SQUARE: Valid Proof? There are 15 questions, a few True/False but mostly MultipleChoice. Undecidable languages are … The existence of certain malware unpacking behaviour in code is shown to be decidable and NP-complete [3]. A decision problem P is called “undecidable” if the language L of all yes instances to P is not decidable. The halting problem can be used to show that other problems are undecidable. Generally, all the undecidable problems revolve around the difficulty of determining properties about the input and output of programs. In this section, we will discuss all the undecidable problems regarding turing machine. Let be an alphabet containing at least two symbols. 1) This is a variation of Turing Machine Halting problem and it is undecidable. The reduction is used to prove whether given language is desirable or not. This is often done via an intermediate step, where a RAM machine with a single register is used. •Example: 6x3yz2+3xy2-x3-10 has root x=5, y=3, z=0 General algorithm for Problem 10 does not exist! • EDFA = { M ⃒M is a DFA and L(D) = ∅} ‣By inspecting the DFA’s transitions to see if there is any path to a final state. This problem has been solved! This closes the gap between decidable and undecidable second-order uni cation problems w.r.t. A decision problem is decidable if there exists a decision algorithm for it. In other words, the decidable languages are a subset of the semi-decidable languages. A similar result exists, where, under some 2 Properties of Languages Any set of languages is a property of ... which would also be decidable by the lemma. P3 is undecidable if P3 is reducible to P2. ELBA is undecidable. More undecidable problems O C D O. The Totality Problem is Undecidable. We adopt the model presented in [EWY98]. In Python, the code would look like this: # E(M) is a decider for E TM = {Machines that recognize empty langs} def E(M): M1 = Some TM that rejects all strings (ie L(M1) = {}) return EQ(M, M1) # EQ(M, M1) is a decider for EQ TM # = {Pairs of machines that … Decidable: If the problem and its complement are both semidecidable (or recursively enumerable), then the problem is decidable (recursive). Undecidable: If the problem is semidecidable and its complement is not semidecidable (that is, is not recursively enumerable). The Value 1 Problem is the special case of the Isolation Problem when λ= 1 or λ= 0. Decidable Undecidable Undecidable Undecidable Undecidable Undecidable Lecture 17: Proving Undecidability 22 Next Class •Examples of some problems we actually care about that are undecidable •Are there any problems that we don’t know if they are decidable or undecidable? Suppose, if a language is not even partially decidable, then there is no Turing machine that exists for the respective language. 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. Note that there is some ambiguity in problem (1). Rice’s Theorem and Other Undecidable ProblemsRice’s Theorem Rice’s Theorem (1) IWe have shown that a number of (related) problems are undecidable: I special halting problem K I general halting problem H I halting problem on empty tape H 0 IMany more results of this type could be shown. */*** (5) Everyone Wants to Feel Needed, Sometimes (From Michael Sipser, Introduction to the Theory of Computation, 2nd ed., Problem … The problems which have no algorithm, regardless of whether or not they are accepted by a turing machine that fails to halts on some input are referred as: a. Decidable: b. Undecidable: c. Computable: d. None of the mentioned We identify a decidable synthesis problem … An undecidable problem is a computing question that cannot be resolved with the use of one algorithm. A decision problem A is called decidable or effectively solvable if A is a recursive set and undecidable otherwise. If you assume that the inputs can only be natural numbers then your solution works and the problem is decidable. We will need the following fact: Enumerate the turing machines as T M n. For every computable Q ( x, y), there is an e so that T M e ( y) … 1. Decidable and Undecidable problems in Theory of Computation. Rice’s Theorem and Other Undecidable ProblemsRice’s Theorem Rice’s Theorem (1) IWe have shown that a number of (related) problems are undecidable: I special halting problem K I general halting problem H I halting problem on empty tape H 0 IMany more results of this type could be shown. Undecidable problems are two types: Partially decidable (Semi-decidable) and Totally not decidable. Computer scientists and mathematicians have discovered many more undecidable problems. So we want to imitate the proof that H a l t s is undecidable and see what happens. 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). Undecidable Problems. (a) Decide whether M halts on some input within 2021 steps. problem is undecidable even for a very restricted form of communication be-tween the control unit of a system and the tasks. We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? Which one of the following is TRUE? Undecidable Problems (unsolvable problems) Undecidable Languages Fall 2006 Costas Busch - RPI Undecidable Problems (unsolvable problems) Undecidable Languages Theorem: Proof: Assume for contradiction that the halting problem is decidable; (The halting problem is unsolvable) is undecidable we will obtain a … De nition I Let A, B be languages over . More Undecidable Problems Rice’s Theorem Post’s Correspondence Problem Some Real Problems. Post Correspondence Problem The Post Correspondence Problem (named after Emil Post) is a particularly simple un-decidable problem that is useful for establishing the undecidability of, for instance, many properties concerning context-free grammars. The problems studied