Recall that a language L is called decidable there is some machine M such that if M is given any string w as input, M will give the output "I' if w E L, ", if w L. Decidable languages are also called recursive. A function is said to be computable, or recursive, if it is computed by some machine. There are uncom putable functions, such as the Busy Beaver function: http://googology.wikia.com/wiki/Busy_beaver function In fact, there are more uncomputable functions than computable functions. 1. True or False. T true, F false, and O open, meaning that the answer is not known to science at this time. In the questions below, P and NP denote P-TIME and NP-TIME, respectively. Every language generated by an unambiguous context-free grammar is accepted by some DPDA The language {a"b"ed n2 0 is recursive. Let L be the language over fa, b, c consisting of all strings which have more a's than b's and more b's than c's. There is some PDA that accepts L. d) -1 aigua The language Ia"b"c n20 is in the class P. There exists a polynomial time algorithm which finds the factors of any positive integer, where the input is given as a binary numeral (f)The language a"b" |n 20} is context-free The language a"b"c n 2 0) is context-free. (h)The language {a'bic* |j-ik is context-free The intersection of any regular languages with any context-free language is context-free If L is a context-free language over an alphabet with just one symbol, then L is regular. Recall that a langnnge L is called deadable there is some machine M such that if M is given any string as input, M will give the output "I if L. "O ftcg L. Decidable languages are also called recursive. A function is sald to be oputable, or recursive, if it is computed by some machine. There are uncom- patable functions, such as the Busy Beaver function: http://googology.wikia.com/viki/Busy_beaver function In fact, there are morputable functions than computable functions. 1. True or False. T = true, F = false. and O = open, meaning that the answer is not known to science at this time. In the questions below, P andNP denote P-TIME and NP-TIME, Tespectively Every language generated by an unambiguous context-free grammar is accepted by sone DPDA (b)--The language {e'V'"d" I ti2 0 is recursive. (c)Let L e the language over fa, b,c consisting of all strings which have more a's than bs and more 's than e's. There is some PDA that acoepts L The language is in the class P (e)There exists a polynomial time algorithm which finds the factors of any positive integer where the input is given as a binary meral. ) _ _ The larguage {a"6" | 3120) is context-free. The language is context-free. (h) _ The language {r,#1 j =it k} iscontext-free. The intesection of any regular languages with any context-free language is coutext-free. If L is a context-free language over an alphabet with just one symbol, then L is regular There is a deterministi e parser for any context-free grammar m)- The Boolean Cireuit Problem is in P (n)The Boolean Cireuit Problem is in Nc (o)The set of strings that your high school algebra teacher would accept as legitimate expressions There exists a polynomial tme algorithm which finds the factors of any positive integer The language consisting of all strings over [a, b which have more a's than b's is context-free. is a contexct-free language where the inpt is given as a binary numeral. (r)Every context-free lauin P Every language accepted by a nou-deterministic machine is accepted by some deterministic (t)The problenm of wbether two given context-free grammars generate the same language is (u)The problem of whether a given string is generated by a given context-free grammar is (v) Every bounded function is reemrsive. (w)There exists a mathematical proposition that can be neither proved nor disproved. There is a non-recursive fanction which grows faster than any recursive function. There exists a machine1 that runs forever and outputs the string of decimal digits of (the well-knoam ratio of the e of a circle to its diameter). (x)For every real number r, there exists a machine that runs forever and outputs the string of decimal digits of a Recall that a lagugeis called decidale there i ahiM uch that d3M giwn any string tp:/googology.wikia.com/iki/Bury beaver function sstable Suwti In fart, twee are thn compstale fuctio DPDA PN (o) Thr set of,tnip that your high Khol detra teader wuld .ep. as kritimar expresias p) __ Thrre exits a Pay.onial tine alprkIm which 1trls the tar, of say Peitin .teg", luve the ispat is give binary ral )Every contet-ree age is in Eery langgr arcepted boy aon-teministic machine is accepted by oe detlt decidable ()Every )Te eitsaahin that r wend stpts the string o decinal digits of (the well-sos ratio of the circundece ot a cleve to its diame cinal digits