Nfa to-dfa
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The document discusses the conversion of nondeterministic finite automata (NFA) to deterministic finite automata (DFA). It defines NFAs, including how they allow multiple transition options from each state, unlike DFAs which only allow one transition. It also describes how an NFA accepts a string if any sequence of transitions leads to an accepting state. The document then explains that any language accepted by an NFA can also be accepted by an equivalent DFA, which is constructed by using the power set of the NFA states as the DFA states.
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Toc(df avs nfa)avishek130650107020
This document discusses the differences between non-deterministic finite automata (NFA) and deterministic finite automata (DFA). It states that NFAs can recognize the union, concatenation, and Kleene closure of regular languages. It also notes that any NFA can be converted to an equivalent DFA by constructing transition sets representing the lambda-closures of NFA states. The conversion procedure involves identifying the lambda-closure of each NFA state and making those closures the states of the DFA. Transitions between DFA states are determined by the possible transitions between NFA lambda-closures on given input symbols. This ensures the resulting DFA recognizes the same language as the original NFA.
NFA DFA Equivalence theorem
These slides were submitted by Muskan Bathla, Nivedit Jain and Sanskar Mani (all sophomore undergrad in Computer Science and Engineering) as a part of lecture scribing for Theory of Computation Course at Indian Institute of Technology Jodhpur, under the guidance of Dr. Anand Mishra, IIT Jodhpur
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The document discusses non-deterministic finite automata (NFAs) and how they are equivalent to deterministic finite automata (DFAs). It shows examples of NFAs accepting various strings and languages. It then proves that NFAs and DFAs have equal computational power by showing that any language accepted by an NFA is also accepted by a DFA, and vice versa. This is done by describing a procedure to convert any NFA into an equivalent DFA, demonstrating that the languages they accept are the same. Therefore, NFAs and DFAs recognize the same class of formal languages called regular languages.
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simple problem to convert NFA with epsilon to without epsilon
This document discusses the steps to construct the transition table for an NFA with epsilon transitions. It begins by taking the epsilon closure of each state. It then determines the output states for each input symbol applied to each state/closure set by taking the epsilon closure. This information is used to construct the transition table and diagram. The transition table shows the output state(s) for each input applied to each state. The transition diagram visually depicts the transitions.
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This document discusses the differences between non-deterministic finite automata (NFA) and deterministic finite automata (DFA). It states that NFAs can recognize the union, concatenation, and Kleene closure of regular languages. It also notes that any NFA can be converted to an equivalent DFA by constructing transition sets representing the lambda-closures of NFA states. The conversion procedure involves identifying the lambda-closure of each NFA state and making those closures the states of the DFA. Transitions between DFA states are determined by the possible transitions between NFA lambda-closures on given input symbols. This ensures the resulting DFA recognizes the same language as the original NFA.
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These slides were submitted by Muskan Bathla, Nivedit Jain and Sanskar Mani (all sophomore undergrad in Computer Science and Engineering) as a part of lecture scribing for Theory of Computation Course at Indian Institute of Technology Jodhpur, under the guidance of Dr. Anand Mishra, IIT Jodhpur
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This document discusses the steps to construct the transition table for an NFA with epsilon transitions. It begins by taking the epsilon closure of each state. It then determines the output states for each input symbol applied to each state/closure set by taking the epsilon closure. This information is used to construct the transition table and diagram. The transition table shows the output state(s) for each input applied to each state. The transition diagram visually depicts the transitions.
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The document describes how to convert a given NFA-ε into an equivalent DFA. It finds the ε-closure of each state in the NFA to create the states of the DFA. It then determines the transitions between these DFA states on each input symbol by taking the ε-closure of the NFA state transitions. This results in a DFA transition table and diagram that is equivalent to the original NFA.
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This document provides an introduction to regular expressions and regular languages. It defines the key operations used in regular expressions: union, concatenation, and Kleene star. It explains how regular expressions can be converted into finite state automata and vice versa. Examples of regular expressions are provided. The document also defines regular languages as those languages that can be accepted by a deterministic finite automaton. It introduces the pumping lemma as a way to determine if a language is not regular. Finally, it includes some practical activities for readers to practice converting regular expressions to automata and writing regular expressions.
Lecture: Automata
The document provides an introduction to automata theory and finite state automata (FSA). It defines an automaton as an abstract computing device or mathematical model used in computer science and computational linguistics. The reading discusses pioneers in automata theory like Alan Turing and his development of Turing machines. It then gives an overview of finite state automata, explaining concepts like states, transitions, alphabets, and using a example of building an FSA for a "sheeptalk" language to demonstrate these components.
Finite Automata
The document discusses finite automata including nondeterministic finite automata (NFAs) and deterministic finite automata (DFAs). It provides examples of NFAs and DFAs that recognize particular strings, including strings containing certain substrings. It also gives examples of DFA state machines and discusses using finite automata to recognize regular languages.
Turing machines
Turing Machines are a simple mathematical model of a general purpose computer invented by Alan Turing in 1936. A Turing Machine consists of an infinite tape divided into cells, a head that reads and writes symbols on the tape, a finite set of states, and transition rules determining the behavior of the machine. The machine operates by reading a symbol on the tape, updating the symbol according to its transition rules, moving the head left or right, and transitioning to a new state. Turing Machines can simulate any algorithm and are capable of performing any calculation that can be performed by any computing machine.