are simply formulated, however most of them are undecidable. This happens, for example, for one-variable problems where the variable occurs at most twice (because rigid E-unification is decidable for just one equation). The essence of "reducing one problem … Decidable and Undecidable Problems in Schedulability Analysis 237 automata is undecidable [ACH+95] there is no guarantee for termination in the general case. We will use $K$ to denote the undecidable set corresponding to the halting problem. • Use reduction from a non-semidecidable problem like HP. The decidability of the Value 1 Problem was an open question. Hopefully, our result can be The biggest issue is that we cannot directly plug our function into itself for a contradiction. Semi-decidable Problems A semi-decidable problem is subset of undecidable problems for which Turing machine will always halt in finite amount of time for answer as ‘yes’ and may or may not halt for answer as ‘no’. Undecidable problems are a subcategory of unsolvable problems that include only problems that should have a yes/no answer (such as: does my code have a bug?). So we want to imitate the proof that H a l t s is undecidable and see what happens. We can construct an undecidable problem which is not NP-hard using diagonalization. Viewed 1k times 9. The associated language is called a decidable language. 2)CFL are not closed under complement so it is undecidable. Of course, this depends on the choice of M. The history of theoretical computer science is interesting in its own right, especially given Hollywood’s recent interest in Turing. languages = the set of all Undecidable language -– A decision problem P is said to be undecidable if the language L of all yes instances to P is not decidable or a language is undecidable if it is not decidable. An undecidable language maybe a partially decidable language or something else but not decidable. Active 9 years, 5 months ago. Namely, a decidable problem is a set of natural numbers whose characteristic function is computable by a Turing machine. • Because the answer is a contradiction, such a program cannot exist –The problem is therefore undecidable –This is called the Halting Problem, and the contradiction proved by Alan Turing We also prove decidability when no variable occurs more than once, hence significantly narrowing the gap between decidable and undecidable second-order unification problems … The cases discussed in 8.2 on that page should use “semi-decidable (and not decidable).” As another example, the list of undecidable problems on page 173 contains: “Does M halt on w?” where M is a fixed TM, and w is a varying input word. See also decidable problem, unsolvable problem, undecidable language, ... 1999, "undecidable problem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. It is known that P1 is decidable and P2 is undecidable. An undecidable problem is a set of natural numbers not computable in this way. The biggest issue is that we cannot directly plug our function into itself for a contradiction. An undecidable language may be partially decidable but not decidable. Definition: A decision problem that can be solved by an algorithm that halts on all inputs in a finite number of steps. Our goal is to identify as closely as possible the borderline between decidable and undecidable problems in schedulability analysis using timed automata. We will need the following fact: Enumerate the turing machines as T M n. For every computable Q ( x, y), there is an e so that T M e ( y) = Q ( e, y). (But not all choices are as simple and elegant.) A decision problem P is undecidable if the language L of all yes instances to P is not decidable. One type of reduction: mapping reduction. QFA undecidable decidable undecidable decidable In this contribution, we consider the problem of determining for a quantum au-tomaton A and threshold λ if there exists a word w for which Val A(w) ≥ λ and if there exists a word w for which Val A(w) >λ. The problems for which we can’t construct an algorithm that can answer the problem correctly in finite time are termed as Undecidable Problems. These problems may be partially decidable but they will never be decidable. See the answer. a. P3 is decidable if P1 is reducible to P3: b. P3 is undecidable if P3 is reducible to P2: c. P3 is undecidable if P2 is reducible to P3: d. P3 is decidable if P3 is reducible to P2's complement This result is in contrast with the corresponding situation for … CSCI 2670 Decidability (What, stu is unsolvable?) Namely, a decidable problem is a set of natural numbers whose characteristic function is computable by a Turing machine. An undecidable problem is a set of natural numbers not computable in this way. ... • Some properties of programs are decidable because they are not about the function the program computes, but instead, are about some details of the program itself •Examples: – the program contains the transition ((q,0),(p,1)) Kublanovskii, S. Margolis, M.V. Warmup 6: TMs, Recursive, R.e., Decidable and Undecidable Testlet 6 will be administered on Canvas. Proof : ⇐ Assume A ≤m ATM. Undecidable Problems Costas Busch - LSU * Costas Busch - LSU * Recall that: A language is decidable, if there is a Turing machine (decider) that accepts and halts on every input string Turing Machine Input string Accept Reject Decider for Decision on halt YES NO Costas Busch - LSU * Undecidable Language there is no Turing … An Undecidable Problem for Context Free Languages The following language/problem is NOT decidable. A decision problem is said to be decidable if there exists an effective method or algorithm that returns a correct yes/no answer to that problem. ... Decidable Undecidable Undecidable Undecidable Undecidable Note: for PS5 problems 2 and 4, … (b) Decide whether M … Run M on w. Although it might take a staggeringly long time, M will eventually accept or reject w. The set R is the set of all decidable languages. halting problem, Post's correspondence problem. 