Name: Student ID: 0 CSE 322 Spring 2010: Take-Home
Show that every infinite prefix-closed context free language contains an every infinite Turing-recognizable language has an infinite decidable subset.
Answers to the CSCE 551 Final Exam April 30
https://cse.sc.edu/~fenner/csce551/final-ans.pdf
Harvard University
Nov 11 2014 (A) To prove that L is not Turing-recognizable
CS46 lab 8
Mar 20 2022 Show that every infinite Turing-recognizable language has an infinite decidable subset. 4. Computable functions.
Solutions for Problem Set 7
Solution: Let L be an infinite recursively enumerable language. characterization of decidable languages in terms of enumeration: L1 is decidable iff ...
Homework 4 – Due Wednesday March 18
https://cs-people.bu.edu/mbun/courses/332_S20/handouts/hw4.pdf
Practice Problems for Final Exam: Solutions CS 341: Foundations of
In each part below if you need to prove that the given language L is decidable
Enumerators
(Sipser 3.19) Show that every infinite Turing-recognizable language has an infinite decid- able subset. (Hint: use the result from the previous problem.).
CS660 Homework 1
Apr 8 2018 True or false: every infinite Turing-recognizable language has an infinite decidable subset. (This comes from problem 1 on Problem Set 6
Enumerators
(Sipser 3.18) Show that a language is decidable iff some enumerator (Sipser 3.19) Show that every infinite Turing-recognizable language has an infinite ...
CS1010: Theory of Computation - Brown University
Turing Recognizable & Decidable Languages The set of strings that a Turing Machine M accepts is the language of M denoted as 6(=)or the language recognized by M –A language 6is Turing-recognizableif some Turing machine recognizesit •I e There exists a TM =such that =halts in the accept state for all and only the strings ??6
CSE 322 Spring 2010: Take-Home Final Exam SOLUTIONS Where
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
CSE 431 Spring 2006 Assignment - University of Washington
1 Prove that a language is decidable if and only if there is an enumerator that enumerates it in lexicographic order (Hint: Handle the case where the language is ?nite separately from the case when it is in?nite ) 2 Use the above to show that any in?nite Turing-recognizable language contains an in?nite decidable subset 3
CS46 lab 8 - Swarthmore College
Show that there is a decidable language C consisting of Turing machine descriptions such that every machine described in B has an equivalent machine in C and every machine described in C has an equivalent machine in B 6 (extra challenge) A TM is a language consisting of descriptions of Turing machines and it is Turing-recognizable Why does
CSE 431 Spring 2007 Assignment - University of Washington
an in?nite decidable subset 4 Let INFINITE PDA = {hMi M is a PDA and L(M) is an in?nite language} Show that INFINITE PDA is decidable 5 Show that the set of complex numbers QUADRATIC-ROOT = {x ? C there are integers a 6= 0 b and c such that ax2+bx+c = 0} is countable 6 (Bonus) Let C be a language Prove that C is Turing
Homework 9 Solutions - New Jersey Institute of Technology
We showed in a previous homework that the class of Turing-recognizablelanguages is closed under union soEQCFGis Turing-recognizable Here are the details of a TMTthat recognizesEQCFG wheres1 s2 s3 is anenumeration of strings in??in string order: = “On input G1 G2 whereG1andG2are CFGs: 0 Check ifG1andG2are valid CFGs
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.
Is there an enumerator for every string in a Turing-recognizable language?
(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. Then, there exists an enumerator E that enumerates all strings in A (in some order, possibly with repetitions).
Is E' a decidable subset of a?
Therefore, the language of E’ is also infinite. Finally, since E’ only prints strings in lexicographic order, its language is decidable as proved in (a). Thus, the language of E’ is an infinite decidable subset of A.
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.
CS46 lab 8
This homework is due at 11:59pm on Sunday, March 20. This is a 10-point homework. For this homework, you will work with a partner. It's ok to discuss approaches at a high level with other students, your discussions should be just with your partner. The only exception to this rule is work you've done with another studentwhile in lab. In this case, note who you've worked with and what parts were solved during lab. Your partnership's write-up and code is your own: donot share it, and do not read other teams' write-ups. If you use any out-of-class references (anything
except class notes, the textbook, or asking Lila), then youmustcite these in your post-homework survey. Please refer to the course webpage or directly ask any questions you have about this policy. The mainlearning goalof this homework is to work with and think about Turing machines and decidability. You should feel free as always to cite and use techniques and theorems from class or the textbook. 1.Pro vethat the follo winglanguage is decidable:
fhMi jMis a DFA and8w;ifw2L(M) thenwR2L(M)g 2. Sho wthat ALLDFAis decidable, whereALLDFAis dened as: ALLDFA=fhAi jAis a DFA andL(A) = g
(Hint: you may want to refer to the textbook for some other decidable languages related to DFAs, and recall back when we proved things like \regular languages are closed under intersection". I suggest you also look at the textbook solution for showing thatINFINITEDFA is decidable (Sipser 4.10), which is dierent from what any group came up with during lab.) 3. Sho wt hatev eryinnite T uring-recognizablelanguage has an innite decidab lesubset.4.Computable functions.Recall that a functionf: !iscomputableif some Turing
machineM, on everyw, halts and accepts with justf(w) on its tape. (a) Let f: !be a partial computable function which is one-to-one and onto. Prove thatf1is a total computable function. (b) Sho wthat if functions fandgare computable, then their compositionfgis computable.5.(extra challenge)(Sipser 3.17) LetB=fhM1i;hM2i;:::gbe a Turing-recognizable lan-
guage consisting of Turing machine descriptions. Show that there is a decidable language Cconsisting of Turing machine descriptions such that every machine described inBhas an equivalent machine inC, and every machine described inChas an equivalent machine inB.6.(extra challenge)ATMis a language consisting of descriptions of Turing machines, and it
is Turing-recognizable. Why does the previous question not imply thatATMis decidable? 1quotesdbs_dbs2.pdfusesText_2[PDF] show that f is continuous on (?? ?)
[PDF] show that for each n 1 the language bn is regular
[PDF] show that if a and b are integers with a ? b mod n then f(a ? f(b mod n))
[PDF] show that if an and bn are convergent series of nonnegative numbers then ? anbn converges
[PDF] show that if f is integrable on [a
[PDF] show that if lim sn
[PDF] show that p ? q and p ? q are logically equivalent slader
[PDF] show that p ? q and p ? q ? p ? q are logically equivalent
[PDF] show that p(4 2) is equidistant
[PDF] show that p2 will leave a remainder 1
[PDF] show that the class of context free languages is closed under the regular operations
[PDF] show that the class of turing recognizable languages is closed under star
[PDF] show that the family of context free languages is not closed under difference
[PDF] show that the language l an n is a multiple of three but not a multiple of 5 is regular