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Graph representation of DFA’s Da
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In the automata theory, a nondeterministic finite.pdf
In the automata theory, a nondeterministic finite automaton (NFA) or
nondeterministic finite state machine is a finite state machine where from each state and a given
input symbol the automaton may jump into several possible next states. This distinguishes it
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introduced in 1959 by Michael O. Rabin and Dana Scott,[1] who also showed their equivalence
to DFAs. Informal introduction An NFA, similar to a DFA, consumes a string of input
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accepting state. Formal definition An NFA is represented formally by a 5-tuple, (Q, S, ?, q0, F),
consisting of a finite set of states Q a finite set of input symbols S a transition relation ? : Q × S
? P(Q). an initial (or start) state q0 ? Q a set of states F distinguished as accepting (or final) states
F ? Q. Here, P(Q) denotes the power set of Q. Let w = a1a2 ... an be a word over the alphabet S.
The automaton M accepts the word w if a sequence of states, r0,r1, ..., rn, exists in Q with the
following conditions: r0 = q0 ri+1 ? ?(ri, ai+1), for i = 0, ..., n-1 rn ? F. In words, the first
condition says that the machine starts in the start state q0. The second condition says that given
each character of string w, the machine will transition from state to state according to the
transition relation ?. The last condition says that the machine accepts w if the last input of w
causes the machine to halt in one of the accepting states. Otherwise, it is said that the automaton
rejects the string. The set of strings M accepts is the language recognized by M and this language
is denoted by L(M). We can also define L(M) in terms of ?*: Q × S* ? P(Q) such that: ?*(r, e)=
{r} where e is the empty string, and If x ? S*, a ? S, and ?*(r, x)={r1, r2,..., rk} then ?*(r, xa)=
?(r1, a)?...??(rk, a). Now L(M) = {w | ?*(q0, w) n F ? Ø}. Note that there is a single initial state,
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This chapter introduces nondeterministic finite automata (NFAs) as a relaxation of deterministic finite automata (DFAs). NFAs allow more than one possible transition from a state on a given input, whereas DFAs have exactly one. NFAs can define languages with smaller or simpler machines than DFAs. They use nondeterminism to accept a string if any sequence of transitions leads to an accepting state. Epsilon transitions allow spontaneous moves without reading an input symbol.
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The document provides an introduction to automata theory and finite automata. It discusses key concepts such as alphabets, strings, languages, deterministic finite automata (DFAs), nondeterministic finite automata (NFAs), epsilon-NFAs, and the process of converting an NFA to a DFA using subset construction. The summary is:
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Deterministic Finite State Automata (DFAs) are machines that read input strings and determine whether to accept or reject them based on their state transitions. A DFA is defined as a 5-tuple (Q, Σ, δ, q0, F) where Q is a finite set of states, Σ is a finite input alphabet, q0 is the starting state, F is the set of accepting states, and δ is the transition function that maps a state and input symbol to the next state. The language accepted by a DFA is the set of strings that cause the DFA to enter an accepting state. Nondeterministic Finite State Automata (NFAs) are similar but δ maps to sets of states rather
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The document provides information about formal languages and automata theory, including:
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Nfa to-dfa
- 1. Theory of Computation NFA Conversion of NFA into DFA Sivashankari.R SITE VIT University January 27, 2016 Sivashankari.R Theory of Computation
- 2. NFA Modifying the finite automaton model to allow zero, one, or more transition from a state on the same input symbol.This new model is called NFA. DFA is special case of NFA in which for each state there is unique transition on each symbol. Nondeterminism means a choice of moves for an automaton. Sivashankari.R Theory of Computation
- 3. NFA NFA is defined by M = {Q, Σ, δ, q0, F}, where where Q, Σ, q0, F are defined as for DFA, but δ : Q × Σ → 2Q In NFA the range of δ is in the powerset 2Q, defines the set of possible states that can be reached by the transition. If for instance current state is q1, the symbol a is read and δ(q1, a) = {q0, q2} then either q0 or q2 could be the next state of NFA. Sivashankari.R Theory of Computation
- 4. NFA String is accepted by an NFA if there is some sequence of possible moves that will put the machine in a final state at the end of the string. Extended transition function δ∗(qi, w) = Qj where Qj is set of all possible states that automaton may be in, having stared in state qi and having read w. If P ⊆ 2Q then δ(P, w) = q in p δ(q, w) The language accepted by NFA M = {Q, Σ, δ, q0, F} is the set of all the strings on Σ accepted by M. L(M) = {w ∈ Σ∗ : δ∗(q0, w) ∩ F = φ}. Sivashankari.R Theory of Computation
- 5. NFA : Example δ∗(q0, 01001) = {q0, q1, q4} δ∗(q0, 1010) = {q0, q3} NFA will accept 01001 but it will not accept 1010 Sivashankari.R Theory of Computation
- 6. Equivalence of NFA’s and DFA’s L be set accepted by NFA then there exist a DFA that accept L. DFA and NFA are equally powerful. Let M = {Q, Σ, δ, q0, F} be an NFA accepting L, we can define equivalent DFA M = {Q , Σ, δ , q0, F } as follow: Q = 2Q F = set of the states in Q containing a final state of M q 0 = [q0] δ ([q1, q2, · · · , qi], a) = [p1, p2, · · · , pj] iff δ({q1, q2, · · · , qi}, a) = {p1, p2, · · · , pj} Sivashankari.R Theory of Computation
- 7. Equivalence of NFA’s and DFA’s : Example Sivashankari.R Theory of Computation