Discuss rice's theorem
WebAug 5, 2024 · Here's Rice's theorem from recursion theory: Let $\mathscr F$ be the class of all unary computable functions. Let $\mathscr A\subset \mathscr F$ be an arbitrary nontrivial property of computable functions ('nontrivial' means that there are both functions satisfying the property and functions not satisfying it). WebRice’s Theorem is kind of an analogue of the well-known saying “you can’t tell a book by its cover”. Instead it says, in general, “You can’t tell what a TM/program does just by looking …
Discuss rice's theorem
Did you know?
Web4 Rice’s Theorem Generalizing the arguments above, we will prove that essentially every nontrivial property of TM languages is undecidable. More precisely, Theorem 5 (Rice’s theorem). Any nontrivial property P of TMs is undecidable. Here a property is a collection of TM descriptions hMisuch that, for any two M 1 and M 2, if L(M 1) = L(M 2 ... WebRice's theorem says that for any subset F of the class T of partial computable functions, the set { i ∣ ϕ i ∈ F } is recursive iff F = ∅ or F = T. Let F be the set of partial computable functions that are constant on their domain.
WebAug 30, 2024 · My understanding of Rice Theorem: The purpose of this Theorem is to proof that some given language L is undecidable iff the language has a non-triv... Stack Exchange Network Stack Exchange network consists of 181 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, … WebDefinition of Rice's Theorem Let T be the set of binary encodings of all Turing Machines. T = { (M) : M is a Turing Machine with input alphabet {0, 1}}. Rice Theorem states that: If P is a subset of T such that: P != EMPTY that is there exists a Turing Machine M such that (M) is …
WebHow to Use Rice's Theorem in 5 Minutes Easy Theory 15.2K subscribers Subscribe 455 Save 26K views 2 years ago Here we look at the language of TMs that accept at most 3 strings, and show via... WebNow let’s proceed with the core of the proof of Rice’s theorem. First we’ll complete the core reduction under a set of assumptions about our property \(P\) . We’ll then discuss after …
WebJun 26, 2024 · Meta Discuss the workings and policies of this site ... Thank you for your excellent answer! I was under the impression that since Rice's Theorem is proved by using reductions, the two techniques would be essentially equivalent in scope. $\endgroup$ – MatteoBelenchia. Jun 26, 2024 at 17:05.
WebProof of Rice’s Theorem Rice’s Theorem If P is a non-trivial property, then L P is undecidable. Proof. Suppose P non-trivial and ;62P. If ;2P, then in the following we will be showing L P is undecidable. Then L P = L P is also undecidable. Recall L P = fhMijL(M) satis es Pg. We’ll reduce A tm to L P. Then, since A tm is undecidable, L P ... lauri tiitusWebJan 5, 2015 · Rice's theorem states that any nontrivial property P of a partial recursive function ψ e is undecidable (computably unsolvable by T e ). We take P to be decidable (either ψ e ( n) = 0 ∨ ψ e ( n) = 1 if P holds or does not hold, respectively). More directly, let 0 ′ be the degree of unsolvability of the problem for deciding if T e halts ... lauri tiensuuWebAlternative Proof Technique for Undecidability. We can use Rice’s Theorem to directly prove that a language is undecidable by showing that the language fulfills the two conditions of the theorem. Claim: E TM = { M ∣ M is a TM and L ( M) = ∅ } is undecidable. Proof. By Rice’s theorem, we must show that E T M satisfies two properties: Non ... lauri tannerWebRice's theorem is very simple once the basics are understood, but it has little implications ... whatever you are trying to do, is my gut feeling. – Raphael ♦ Mar 3, 2015 at 7:35 Add a comment 4 Answers Sorted by: 6 What you forget is that all the mappings you use have to be computable. lauri teivaalaWebThe Work–Energy Theorem In physics, the term work has a very specific definition. Work is application of force, f, to move an object over a distance, d, in the direction that the force is applied. Work, W, is described by the equation W = f d. Some things that we typically consider to be work are not work in the scientific sense of the term. lauri timonenWebAnswer (1 of 2): Consider the set of all Turing Recognizable(TR) Languages. Now, a property of languages is something that partitions this set into two sets of languages, one … lauri tiilikainenWebStrong Rice's Theorem Easy Theory 16.1K subscribers 3.4K views 2 years ago Reducibility - Easy Theory Here we prove a "stronger" version of Rice's theorem, which involves nontrivial... lauri tammela