Let E be an alphabet and A C E*. (a) If c E £ and AC E*, we define APPEND.(A) as {wc ɛ E* | w E A}. Prove that, if A is a regular language, then APPEND(A) is a regular language. (b) Let Da be a DFA recognizing A. Describe an NFA NA recognizing APPEND.(A) using only one more state than DA. Give a brief argument that your NFA recognizes A.

Let E be an alphabet and A C E. (a) If c E £ and AC E, we define APPEND.(A) as {wc ɛ E* | w E A}. Prove that, if A is a regular language, then APPEND(A) is a regular language. (b) Let Da be a DFA recognizing A. Describe an NFA NA recognizing APPEND.(A) using only one more state than DA. Give a brief argument that your NFA recognizes A.

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

See similar textbooks

Similar questions

1.Let Σ = {a, b, c} and f : Σ∗ → Σ ∗ the function that for input w yields the string obtained by duplicating each a. E.g. f(baaca) = baaaacaa. Prove that if L is a regular language, then so is {f(w) | w ∈ L}. [Hint: Use induction on regular expressions.] 2.Assume given a non-basic language K . Find an infinite collection of basic languages, all different, whose intersection (i.e. the strings that are in at least one of them) is not basic. Hint: This problem is dual to the previous one. But in place of the union of trivial finite languages, consider here the intersection of trivial co-finite languages.
Show that the language S is decidable, where S is defined as follows. S = {(M) | M is a DFA that accepts wf whenever it accepts w}.
For each of the following regular expressions over Σ = {a, b}, state 5 strings that are in the language of the regular expression, and 5 strings that are not. 1. (a∗b)∗|a∗2. (Σ∗aaΣ∗)|(Σ∗bbΣ∗)|(ab)∗|(ba)∗|a|b
Let Σ={a,b}. For each of the following languages over Σ, prove that the language is regular (a) La={w∈Σ∗:n0(w)is divisible by 4 andwends in aab}
Question 1 Let LC * be a regular language over some alphabet Σ. The Kleene-closure L* of L is given by {V1V2 • Vn | n ≥ 0, V1, V2, . . . , Vn € L}. (a) Suppose DFA D = (Q, Σ, 8, qo, F) satisfies L(D) = L. Construct an NFA N = (Q', Σ, 8', %, F') such that L(N) = L*. L* (b) Prove by induction on n that each word v₁v2 Un with n ≥ 0, V₁, V2, ..., Un E L is accepted by the NFA N proposed in item (a). (c) Prove that each word accepted/recognized by the NFA N proposed in item (a) is a word of the language L*.
Please solve complete
Question 1.2. Let G be a CFG. Let B be the language defined as B = {(M, w) | M is a DFA and w E L(G) N L(M)}. Prove that B is decidable.
Question 3. Consider the language L = {w€ {0, 1}* | the strings 01 and 10 occur the same number of times in w). Is this language regular or non-regular? Prove by building a DFA (if regular) or using the pumping lemma (if non-regular)
Given a ∈ {0, 1} *. let V(a) be decimal value when a is binary representation i.e. V(1111) = 15 Given a decimal d >= 2 define a language: ? = {a ∈ {0, 1} * , V(a) is divisible by d} Prove that ? is regular.
Question 5 Let I be the set of all even length binary strings. (So I is decidable.) Give an example of a language K ⊆ I with K undecidable. Here you need to define the set K and state your reasoning why the K you define is undecidable. Full explain this question very fast solution sent me step by step text typ work only
Design a deterministic finite-state automaton over the alphabet {a; b; c}that accepts words where each character is immediately followed by atleast one identical character. For example, it accepts the wordsY(gamma sigh), aa, aaa,aabbbbaacc, but it rejects the words a, baba, cbbba. Write the transition function of the automaton as a table and draw the automaton in the form of a transition diagram. Try to design the simplest possible automaton, i.e., an automaton with the smallest number of states.
Let Σ = { a, b }. For each positive integer k, let Ck be the language consisting of all strings that contain an a exactly k places from the right-hand end; in other words, Ck is all strings Σ*aΣk-1. Describe an NFA with k + 1 states that recognizes Ck in with a state diagram and a formal description.