Decidable and undecidable problems about quantum automata torrent

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. Definition of undecidable problem, possibly with links to more information and implementations. 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. Reducibility how do we show a new problem b is undecidable. Why is a quantum computer not capable of solving more.

Why is a quantum computer not capable of solving more problems than a classical computer. General problems for linear contextfree grammars are the topic of section 3. This is decidable as emptiness of contextfree languages is decidable and cfl. Lets assume that you have an procedure that determines whether a bit of code has an infinite loop. Examples and counterexamples every contextsensitive grammar is recursive.

This result is in contrast with probabilistic automata. As a testament to how differently things work in the quantum and classical regimes, physicists have found that a problem that is easily solved in. The emptiness problem asks, given some probability 0. Let n be the set of natural numbers 1,2, and e is the set of even natural numbers 2,4. Show that if b was decidable, then you can use the decider for b as a subroutine to decide atm contradiction, therefore b must also be undecidable. For those cases where planning is decidable, we explain how the time complexity varies. Tm was decidable, but that some other undecidable language bwas turingrecognizable. Cs311 computational structures decidable and undecidable problems 1 lecture 15 andrew black andrew tolmach monday, 24 may 2010. The question of whether a context free language is inherently ambiguous is a separate one. What are the most attractive turing undecidable problems. Several types of automata may be defined, including measureonce and measuremany automata. A correspondence system is a finite set of pairs of strings over an alphabet. 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. We study the reachability problem of a quantum system modeled by a quantum automaton, namely, a set of processes each of which is formalized as a quantum unitary transformation.

The undecidability of inherent ambiguity of a cfl was proved by. The essential thing is that the procedure outputs true if the code has an infinite loop, and does. Undecidable languages ryan bernstein 1 introductory remarks assignment 3 is available online, and is due a week from today 0519. That may be a good hint, and new computer designs should be supposed not to be able. Undecidable problems for contextfree grammars liacs. The correspondence f mapping n to e is simply fn 2n. This result is in contrast with probabilistic automata, for which both problems are undecidable. Can a turing machine accept a string of length 2014. The answer by apolge presents the proof that it is undecidable whether an arbitrary context free grammar is undecidable. This result is in contrast with the corresponding situation for probabilistic finite automata, for which it is known that strict and nonstrict thresholds both lead to undecidable problems. Recursive languages correspond to decidable problems.

However, if i understand the question correctly, youre referring to a problem of determining language l over the binary alphabet such that. We prove that this problem is decidable or undecidable depending on whether reco. Cs311 computational structures decidable and undecidable. 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. It has been widely studied and can be used to prove the undecidability of a number of other problems.

I would like to get an example if possible of an undecidable problem that is defined without using turing machines explicitly. We prove that this problem is decidable or undecidable depending on whether recognition is. Decidable and undecidable problems in matrix theory. This paper tackles three algorithmic problems for probabilistic automata on finite words. Check out the full advanced operating systems course for free at. What is the proof that the halting problem is undecidable. Undecidable languages in automata theory undecidable languages in automata theory courses with reference manuals and examples pdf. We show conditions under which planning is decidable and undecidable. The aim of this textbook is to provide undergraduate students with an introduction to the basic theoretical models of computability, and to develop some of the models rich and varied structure. This result is in contrast with the corresponding situation for probabilisticfinite automata for which it is known that strict and nonstrict thresholds both lead to undecidable problems. This result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and nonstrict thresholds both lead to undecidable problems. Is the following language l undecidable l m m is a turing machine description and there exists an input x of length k such that m halts after at most k steps. Classical problem becomes undecidable in a quantum setting. The problem of determining whether a quantum mechanical system has a spectral gap.

For undecidability in axiomatic mathematics, see list of. Given a language that is turingdecidable, if you add the empty string to the language then is the new language turingdecidable. I will explain and prove the statement of the title. Complexity, decidability and undecidability results for. Blondel, emmanuel jeandel, pascal koiran, and natacha portier abstract. Dragan, kent state university 4 countable sets example 1.

