. State which of the following classes each of the given languages belong to, and then prove our claim: • Regular Context-free, but not regular (E requires a proof of non-regularity + a CFG or PDA to show context-freeness) Not context-free a) {a" bm | 0

. State which of the following classes each of the given languages belong to, and then prove our claim: • Regular Context-free, but not regular (E requires a proof of non-regularity + a CFG or PDA to show context-freeness) Not context-free a) {a" bm | 0

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Predicates

A predicate is a function defined with set of variables, which returns the result True or False. The output of a predicate is a Boolean value as a response when given a set of parameters:

Question

2. State which of the following classes each of the given languages belong to, and then prove
your claim:
Regular
• Context-free, but not regular (E requires a proof of non-regularity
+ a CFG or PDA to show context-freeness)
• Not context-free
a) {a" bm | 0<m <n}
b) {w e {a, b, c}* | w has the same number of a's, b's, and c's }
c) {a2" |n 2 0}
d) {wwreversew |w € {0,1}* }
e) language of palindromes over {a, b} that have the same number of a's and b's
f) { wv | w,v e {a, b, c}* such that w and v have the same length }
g) {w$x | w,x € {0,1}", and w is a substring of x} // here, $ is a symbol in the alphabet

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Can you please help me with parts E beause I am really really struggling.
1b) Let A = {aibjck∶0 ≤ i ≤ j ≤ k}. Use the pumping lemma for context-free languages to prove that A is not a context-free language. 1c) Let A = {w#w∶w ∈ {a,b}*}. Use the pumping lemma for context-free languages to prove that A is not a context-free language.
1) Given the following English descriptions of a language, write a regular expression that defines the language, and draw the state diagram of a DFA that accepts the language. For all languages, let Σ = {a, b}.a) The language consisting of all words having a number of a's that is a multiple of 3.b) The language consisting of all words that contain "babb".c) The language consisting of all words that end in "ba".d) The language consisting of all words that do not end in "ba".
8.3
Here in question given:- Given two languages: L1 = { x ∈{a,b}* | x starts with b} L2 = { x ∈ {a,b}* | x ends with a} Construct a FA for each of L1,L2. Be sure that the Q sets for the two FA are disjoint where the names of the states are not the same. Then using the construction technique, generate a FA that accepts L1*L2 where * is intersection. Draw the FAs.
2. Morphology, syntax (a) In German, the ending of a regular verb in present tense is normally t for third person singular, unless the stem ends on t or d, in which case the ending is et. Examples are: stem 3rd sing. lern lernt arbeit arbeitet red redet Draw a finite-state transducer that maps a stem to this verb form. To be precise, the input is the stem of a regular verb followed by the symbol #, and the output is the third person singular present tense form of that stem, without the final #. As transition label you can use the abbreviation other, which is short for a:a, b:b, c:C, e:e, ..., that is, a mapping from any letter (other than t or d) to that same •.•/
(1) Fill the blanks to complete the following sentences that describe the relations between regular expression, regular language, and regular gramma. You can also use your own statements to describe the relations. there is an NFA machine to (i) A language L is regular (ii) A language L is regular (ii1)A language L is regular it. there is a regular expression r to it. there is a regular grammar G to it.
2) Give examples of each of the following: a) A language that is not context free. b) A language that is context free but not deterministic context free. c) A language that is accepted by a deterministic pushdown automaton but is not regular.
2. Are the following languages context-free or non-context-free? • If a language is context-free, give a context-free grammar that generates it. • If a language is not context-free, prove this using the pumping lemma. A = { a*b'c*d² |k > i > 0, l>0 } B = {a²i+1fk+1c3l (2k+1q* | i > 1, k > 1, l > 1 } (a) (b)
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