Decidable and undecidable problems about quantum automata torrent

Dragan, kent state university 4 countable sets example 1. Why is a quantum computer not capable of solving more problems than a classical computer. 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. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with skolems and positivity problems. 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. A decision problem a is decidable or effectively solvable if a is a recursive set. Decidable and undecidable problems in theory of computation. Complexity, decidability and undecidability results for. 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. 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. For those it is not possible to create an algorithm, efficient or.

Are there undecidable properties of linear bounded automata avoiding the empty set language trick. What are the most attractive turing undecidable problems. This result is in contrast with probabilistic automata. In computability theory, an undecidable problem is a type of computational problem that. 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 recognition is defined by strict or nonstrict thresholds. Some examples already appear on the wikipedia page. That may be a good hint, and new computer designs should be supposed not to be able. We prove that this problem is decidable or undecidable depending on whether recognition is. Gruska4 1department of computer science, sun yatsen university, guangzhou, 56, china.

If you like geeksforgeeks and would like to contribute, you can also write an article. I convinced myself that this problem is decidable, but i am having trouble proving so. 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. Using cantors definition of size we can see that n and e have the same size. In quantum computing, quantum finite automata qfa or quantum state machines are a quantum analog of probabilistic automata or a markov decision process. Quantum finite automata, quantum pushdown automata. Many, if not most, undecidable problems in mathematics can be posed as word problems. Let n be the set of natural numbers 1,2, and e is the set of even natural numbers 2,4. 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. As pointed out below, the set of all strings of length 2014 is a regular language and therefore decidable. Partially decidable semidecidable and totally not decidable.

Examples and counterexamples every contextsensitive grammar is recursive. This result is in contrast with probabilistic automata, for which both problems are undecidable. Blondel, emmanuel jeandel, pascal koiran, and natacha portier abstract. Cs311 computational structures decidable and undecidable. General problems for linear contextfree grammars are the topic of section 3. Which of the following problems about turing machines are solvable, and which are undecidable. Recursive languages correspond to decidable problems. The problem of determining whether a quantum mechanical system has a spectral gap. 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. Decidable and undecidable problems about quantum automata. A problem is called partially decidable, semidecidable, solvable, or provable if a is a recursively enumerable set. 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. 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.

An undecidable language georgia tech computability. Why is a quantum computer not capable of solving more. A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. We also introduce the concept of linear recurrence automata in order to show the. A problem that cannot be solved for all cases by any algorithm whatsoeverequivalently, whose associated language cannot be recognized by a. 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. Can a turing machine accept a string of length 2014. It is also undecidable whether the shuffle of two timed regular languages is timed regular. Reducibility how do we show a new problem b is undecidable. This paper tackles three algorithmic problems for probabilistic automata on finite words.

Undecidable problems for contextfree grammars liacs. Show that atm is reducible to the new problem b what does this mean and how do we show this. Are languages that contain the empty string turingdecidable. This is decidable as emptiness of contextfree languages is decidable and cfl. A correspondence system is a finite set of pairs of strings over an alphabet. We show conditions under which planning is decidable and undecidable. 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 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. Decidability of the equivalence and minimization of states d.

It has been widely studied and can be used to prove the undecidability of a number of other problems. 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. I tried to think of a reduction from the halting problem. 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.

A problem is semidecidable if there is an algorithm that says yes. Check out the full advanced operating systems course for free at. In particular, we study some promise problems in terms of classical and quantum finite automata in section 5, and obtain the following results. The emptiness problem asks, given some probability 0.

Undecidable problems about reachability of quantum. Undecidable problems about timed automata springerlink. The correspondence f mapping n to e is simply fn 2n. Undecidable languages ryan bernstein 1 introductory remarks assignment 3 is available online, and is due a week from today 0519. 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.

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. Department of software systems 186 ohj2306 introduction to theoretical computer science, fall 2011 27. Decidable and undecidable problems in matrix theory. I would like to get an example if possible of an undecidable problem that is defined without using turing machines explicitly.

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. Several types of automata may be defined, including measureonce and measuremany automata. 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. 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. Partially decidable problems and any other problems that are not decidable are called undecidable. Grammar undecidable problems undecidability for unrestricted grammars. Our main result is that already its quasiidentities are undecidable. The essential thing is that the procedure outputs true if the code has an infinite loop, and does. Given a language that is turingdecidable, if you add the empty string to the language then is the new language turingdecidable. 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. Tm was decidable, but that some other undecidable language bwas turingrecognizable. They provide a mathematical abstraction of realworld quantum computers.

This is because if a is undecidable even when it can be. For those cases where planning is decidable, we explain how the time complexity varies. Decision problems on unary probabilistic and quantum automata. 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. 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.

Cs311 computational structures decidable and undecidable problems 1 lecture 15 andrew black andrew tolmach monday, 24 may 2010. Are problems in quantum information theory undecidable. This paper tackles three algorithmic problems for probabilis tic automata on finite words. Classical problem becomes undecidable in a quantum setting. Are there undecidable properties of nonturingcomplete.

Lets assume that you have an procedure that determines whether a bit of code has an infinite loop. This is a contradiction with theorem f and the counterassumption does not hold. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. The question of whether a context free language is inherently ambiguous is a separate one. This is arguably the most famous of the undecidable problems.

Our results on this topic solve an open problem posed by chapman 1987, and clear up some difficulties with his undecidability theorems. Undecidable languages are not recursive languages, but sometimes, they may be recursively enumerable. We prove that this problem is decidable or undecidable depending on whether reco. The answer by apolge presents the proof that it is undecidable whether an arbitrary context free grammar is undecidable. The proof relies on a recent result of slofstra in combinatorial group theory and. The undecidability of inherent ambiguity of a cfl was proved by. However, if i understand the question correctly, youre referring to a problem of determining language l over the binary alphabet such that. I will explain and prove the statement of the title. For undecidability in axiomatic mathematics, see list of. A decision problem is a problem that requires a yes or no answer definition.