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. • Use reduction from an undecidable problem like HP. P3is undecidable if P2 is reducible to P3. 2 Preliminary De nitions We assume that the reader is familiar with uni cation problems, second-order typed -calculus and related topics. Decidable and Undecidable Problems 1 Lecture 15 Andrew Black Andrew Tolmach Monday, 24 May 2010. Any question not answered will be graded as incorrect. A language is said to be Decidable if there is a Machine that will accept strings in the language and reject strings not in the language. Determining whether or not a function F is total is undecidable. Assume the problem is decidable, Strategy to prove a problem is undecidable: Given a TM M = Q, , test if La(M) = Claim: is undecidable … So that’s an algorithm which solves this problem. D Sub must be a decidable subset of D Prob. 9 August 2004. Tutorial Exercises 1. The decidability of the Value 1 Problem was an open question. Go over this whole proof again … w ∈ L ( G) L ( G) = ϕ. L ( G) = Σ ∗. However, if you say the problem is decidable, then you should describe a TM that decides it (You do not have to … recognize the same language). Problem 5.22: Prove that A is Turing-recognizable iff A ≤m ATM. Time Limit = 20 minutes. D8. This subject involves decision problems, questions with yes or no answers. Decidable Languages A language L is called decidable iff there is a decider M such that (ℒ M) = L. Given a decider M, you can learn whether or not a string w ∈ (ℒ M). Let L be any language with property P, and let M L be a TM that accepts L. Undecidable Problem about Turing Machine. Hall, S.I. Semi-Decidable problems are those for which a Turing machine halts on the input accepted by... Undecidable Problems –. Theorem: The Post’s correspondence problem is undecidable when the alphabet has at least two elements. Moreover, we introduce a new class of probabilistic automata, ♯-acyclic automata, for which the Value 1 Problem is decidable. 24 These came to be known as undecidable problems, while those that can be solved mechanistically were called decidable. Mathematician Gareth Jones on Gödel’s incompleteness theorem, the halting problem and why the subsets of the natural numbers are uncountably infinite. The essential idea behind the model is to use a timed automaton (control automaton) to describe the release (or ar-rival) patterns of the tasks. ... Decidable Undecidable Undecidable Undecidable Undecidable Note: for PS5 problems 2 and 4, you may use Rice’s theorem to get an intuition Proof will involve the following Suppose there’s some TM H that decides HALT. Then a DFA that accepts the complement of L, i.e. This result is in contrast with the corresponding situation for probabilistic fi- nite automata for which it is known that strict and non-strict … A problem is undecidable if it is not decidable. Paul Goldberg Intro to Foundations of CS; slides 3, 2017-18 19/42 Trotter January 20, 1996 Abstract The undecidable problems of the title are concerned with the question :- is a given nite semigroup embeddable in a given type of completely 0-simple semi … IEQ CFG = fhG;HijG;H are CFGs and L(G) = L(H)g Context free grammars are not closed under complementation or intersection, and so we cannot use (L(G) \L(H)) [(L(H) \L(G)) as was done for EQ DFA. The decision problem … Theory of computation | Decidable and undecidable problems Semi- Decidable Problems –. This means there are problems (and possibly, or probably, an infinite number of problems) that are undecidable, and not related to the Halting problem. Otherwise it is undecidable. A problem is a yes/no question about a given input. Semi decidable: A problem is semi-decidable if there is an algorithm that says yes. ∑* – L, can be obtained by swapping its accepting states with its non-accepting … In these cases, knowing that certain problems are undecidable could give physicists a new perspective of these problems. Therefore ATM is decidable. I Function f is called the reduction of A to B. We show that the Value 1 Problem is undecidable. Undecidable language-– A decision problem P is said to be undecidable if the language L of all yes instances to P is not decidable or a language is undecidable if it is not decidable. De nition We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict thresholds. P3 is decidable if P1 is reducible to P3. A.X is decidable B. X is undecidable but partially decidable C. X is undecidable and not even partially decidable D. X is not a decision problem Undecidability Answer: b 14. We say that a problem is decidable if there is an algorithm to solve it, … The essential idea behind the model is to use a timed automaton (control automaton) to describe the release (or ar-rival) … Let L(R) be the language represented by regular expression R. Let L(G) be the language generated by a context free grammar G. Abstract. B We can formulate this problem as showing the decidability of A=fhGijG is a CFG over f0;1g and L(1)\L(G)6=?g B We know that 1 defines a regular language, that L(G) is a CFL, and that L(1)\L(G) is a CFL. Decidable and Undecidable Languages The Halting Problem and The Return of Diagonalization Friday, November 11 and Tuesday, November 15, 2011 Reading: Sipser 4; Kozen 31; Stoughton 5.2 & 5.3 30-2 Recursively Enumerable Languages L(M) = {w | w is accepted by the Turing Machine M} The recursively enumerable …
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