Problem 2 Consider the DFA M₂ shown in Figure 1. 1. Convert the DFA M₂ into an equivalent Generalized Nondeterministic Finite Automata (GNFA). 2. Remove state q3 using the method described in class to make a GNFA with one fewer state. Draw the new state diagram. 3. Remove state 92 using the method described in class to make a GNFA with one fewer state. Draw the new state diagram. 4. Give the regular expression for the language recognized by the DFA M2. Ideally, give the regular expression that one gets from running the algorithm given in class and in the book after removing states 93, 92, and q₁ in that order. 91 0 93 92 1 0 0 Figure 1: Figure depicting the DFA M₂ for Problem 2.

Problem 2 Consider the DFA M₂ shown in Figure 1. 1. Convert the DFA M₂ into an equivalent Generalized Nondeterministic Finite Automata (GNFA). 2. Remove state q3 using the method described in class to make a GNFA with one fewer state. Draw the new state diagram. 3. Remove state 92 using the method described in class to make a GNFA with one fewer state. Draw the new state diagram. 4. Give the regular expression for the language recognized by the DFA M2. Ideally, give the regular expression that one gets from running the algorithm given in class and in the book after removing states 93, 92, and q₁ in that order. 91 0 93 92 1 0 0 Figure 1: Figure depicting the DFA M₂ for Problem 2.

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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Question 2 1. Give the examples/applications designed as finite state system. 2. What are the applications of automata theory? Note- I need fresh ans because I find there have ans in bartleby so that's why I need new type ans
Example: Consider a nondeterministic PDA M, = ({q.}, {a,b}. {a,b,S}, 8,9.S.4) which accepts the language L = {a"b" : n21} by empty store, where 8 is defined as follows: 8 (g0.E,S) = {(40,ab), (90,asb)} (Two possible moves), 8 (q,,a,a) = {(4,,e)} , and 8(go,b,b) = {(40,e}} Construct an equivalent PDA M, which accepts Lin final state and check whether string w = aabb is accepted or not ?
Consider the languages in Table 1. Match them with the suitable PDA from Table 2. Table 1. Table 2. No. Push-down Automata (a,E/A) (b,e/B) (c,B/E) (d,A/c) (6,E/8) {amb^cdm | m, n > O}. (c,X/8) (d,X/8) {ambmc^dn | n > 0, m >= 0} 8 (d,X/8) {a'b/ckd \ i, j, k, I≥ 0; i = T and j = k}. {amb^c?d9 | m + n = p + q}. {ambmtnc¢ [ m,n >= 0} {amb^c+1 | m ≥0, n >0}. {am+1b^cm | m>0, n ≥ 0}. 5. No. Language 1. 2. 3. 4. 5. 6. 7. (6,8/8) (a,8/X) (b,8/X) (b,e/x) c,X/8) 31 (d,X/e) 9⁰ 91 (a,8/X) (b,E/Y) (c,Y/8) €o (b,e/Y) WA (d,X/8) (b,8/A) (c,A/8) (c,e/8) (a,c/A) (b,E/E) (c,A/8) (a,e/8) (e,e/6) (c,A/E) qo 91 q2 (a,&/X) (b,X/8) (c,&/Y) (d,Y/8) (6,8/8) (c,&/Y) (d,Y/e) ஏo 91 92 (a,e/X) (b,X/E) (b,e/Y) (c,Y/E) (E,6,8) (E,E,E) (a,8/8) .8. (b,E/A) (E,E/E) (E,E,E)
Apply the Paint Blue algorithm discussed in class to the following Finite Automata. a a a b b a a + a b Show the status of the Finite Automata at the conclusion of the Paint Blue Algorithm (mark the visited states with an X and only include edges that have not been followed).
2. [15 points] Draw a state diagram of a Turing machine accepting the language L = {x#ry | x € {0,1}* and y E {0,1,#}*}, i.e., L consists of all strings which have a prefix of the form x#x with x E {0, 1}*. Assume the tape alphabet is I = {0, 1, #, &, -}.
Finite state machines often don't address the totality of problems, an example is when it is necessary to use arithmetic expressions. To meet this need, Stack Automata (AP) are used, mechanisms of great importance for computing. About AP's, analyze the following statements. I. An AP is a state machine very similar to a Deterministic Finite Automata (AFD), but with the addition of a LIFO (Last in, First out) data structure. II. One of the examples of using an AP is in compilers of programming languages, in the stage of syntactic analysis of a code. III. There are deterministic and non-deterministic APs, and the non-deterministic ones have a much greater scope than the deterministic ones. IV. It is not necessary to mark an empty stack for an AP to work, because at the end of reading a string, if the AP is in a final state, it is because the stack is necessarily empty. The following items are correct: A) I, II, III B) I, II, IV C) I, III, IV D) II, III, IV E) I, II, III, IV
Automata Theory Create a PDA to recognize the following language: L = {0n12n | n >= 0}.Since drawing is difficult in this environment, you may create the PDA as follows:1. First specify the 6 elements of the PDA (e.g., Q = {...}, SIGMA = {...} etc) and their contents.2. Then specify the transitions in a list as follows. (When you specify the transition, use the same notation that Sipser would use in a state transition diagram.)q1 to q2: <here specify the transition>q2 to q3: <here specify the transition>etc.
Let = {0, 1} and consider the following languages 1. LBOUNDED = {(M, x) : M is a TM, x € Σ*, M never moves its pointer more than |x| tape symbols away from the left endmarker |} 2. LDEC = {(M): M is a TM, L(M) is decidable} For each language, determine whether it is decidable or undecidable. If it is decidable, give a decision procedure which decides it. If it is undecidable, you must use Rice's theorem, if applicable, or a mapping reduction, otherwise. [Hint: Given some input string x, you may assume that the number of possible instantaneous configurations of a TM where the pointer never moves more than |x| tape symbols away from the left endmarker is at most |T||*|. (²[+¹). (¹).]
Nfa to dfa confused conversation Deterministic Finite Automata) (Non-Deterministic Finite Automata).
QUESTION 1 1. Finite Automata Let us consider the following -NFA defined over the alphabet = {0,1}. F- 0,1 €,0 0,1 start → A B 1. Transform the automaton into an NFA, that is remove the transitions. Show, and com- ment on, all the steps. Show the resulting transition function (as a table) and also the diagram of the resulting automaton. 2. Transform the resulting NFA into a DFA. Show, and comment on, all the steps. Show the resulting transition function (as a table) and also the diagram of the resulting automaton. 3. Minimise, if possible, the resulting DFA by applying the method of partitions. Show, and comment on, all the steps. Show the resulting transition function (as a table) and also the diagram of the resulting automaton. 4. Apply the appropriate algorithm to verify that the DFA before and after minimisation are equivalent. 5. Determine for the most minimal DFA available the language that this automaton accepts by finding its regular expression. Manipulate the found regex to…
Problem 1: Constructing a DFA Consider the following language. L = {w = {0,1}*: w = 10" where m is odd} In other words, L consists of strings that start with a 1 which is followed by an odd number of Os. (a) Write down a string that is in L. (b) Give the state diagram for a DFA that recognizes L.
Workbook Exercise Draw the diagram of the DFA, which recognizes the entries containing an odd number of '0', an even number of '1' and an odd number of '2' symbols, with Σ = {0, 1, 2}. (DFA: Determined Finite Automata) Thanks.