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![Regular Expression
• letter = [a –z] or [A –Z]
• digit = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 or [0-9]
• sign = [ + | -]
• Decimal = (sign)?(digit)+
• Identifier = (letter)(letter | digit)*
• Float = (sign)? (digit) +.+ (digit)*](https://image.slidesharecdn.com/cd7-nfadfa-210716085922/75/NFA-DFA-2-2048.jpg)
Uploaded byAkhil Kaushik
NFA & DFA
The document outlines concepts related to finite state automata (FSA), detailing the differences between non-deterministic finite automata (NFA) and deterministic finite automata (DFA). It explains their definitions, operational mechanisms, and includes examples along with the transition states and functions for both types of automata. The document also discusses the minimization process for DFA and provides illustrative states and transitions.
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Presentation introduction by Akhil Kaushik, Asstt. Prof. at TIT Bhiwani, on NFA and DFA.
Defines components of Regular Expressions: letters, digits, signs, decimals, identifiers, and floats.
Introduction to Finite State Automata (FSA) concepts including NFA and DFA.
Explains NFA and DFA: NFA has multiple paths for an input, while DFA has a unique path for each input.
Every non-deterministic automata (NFA) has an equivalent deterministic automata (DFA) using regular expressions.
NFA can transition to multiple states simultaneously; described using a 5-tuple representing its elements.
NFA represented by state diagrams, graphically showcasing system behaviors.
Examples of NFA transitions and patterns including 00 and (0 + 1)*.
DFA has a single next state per input; also defined by a 5-tuple, ensuring determinism.
Contrasts NFA and DFA: NFA has multiple next states, easier to create, uses ε transitions; DFA is deterministic.
Describes the step-by-step process to convert NFA to DFA.
Discusses technique for minimizing DFA through partitioning final and non-final states.
Akhil Kaushik's contact details and a concluding thank you note.
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NFA & DFA
- 1. Akhil Kaushik Asstt. Prof.,CE Deptt., TIT Bhiwani NFA & DFA
- 2. Regular Expression • letter= [a –z] or [A –Z] • digit = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 or [0-9] • sign = [ + | -] • Decimal = (sign)?(digit)+ • Identifier = (letter)(letter | digit)* • Float = (sign)? (digit) +.+ (digit)*
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- 4. Finite State Automata(FSA) • There are two main kinds of FSA:- – Non-Deterministic Finite Automata (NFA): at a particular state, a unique path may not be determined for each input alphabet. – Deterministic Finite Automata (DFA): at a particular state, a unique path determined for each input alphabet.
- 5. Finite State Automata(FSA) • For every non-deterministic automata, there is an equivalent deterministic automata. • The below NFA is equivalent to the regular expression/ab*ca?/.
- 6. NFA • In aNFA, for each state there can be zero, one, two, or more transitions corresponding to a particular symbol. • For a particular input symbol, the machine can move to any combination of the states in the machine. Hence, it is called NFA. • Only NFA state automaton can have an ε transition. • The procedure is like: RE → NFA → DFA → Tables
- 7. NFA An NFA canbe represented by a 5-tuple (Q, Σ, δ, q0, F) where:− • Q is a finite set of states. • Σ is a finite set of symbols called the alphabets. • δ is the transition function where δ: Q × Σ → 2Q • q0 is the initial state & F is the final state (Here the power set of Q (2Q) has been taken because in case of NFA, from a state, transition can occur to any combination of Q states)
- 8. NFA – StateDigrams • Represented by digraphs called state diagram: used to graphically represent finite state machines to give an abstract description of the behavior of a system.
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- 10. NFA Examples 00 (0+ 1)*
- 11. DFA • In DFA,for each input symbol, one can determine the state to which the machine will move. Hence, it is called Deterministic Automaton. • As it has a finite number of states, the machine is called Deterministic Finite Machine. • Q is a finite set of states. • Σ is a finite set of symbols called the alphabet. • δ is the transition function where δ: Q × Σ → Q
- 12. NFA vs DFA •In NFA each pair of state and input symbol can have many possible next states. • NFA can use empty string transition. • NFA is easier to construct. • NFA requires less space. • In DFA the next possible state is distinctly set. • DFA cannot use empty string transition. • It is more difficult to construct DFA. • DFA requires more space.
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- 21. DFA Minimization • Makea partition of final & non-final states: • T = { {E}, {A, B, C, D} } • T = { {E}, {A, B, C}, {D} } • T = { {E}, {A, C}, {B}, {D} } or • T = { {E}, {A1}, {B}, {D} }
- 22. Akhil Kaushik [email protected] 9416910303 CONTACT MEAT: Akhil Kaushik [email protected] 9416910303 THANK YOU !!!