(10pts)Use the subset construction to build a DFA that recognizes the language recognized by the following...
2. (a) Using Thompson's construction, construct an NFA that recognizes the same language as defined by the following regular expression (1 010) *1 (b) Using the subset construction, convert the NFA into a DFA. Optimize the resulting DFA by merging any equivalent states
Show that the following language is decidable. L={〈A〉 | A is a DFA that recognizes Σ∗ } M =“On input 〈A〉 where A is a DFA:
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that the number of 0s is divisible by 2 and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a methodical way to do this: Figure out all the final states and label each with the shortest string it accepts, work backwards from these states to...
Let R = (0*0 ∪ 11)*∪(10). Use the construction from the lecture (given any regular expression, we can construct an NFA that recognizes the described language) to construct an NFA N such that L(N) = L(R). Apply the construction literally (do not optimize the resulting NFA–keep all those ε arrows in the NFA). Only the final NFA is required, but you can get more partial credit if you show intermediate steps
Consider the NFA N with states labeled q1, q2 and q3, where q1 is the start state and q2 and q3 are the final (accepting) states. The transition function for N is δ(q1,a) = {q1}, δ(q1,b) = {q1,q2}, δ(q2,a) = {q3}, δ(q2,b)= ∅, δ(q3,a)= ∅, and δ(q3,b)= ∅. Let L be the language recognized by N i.e. L(N). a) Draw the state diagram for N. b) Describe in plain English what's in the language L. c) Via the construction NFA to...
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...
Three. Show a DFA over the alphabet {a, b} for the following language via complement construction (as in Exercise l.5.d): {w belongs to Sigma* | w is not in a*b*}.
Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that there are no consecutive 0s, and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a way to approach the problem: First focus only building the DFA which accepts the language: As you build your DFA, label your states with an explanation of what the state actually represents in terms...
3. [20 points] Give short answers to each of the following parts. Each answer should be at most three sentences. Be sure to define any notation that you use. (a) Explain the difference between a DFA and an NFA. (b) Give a regular expression for the language consisting of strings over the alphabet 2-(0, 1) that contains an even number of 0's and an odd number of 1's and does not contain the substring 01. (c) Give the formal definition...
Question2 in the photo. Please help. Thanks 1. Construct an NFA that accepts the language La = {zaaabyaaabzla, y, z E {a, b)' } 2. Eliminate the e-transitions (denoted as E's below) from the following NFA s.t. the resulting machine accepts the same language with the same mumber of states. ql a,b go q3 2 3. Text problem: page 62, number 3. Finish by reducing the DFA. Note that you may want to do this in stages, first eliminating the...