If P = aabaab and = {a, b}, give a deterministic finite automaton for L(P), that is, the language of all strings which contain P as a substring.
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- 1. Show that the language of even strings over (0,1} that begin and end with 0 is regular. Give both the regular expression and finite automaton.Let Σ be the alphabet {a,b}. Let L be the language describe by Σ∗ − (ε|Σ∗b)aa(ε|bΣ∗), where the hyphen denotes set difference and ε de- notes the empty string. (Hint: L consists of the strings over Σ in which no maximal substring consisting solely of a’s is of length 2.) Draw a finite automa- ton that accepts L.Use a closure operation to reduce the language L of all even-lengthed strings of as and bs where both halves of the string end with an a, that is L = {w0aw1a | w0,w1 ∈ {a,b}∗ ∧ |w0| = |w1|}, to a simpler language L0 which must also be regular if L is regular. Use the pumping lemma to show L0 is not regular.
- Give a DFA over {a,b} that accepts all strings of length exactly 5 For each state in your automaton, give a brief description of the strings associated with that state.Design a deterministic finite state automaton (DFA) that accepts exactly the strings over the alphabet {A, B, ...,Z} that contain at least two R, at most one T, and where every E comes after some S (there may be other letters in between). For instance, your DFA should accept the strings: • MYSTICWARRIORS • MARSMATRIX • SHOCKTROOPERS • CONTRAHARDCORPS STRIDER but not the strings • CRAZYTAXI (it does not contain at least two Rs) LASTRESORT (it contains more than one T) AFTERBURNER (there are Es without a S somewhere before them) • BATTLECIRCUIT (all of these at the same time) Clearly indicate the meaning of each state. One way to do this is to number the states and have a numbered list of their meanings, but any readable method you use to label and explain your states is fine. Hint: there are three separate conditions accepted strings must meet; states will need to encode whether or not each one is met (or perhaps partially met). You can label an edge with the word “else" to indicate it…Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar. I want a CFG
- Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar.Let E = {0,1} and La be the language of all strings that represent binary numbers that are not divisible by 4. L, be the language of all strings that end with 0. d) We know that La and L, are both regular. But what about their complements, La and L,? Justify your answer. e) Show that (L. n L,), the intersection between La and Lp, is also a regular language.Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar. Please make sure to test the answers onhttps://web.stanford.edu/class/archive/cs/cs103/cs103.1156/tools/cfg/
- Build a DFA and TG that accepts all those strings that have an ‘oddnumber of a’s’ but ‘any number of b’s’. DFA (deterministic Finite Automata) TG (Transition Graph) Theory of autometaProve that the language L2={} is not regular language with the pumping lemma.Suppose L is a subset of {a, b}*. If xo, x1,... is a sequence of distinct strings in {a, b}* such that for every n20, xn and xn+1 are L-distinguishable, does it follow that the strings xo, X1,... are pairwise L- distinguishable?