can the union of two undecidable languages be finite

PDF	Undecidable Languages The set of decidable languages is infinite 10 True or false: If languages K and L are both undecidable then their union is also undecidable 11 True or

PDF	Decidable and Undecidable Languages Every TM for a semi-decidable+ language halts in the accept state for strings in the language but loops for some strings not in the language

No, there are many infinite languages that are decidable.
One trivial example is the language {n € N a^n} , i.e. the language of words that only contain the letter "a".
This language can be matched by the regular expression a* . so it is a regular language and thus decidable.

Can decidable languages be infinite?

There are many infinite languages which are decidable, for example Σ∗, or the language of all (binary representations of) primes.
However, in some sense "most" languages are undecidable, since there are uncountably many languages, but only countably many decidable languages.

Is the union of two undecidable languages decidable?

If L is the union of two regular languages, then its complement L is context-free.
If L is the union of two decidable languages, then L is decidable.
If L is the union of two undecidable languages, then L is undecidable.

Can an undecidable language be finite?

There are no regular languages which are undecidable and therefore there are no finite languages which are undecidable.

To see that the union of an undecidable language and a finite language must be undecidable, assume L union R is decidable where L is undecidable and R is a finite. That is, there is a TM that decides membership in L union R.

PDF	Final Exam Study Questions of the types of questions that we will ask on the exam—in particular there will If L is the union of two undecidable languages

PDF	Assignment 8: PDAs decidable problems Solutions (a) Can the union of two undecidable languages be finite? Solution. No: Since every finite language is decidable any two undecidable languages.

PDF	The Rational Subset Membership Problem for Groups: A Survey 18.12.2013 state) and qn ? F. Languages of the form L(A) for A a finite ... It is decidable whether the intersection of two given rational subsets.

PDF	Regular Separability and Intersection Emptiness Are Independent trios regular separability can be reduced to intersection emptiness or vice-versa. undecidable for CFL (by this we mean that both input languages are ...

PDF	CSE105 Homework 3 We show that two stacks can simulate a TM an extra stack does not lead to a more Notation for a)

PDF	DECISION PROBLEMS FOR NON-REGULAR LANGUAGES This homomorphisms and intersection with regular languages. A. Then

PDF	Extensions of -Regular Languages It says that the regular languages of finite words are the only decidable Boolean-closed full trio. We will define full trios4.

PDF	Regular Language Representations in the Constructive Type Theory 05.03.2018 2 The languages associated to the various representations of regular languages will always be decidable. 4 Deterministic Finite Automata.

PDF	Lecture Notes 15: Closure Properties of Decidable Languages 1 We will study the closure properties of decidable and Turing recognizable Both decidable and Turing recognizable languages are closed under union.

PDF	Automatic Equivalence Structures of Polynomial Growth that a regular language has growth O(nk) if and only if it can be written as a finite union of languages defined by regular expressions of the form x0y?.

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Final Exam Study Questions

If L has a finite fooling set, then L is decidable If L is the union of two regular languages, then its complement L is regular If L is the union of two regular languages, then its complement L is context-free If L is the union of two decidable languages, then L is decidable

PDF	Undecidability There are two types of TMs (based on halting): (Recursive) Recursive, RE, Undecidable languages LBA Union, intersection, concatenation, Kleene closure

PDF	What Makes Some Language Theory Problems Undecidable* undecidable because of the "ability to count" or "compare" in these languages tions of any counter machine can be represented as an intersection of two languages in ~ each L in ~o there is a finite set 271 C I such that L C 271" 1

PDF	Problem set 6 - Department of Computer Science at the University of convincing enough so that they can be easily made rigorous if necessary To review What is the infinite intersection of all the decidable languages? 21

PDF	Problem Set 5 - Comments - Department of Computer Science at the the original set would be countable, since the union of two countable sets must example, but showing that a known undecidable problem can be reduced to it) We can do this — since we know both languages are finite, from the pumping

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CSE105 Homework 3 - UCSD CSE

We show that two stacks can simulate a TM, an extra stack does not lead to a more powerful Notation for a), b) and e): for any two decidable languages L1 and L2, let M1 and M2 be the TMs We construct a TM M' that decides the union of L1 and L2: to the star of L and M' will accept w after a finite number of steps d

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CSE 105 Homework 7 Due: Monday December 4 - UCSD CSE

4 déc 2017 · Your assignments in this class will be evaluated not only on the correctness of your answers, Key Concepts Turing machines, recognizable languages, decidable languages, undecidability 1 (g) Recognizable sets are closed under intersection Correctness: We prove correctness by two directions

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

Union, intersection, set concatenation, Kleene-star, set subtraction, complement Answer: A set S is countable if it is finite or we can define a correspondence between S and Answer: P is the class of languages that can be decided by a deterministic Turing this is impossible, TM H must not exist, so ATM is undecidable

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6045J Lecture 7: Decidability - MIT OpenCourseWare

Definition: TM M decides language L provided that both of the following The classes of Turing-recognizable and Turing-decidable languages are Obviously • But the other direction does not hold---there are languages For union, accept if either accepts Prints a sequence of finite strings (possibly infinitely many)