CS 373: Theory of Computation

L is said to be Turing-decidable (or simply decidable) if there exists a TM M which decides L. • Every finite language is decidable: For example by a TM that 

BBM401-Lecture 7: Decidable Languages and the Halting Problem

Every finite language is decidable: For e.g. by a TM that has Proposition. If L and L are recognizable

DECIDABLE MODELS t

PROOF. Every recursive type is realized in some decidable model. If there were a finite number of decidable models realizing them all then there would be.

Practice Problems for Final Exam: Solutions CS 341: Foundations of

Answer: A language whose complement is Turing-recognizable. Prove that ATM is undecidable. You may not cite any theorems or corollaries in your proof.

COMP481 Review Problems Turing Machines and (Un)Decidability

So to show a language L is not recursive using Rice's Theorem

Theory of Computation

the binary representation into base 10 and then check whether the any finite language given extensively is recursive

Languages and Finite Automata

on every input string. Also known as recursive languages ... Every decidable language is Turing-Acceptable ... Problem: We will show it is decidable ...

Recursive functions and existentially closed structures

Jul 23 2019 Proof: Let S ? T be decidable. ... in Proposition C.1 that any finite (or uniformly recursive) set of rp and trf is representable in a.

Decidability and ?₀-Categoricity of Theories of Partially

Every Ho-categorical theory of reticles has a decidable theory. for a finite language even one in each Turing degree. In actuality

CSE 135: Introduction to Theory of Computation Decidability and

L is said to be Turing-decidable (Recursive or simply decidable) if there exists a TM M which decides L. ? Every finite language is decidable 

Decidability and Undecidability - Stanford University

Decidable Languages A language L is called decidable iff there is a decider M such that (? M) = L Given a decider M you can learn whether or not a string w ? (? 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 L ? R iff L is decidable

CSE 322 Spring 2010: Take-Home Final Exam SOLUTIONS Where

Prove that any finite language (i e a language with a finite number of strings) is regular Proof by Induction: First we prove that any language L = {w} consisting of a single string is regular by induction on w (This will become the base case of our second proof by induction) Base case: w = 0; that is w = ?

6045: Automata Computability and Complexity Or Great

decidable Proof: – Suppose – Designa that new decides machineM L ?thatbehaves IfMacceptsM?rejects IfMrejectsM?accepts – Formallycandothisbyjust interchanging qlike acc q and Then c M?decidesL is M rej T- but: ecidableandrecognizable languages • AbasicconnectionbetweenTuring-recognizable andTuring-decidablelanguages:

Decidable and Undecidable Languages - Wellesley College

The recursive languages = the set of all languages that are decided by some Turing M hi ll l d ib d b Dec = Recursive (Turing-Decidable) Languages CFL = Context-Free Languages anbn wwR anbncn ww semi-decidable+ decidable Machine = all languages described by a non-looping TM These are also called theTuring-decidableor decidable languages

Lecture 17: Proofs of Proving Undecidability

To prove a language is decidable we can show how to construct a TM that decides it For a correct proof need a convincing argument that the TM always eventually accepts or rejects any input Lecture 17: Proving Undecidability 4 Proofs of Un decidability How can you prove a language is un decidable ? Lecture 17: Proving Undecidability 5

Searches related to prove that any finite language is recursive decidable filetype:pdf

a Show that for any infinite language L L is decidable iff some enumerator TM enumerates L in lexicographic order Proof (Æ) Let L be a decidable language Then there exists a decider TM D such that L(D) = L We can use D to construct an enumerator E for L as follows: E = “Ignore the input 1

How do you show that finitetm is undecidable?

is a TM and L(M) is finite}. Show that FINITETMis undecidable by giving a reduction from a known undecidable language to FINITETM. For your reduction, you may use any of the languages shown to be undecidable in Section 5.1 in the textbook (up to Theorem 5.4 and its proof).

How many points does it take to prove a decidable language?

(30 points: 15, 15 points)For the following proofs, you may use high-level descriptions of the required TMs. a. Show that for any infinite language L, L is decidable iff some enumerator TM enumerates L in lexicographic order.

Why L1-L2 is not decidable?

We know that L2 is Turing- recognizable but not decidable. Now L1-L2is the complement of the language L2. If we have a recognizer for a language and its complement, then we have a decider for the language. This is a contradiction, since ATMis undecidable. Hence we cannot always build a recognizer for the language L1-L2.

Does every infinite Turing-recognizable language have an infinite decidable subset?

Show that every infinite Turing-recognizable language has an infinite decidable subset. (Hint: Use the result in (a) and the result you know regarding Turing- recognizable languages and enumerator TMs (Theorem 3.21 in the text)). Let A be an infinite Turing-recognizable language.