o Find C F Gs for the following language over the alphabet E= {a by: All...
8 Find CFGs that for these regular languages over the alphabet a, b. Draw a Finite Automata first and use this to create the CFG (a) The language of all words that consist only of double letters (aa or bb) (b) The set of all words that begin with the letter b and contains an odd number of a's or begin with the letter a and contains an even number of b's.
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w | the length of w is at least 2 and has the same symbol in its 2nd and last positions} (b)Draw the state diagram for an NFA for accepting the following language over alphabet {0,1} (Use as few states as possible): {w | w is of the form 1*(01 ∪ 10*)*} (c)If A is a language with alphabet Σ, the complement of A is...
4.[10 points] Let A be the language over the alphabet E-(a, b} defined by regular expression (ab U b)*a U b. Give an NFA that recognizes A. Draw an NFA for A here.
4.[10 points] Let A be the language over the alphabet E-(a, b} defined by regular expression (ab U b)*a U b. Give an NFA that recognizes A. Draw an NFA for A here.
Suppose that we have a language L dened over the alphabet {a, b, c} and suppose that L is context-free. We define a new language pm(L) to be the setof all permutations of all words in L. For example, if L = {abc, aab} then pm(L) = {abc, acb, bac, bca, cab, cba, aab, aba, baa}. Show that pm(L) need not be context-free by giving an example of a language L that is context-free but where pm(L) is not context-free.
1. Consider the alphabet {a,b,c}. Construct a finite automaton that accepts the language described by the following regular expression. 6* (ab U bc)(aa)* ccb* Which of the following strings are in the language: bccc, babbcaacc, cbcaaaaccbb, and bbbbaaaaccccbbb (Give reasons for why the string are or are not in the language). 2. Let G be a context free grammar in Chomsky normal form. Let w be a string produced by that grammar with W = n 1. Prove that the...
************Theory of Computing ***************** 1. Generate a regular expression of “all words over the alphabet Σ = {a b} that either begin with a and end with b OR begin with b and end in a.” Thus, the first few shortest words in this language are “ab” “ba” “aab” “baa” “abb” “bba” “aaab” etc. So, if a word begins with a it must in end b, and if it begins with b it must end in a. 2. Consider the...
3) Construct a regular expression defining each of the following languages over the alphabet {a, b}. (a) L = {aab, ba, bb, baab}; (b) The language of all strings containing exactly two b's. (c) The language of all strings containing at least one a and at least one b. (d) The language of all strings that do not end with ba. (e) The language of all strings that do not containing the substring bb. (f) The language of all strings...
This is from CS 4110
1. Find CFGs that generate these regular languages over the alphabet 2 - la bl: (i) The language defined by (aaa + b)*. (iv) All strings that end in b and have an even number of b's in total (vi) All strings with exactly one a or exactly one b.
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt) Draw an automaton accepting L (ideally, deterministic).
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe...
. Terminals: • Any character from the alphabet is a terminal . Epsilon (E) is expressed as: le, leps or lepsilon The empty set is expressed as: lemp or lemptyset • Operations (R is a regular expression) o Union is expressed as RIR o Star as R* o Concatenation as RR o Plus as R+ Problem For the following regular expression: (Elab Over the alphabet: {a,b} Give 2 words that the regular expression recognizes and 3 words that the regular...