Decidable and undecidable problems in matrix theory pdf

Decidable languagea decision problem p is said to be decidable i. Not all properties of programs are functional some properties of programs are decidable because they are not about the function the. Iterated function systems are used as tools to define. By inspecting the dfas transitions to see if there is any path to a final state.

N and square matrices a 1, a k, c, all of the same dimension and with real algebraic entries, decide whether c is contained in the semigroup generated by the matrix exponentials exp a i t, where i. Decidable and undecidable problems related to completely 0simple semigroups t. Assume, furthermore, that for each relation symbol r2. The wikipedia article on nphardness addresses part of your question in the second paragraph of the examples section it lists the halting problem as an example of an undecidable problem that is nphard because of how a turing machine may be transformed into truth value assignments. Decidable languages a language l is called decidable iff there is a decider m such that. With correct knowledge and ample experience, this question becomes very easy to solve. 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. Are there problems that cannot be if there is some turing machine that accepts every string in l and rejects every. Partially decidable semi decidable and totally not decidable. Undecidable problems in fractal geometry simant dube department ofmathematics, statistics, and computing science, university of new england, armidale nsw 2351, australia abstract. Undecidable languages are not recursive languages, but sometimes, they may be. For every matrix x, the sequence x k admits a subsequence that is a decidable and undecidable quantum automata problems 1471 cauchy sequence, by compactness. A decision problem p is decidable if the language l of all yes instances to p is decidable for a decidable language, for each input string, the tm halts either at the accept or the reject state as depicted in the. Contextfree languages are decidable theorem 9 every contextfree language is decidable.

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 conjugacy problems. Complexity of a decidable problem solution complexity is a measure of the number of elementary operations, say, additions, to decide a decidable problem. What is the difference between decidable and undecidable. The halting problem for turing machines is definitely undecidable. The problems studied are simply formulated, however most of them are undecidable. This problem can be seen as a continuous analog of babai et. Examples of undecidable problems for 2generator matrix. Has the halting problem of turing machine been proven to be decidable. If a problem is not semidecidable and not decidable.

Although it might take a staggeringly long time, m will eventually accept or reject w. 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. Three problems on the decidability and complexity of stability. Decidable and undecidable problems related to completely 0. Definition of undecidable problem, possibly with links to more information and implementations. List of undecidable problems from wikipedia, the free encyclopedia in computability theory, an undecidable problem is a type of computational problem that requires a yesno answer, but where there cannot possibly be any computer program that always gives the correct answer.

Decidability and undecidability stanford university. Trotter january 20, 1996 abstract the undecidable problems of the title are concerned with the question. This work is a survey on decidable and undecidable problems in matrix theory. In the case of deterministic nite automata, problems like equivalence can be solved even in polynomial time. The associated language is called a decidable language. Two notions of undecidability there are two common settings in which one speaks of undecidability. A problem is nphard if an oracle for it would make solving npcomplete problems easy i.

The method to prove undecidabilities is the one found by paterson pat in 1970 to prove that the mortality of finitely generated matrix monoids is undecidable. Decidable and undecidable problems in matrix theory 1997. For another survey of undecidable problems, see dav77. The emptiness problem asks, given some probability 0. One can trade the number of matrices with their dimension and show that matrix mortality is undecidable as well for two matrices. Decidable and undecidable problems turing machine pdf bitbin. Pdf this work is a survey on decidable and undecidable problems in matrix theory. What are the most attractive turing undecidable problems. And some of the problems we consider turn out to be decidable or to have unknown decidability status. 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.

An example of an easy to understand undecidable problem. Decidability and undecidability in toc geeksforgeeks. A problem that cannot be solved for all cases by any algorithm whatsoeverequivalently, whose associated language cannot. 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. Complexity is usually stated not in ops, but in time the notation big o describes the order of time involved, i. Basic papers on undecidable propositions, unsolvable problems and computable functions dover books on mathematics. An nphard is a problem that is at least as hard as any npcomplete problem therefore an undecidable problem can be nphard. Pdf decidable and undecidable problems about quantum. L1 known not to be in d l1 in d but l1 not in d r l2 new language whose if l2 in d so l2 not in d decidability we are trying to determine to show l 2 undecidable choose a language l 1. Proving undecidability acceptance language a tm m is a tm description and m accepts input w we proved atm is undecidable last class. Given a decider m, you can learn whether or not a string w. A decision problem p is called undecidable if the language l of all yes instances to p is not decidable. Turing, and post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by kleene and post includes initiation of the classification theory.

The algorithmic theory of matrix groups and semigroups is a staple of computational algebra 3 with numerous applications to automata theory and program analysis 7, 10,11,18,19,26 and has been. Decidable undecidable undecidable undecidable undecidable note. See also undecidable problem, np, npcomplete, solvable, tractable, computable. Dragan, kent state university 1 chapter 4 decidability contents decidable languages decidable problems concerning regular languages decidable problems concerning contextfree languages the halting problem the diagonalization method the halting problem is undecidable a turing. Identifying languages or problems as decidable, undecidable or partially decidable is a very common question in gate. Cubitt, david perezgarcia november 24, 2011 abstract 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.

To relate the solutions of two problems if a solution to a problem b can be used to give a solution to a problem a, it seems that a cannot be harder than b e. On the decidability of membership in matrixexponential. The problems studied are simply formulated, however most of them are. 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. Using that pcp is known to be undecidable for seven dominos, we obtain that matrix mortality is undecidable for sets of fifteen matrices. I suppose for a proof by contradiction that halt tm is decidable. Are there languages that are not decidable by any turing machine tm. That is there will always be a condition that will lead the turing machine into an infinite loop without providing an answer. This paper tackles three algorithmic problems for probabilistic automata on finite words. However, your ta is saying that you can make the strictly stronger statement that the set is not even semidecidable.

Citeseerx document details isaac councill, lee giles, pradeep teregowda. 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 language is called decidable or recursive if there is a turing machine which accepts and halts on every input string w. In this paper, a relationship between the classical theory of computation and fractal geometry is established.

Or, given a string of zeros and ones, is it a palindrome. Are problems in quantum information theory undecidable. Since we know atm is undecidable, we can show a new language b is undecidable if a machine that can decide b could be used to build a machine that can decide atm. These problems may be partially decidable but they will never be decidable. A problem is semi decidable if there is an algorithm that says yes. On the positive side, it is known that it is decidable for two matrices and for instance for an. The problems for which we cant construct an algorithm that can answer the problem correctly in finite time are termed as undecidable problems.

On the positive side, it is known that it is decidable for two matrices and for instance for an arbitrary number of upper. 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. A simple way to see this is to assume that it is decida. This implies that its undecidable, but isnt implied by it is undecidable. If you can figure out a systematic way an algorithm to answer the question correctly. Some examples already appear on the wikipedia page. List of undecidable problems wikipedia republished wiki 2. In all the undecidable decision problems we present, the source of the unde cidability can be traced back to a single undecidable decision problem, namely the halting problem, or equivalently the membership problem for listable sets see sections 2.