Determine whether a Turing machine is a decider • Prove properties of the classes of recognizable and decidable sets Page 3
| Previous PDF | Next PDF |
[PDF] G223520: Honors Analysis of Algorithms
Therefore, L(M ) = L∗, and Turing-recognizable languages are closed under the star operation (d) Let L1 and L2 be two Turing-recognizable languages, and let M1 and M2 be TMs that recognizes L1 and L2 respectively We construct a TM M that recognizes L1 ∩ L2: On input w, 1
[PDF] Tutorial 3
Prove that the class of decidable languages is closed under union, concatenation and Kleene star Hence we have a decider for the concatenation of L1 and L2 We construct the following nondeterministic 2-tape Turing machine M: 1
[PDF] Lecture Notes 15: Closure Properties of Decidable Languages 1
Concatenation Both decidable and Turing recognizable languages are closed under concatenation I will give the proof for Turing recognizable languages The
[PDF] Homework 1 Solution along with Problem Session 1
23 fév 2007 · We need to show that a turing machine with a doubly infinite tape, D is note is that turing recognizable languages are NOT closed under com- for the complement is ML which on input w, accepts if ML rejects, and accepts
[PDF] CSE 6321 - Solutions to Problem Set 1
Show that the collection of decidable languages is closed under the following Proof Let L be a decidable language and M be the Turing machine that decides L 1 concatenation Solution: Proof Let L1, L2 be two recognizable languages
[PDF] CSE 105 theory of computation - UCSD CSE
Determine whether a Turing machine is a decider • Prove properties of the classes of recognizable and decidable sets Page 3
[PDF] CSE105 Homework 3 - UCSD CSE
We show that two stacks can simulate a TM, an extra stack does not lead to a more powerful For any two Turing-recognizable language L1 and L2, let M1 and M2 be the TMs that recognize NP is closed under union and concatenation
[PDF] 6045J Lecture 7: Decidability - MIT OpenCourseWare
Recursively enumerable languages – Turing The classes of Turing- recognizable and Turing-decidable Theorem 3: If L is Turing-decidable then Lc is T- decidable • Proof: decidable languages are closed under concatenation and
[PDF] Closure Properties of Decidable and Recognizable Languages
28 oct 2009 · In Theorem 3 21 we showed that a language is Turing-recognizable iff some enumerator enumerates it The class of decidable languages is closed under Union Intersection Complementation Concatenation Star
[PDF] Turing Machines - Washington
I've talked about most of this in class at one L is Turing decidable if, furthermore , M halts on all inputs regular sets are closed under ∪, ∩, complement class of Turing recognizable languages is not closed under complementation Proof:
[PDF] show that the language l an n is a multiple of three but not a multiple of 5 is regular
[PDF] show that x is a cauchy sequence
[PDF] show that x is a discrete random variable
[PDF] show that x is a markov chain
[PDF] show that x is a random variable
[PDF] show that [0
[PDF] show the mechanism of acid hydrolysis of ester
[PDF] show time zone cisco
[PDF] show ∞ n 2 1 n log np converges if and only if p > 1
[PDF] shredded workout plan pdf
[PDF] shredding diet
[PDF] shredding workout plan
[PDF] shrm furlough
[PDF] shuttle paris
CSE 105
THEORY OF COMPUTATION
Spring 2018
Today's learning goalsSipser Section 3.1
Design TMs using different levels of descriptions.Determine whether a Turing machine is a decider.
Prove properties of the classes of recognizable and decidable sets.Describing TMsSipser p. 184-185
Formal definition:set of states, input alphabet, tape alphabet, transition function, state state, accept state, reject state.Implementation-level definition:English prose to
describe Turing machine head movements relative to contents of tape. High-level desciption:Description of algorithm, without implementation details of machine. As part of this description, can "call" and run another TM as a subroutine.Language of a TMSipser p. 170
L(M) = { w | M accepts w}
If w is in L(M) then the computation of M on w halts and accepts. If the computation of M on w halts and rejects, then w is not in L(M). If the computation of M on w doesn't halt, then w is not in L(M) Deciders and recognizersSipser p. 170 Defs 3.5 and 3.6L is recognizedby Turing machine M if L(M) = L.
M recognizesL if M is a Turing machine and L(M) = L. M is a deciderif it is a Turing machine and halts on all inputs. L is decidedby Turing machine M if M is a decider andL(M) = L.
M decidesL if M is a decider and L(M) = L.
Classifying languages
A language L is
Turing-recognizableif there is a TM M such that L(M) = L in other words, if there is some TM that recognizes it. Turing-decidableif there is a TM M such that M is a decider and L(M) = L in other words, if there is some TM that decides it.Context-free languages
Regular languages
Turing decidable languages
Turing recognizable languages
An example
Which of the following is an implementation-level description of aTM which decides the empty set?
M = "On input w:
A.reject."
B.sweep right across the tape until find a non-blank symbol.Then, reject."
C.If the first tape symbol is blank, accept. Otherwise, reject."D.More than one of the above.
E.I don't know.
Extension
Give an implementation-level description of a Turing machine which recognizes(but does not decide) the empty set. Give a high-level description of this Turing machine.Another example
Suppose M1and M2are Turing machines.
Consider the new TM M = "On input w,
1.Run M1on w. If M1rejects, rejects. If M1accepts, go to 2.
2.Run M2on w. If M2accepts, accept. If M2rejects, reject."
What kind of construction is this?
A.Formal definition of TM
B.Implementation-level description of TM
C.High-level description of TM
D.I don't know.
Another example
Suppose M1and M2are Turing machines.
Consider the new TM M = "On input w,
1.Run M1on w. If M1rejects, rejects. If M1accepts, go to 2.
2.Run M2on w. If M2accepts, accept. If M2rejects, reject."
What's L(M)?
Is M a decider?
Closure
Theorem: The class of decidable languages over fixedȈis closed under union.
Closure
Theorem: The class of decidable languages over fixedȈis closed under union.
Proof: Let L1and L2be languages Ȉand suppose M1and M2are TMs deciding these languages. We will define
a new TM, M, via a high-level description. We will then show that L(M) = L1U L2and that M always halts.