A problem is partially decidable, semidecidable, solvable, or provable if a is a recursively enumerable set. Many, if not most, undecidable problems in mathematics can be posed as word problems. We also introduce the concept of linear recurrence automata in order to show the. Decision problems on unary probabilistic and quantum automata. Undecidable problems about timed automata springerlink. Are there undecidable properties of linear bounded automata avoiding the empty set language trick. An undecidable language georgia tech computability. This is a contradiction with theorem f and the counterassumption does not hold. In this paper we obtain general results for undecidable first order decision problems about groups that is, problems about elements in a particular group, such as the word and. Using cantors definition of size we can see that n and e have the same size.

I convinced myself that this problem is decidable, but i am having trouble proving so. Undecidable languages are not recursive languages, but sometimes, they may be recursively enumerable. This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable in principle rather than in practice. This paper tackles three algorithmic problems for probabilis tic automata on finite words. A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. A problem is called partially decidable, semidecidable, solvable, or provable if a is a recursively enumerable set. Show that atm is reducible to the new problem b what does this mean and how do we show this. This is because if a is undecidable even when it can be. In quantum computing, quantum finite automata qfa or quantum state machines are a quantum analog of probabilistic automata or a markov decision process. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with skolems and positivity problems. Decidable and undecidable problems about quantum automata. A decision problem is a problem that requires a yes or no answer definition.

In computability theory, an undecidable problem is a type of computational problem that. I am very confused at this problem because from my understanding the halting states cannot transition to any other state, and in order to accept the empty string your start state would need to be your accept state. A study tanistha nayak, tirtharaj dash national institute of science and technology berhampur761008, india abstract an important question of quantum computing is that whether there is. Thats not something you can assume, i believe is actually incorrect, and i suspect thats what tryx was really trying to get at with his question. Undecidable problems about reachability of quantum. In particular, we study some promise problems in terms of classical and quantum finite automata in section 5, and obtain the following results. A problem is semidecidable if there is an algorithm that says yes. Which of the following problems about turing machines are solvable, and which are undecidable. A decision problem a is called decidable or effectively solvable if a is a recursive set.

Students who have already some experience with elementary discrete mathematics will find this a wellpaced first course, and a number of supplementary chapters introduce more advanced concepts. Promise problems solved by quantum and classical finite. It is also undecidable whether the shuffle of two timed regular languages is timed regular. Decidability of the equivalence and minimization of states d. Are languages that contain the empty string turingdecidable. If you like geeksforgeeks and would like to contribute, you can also write an article. Quantum finite automata, quantum pushdown automata. This result is in contrast with the corresponding situation for probabilisticfinite automata for which it is known that strict and nonstrict thresholds both lead to. This result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and nonstrict thresholds both lead to.

This is arguably the most famous of the undecidable problems. Some examples already appear on the wikipedia page. Our main result is that already its quasiidentities are undecidable. Partially decidable problems and any other problems that are not decidable are called undecidable.

Are there undecidable properties of nonturingcomplete. Grammar undecidable problems undecidability for unrestricted grammars. As pointed out below, the set of all strings of length 2014 is a regular language and therefore decidable. Department of software systems 186 ohj2306 introduction to theoretical computer science, fall 2011 27. We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds. I tried to think of a reduction from the halting problem. 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. Are problems in quantum information theory undecidable. They provide a mathematical abstraction of realworld quantum computers.

The proof relies on a recent result of slofstra in combinatorial group theory and. A problem that cannot be solved for all cases by any algorithm whatsoeverequivalently, whose associated language cannot be recognized by a. Decision problems on unary probabilistic and quantum. Our results on this topic solve an open problem posed by chapman 1987, and clear up some difficulties with his undecidability theorems.

Prove whether this language is decidable or undecidable. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. Partially decidable semidecidable and totally not decidable. The reachable sets are chosen to be boolean combinations of closed subspaces of the state hilbert space of the quantum system. 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. For those it is not possible to create an algorithm, efficient or. Gruska4 1department of computer science, sun yatsen university, guangzhou, 56, china. Decidable and undecidable problems in theory of computation. A decision problem a is decidable or effectively solvable if a is a recursive set. A set a is countable if either it is finite or it has the.