbolic logic, 1998. In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yesorno answer. Determining whether a finite set of upper triangular.
The essence of reducing one problem to another is the existence of a function from. What are the most attractive turing undecidable problems in mathematics there are thousands of examples, so please post here only the most attractive, best examples. One of the simulations necessarily halts in a nite number of steps. Which of the following problems about turing machines are solvable, and which are undecidable. Highly undecidable problems for in nite computations. Lossy counter machines can be used as a general tool to prove the undecidability of many problems, for example. M does not halt on w does tm m halt on the empty tape. The posts correspondence problem is undecidable when the alphabet has at least two elements. So must show how a tm that decides halttm can be used to decide atm. An anthology of fundamental papers on undecidability and unsolvability, th. Ia central question in computer science and mathematics.
A problem is semidecidable if there is an algorithm that says yes. Decidable languages a language l is called decidable iff there is a decider m such that. A decision problem is a problem that requires a yes or no answer definition. Context a problem is decidable if some turing machine decides solves the. We have reached a contradiction, so as long as nothing else is questionable our assumption must be wrong. Decidable and undecidable problems computer action team. 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. 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. Some undecidable termination problems for semithue. Decidable and undecidable problems turing machine pdf bitbin. We show that many classical decision problems about 1counter.
The complement of the halting problem, denoted by hp, and dened as. An introduction to the undecidable and the intractable. Undecidable languages are not recursive languages, but sometimes, they may be. Cs385assignment 8 due monday, december 10 1 decidable problems on finite automata problems 4. Are there problems that cannot be solved by any algorithm. Examples of solving combination problems with videos and solutions, formula to find the number of combinations of n things taken r at a time, what is the combination formula, how to use the combination formula to solve word problems and counting problems, examples and step by step solutions, how to solve combination problems that involve selecting groups based on. 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. In fact, we can show that any nontrivial property of the inputoutput behavior of programs is undecidable. They allow one to solve many problems undecidable in the realm of recursive algorithms burgin, 2005.
Decidable languagea decision problem p is said to be decidable i. M is a tm and m halts on input w proof is by reduction from atm. Use features like bookmarks, note taking and highlighting while reading limits of computation. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. In these cases, knowing that certain problems are undecidable could. This is often done via an intermediate step, where a ram machine with a single register is used. What is the difference between decidable and undecidable. An example of an easy to understand undecidable problem. The standard example of an undecidable language is. Decidable problems represent problem using language dfa q0. Show that we can build a tm that uses m as a subroutine in order to recognize l. By inspecting the dfas transitions to see if there is any path to a final state. In this handout, i regularly make use of two problems, namely the halting problem, denoted by hp, and dened as hp fhm. Undecidable problems unfortunately the hierarchy of difficulty at the end of the last section didnt tell the whole story.
Recursive languages correspond to decidable problems. Decidable and undecidable languages recursively enumerable. But were still stuck with problems about turing machines only. Am a bit confused about the relationship between undecidable problems and np hard problems. Download it once and read it on your kindle device, pc, phones or tablets. Decidability and undecidability in toc geeksforgeeks. Relationship between nphard and undecidable problems. Posts correspondence problem pcp is an example of a problem that does not mention tms in its statement, yet is undecidable. Identifying languages or problems as decidable, undecidable or partially decidable is a very common question in gate. Some examples already appear on the wikipedia page.
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