DFA Category 3: Contains substring

 DFA accepts strings that contain a specific substring anywhere in the string. For Examples

  • Contains 101
  • Contains ababa
  • Contains 000

DFA Example: 

Construct a DFA that accepts all the strings over ∑ {0,1} where each contains “0” and always starts with “1”.


DFA Example

Construct DFA that accepts all the strings over alphabet ∑ {0,1} where each string contains “00”.


DFA Example: 

Construct a DFA with sigma ∑ = {0, 1}, accepts all strings that contain three consecutive 0’s.


DFA Example: 

Construct a DFA with sigma ∑ = {0, 1}, accepts all strings that do not contain three consecutive 0’s.


DFA Example: 

Construct a DFA that accepts all the strings over the alphabet ∑ {0,1} where each string contains “101” as a substring.


DFA Example: 

Draw a DFA for the language that accepts strings containing neither ’00’ nor ’11’ as a substring over the input alphabet ∑ = {0, 1}.


DFA Example:

Design a DFA that accepts strings that must contain ’01’ or ’10’ as a substring over input alphabets ∑ = {0, 1}.


DFA Example: 

Construct a DFA with sigma ∑ = {0, 1} for the language accepting strings containing exactly two ‘0’.


DFA Example:

Design a DFA with sigma ∑ = {0, 1} for the language accepting strings containing at least two ‘0’.

DFA Example: 

Draw a DFA with sigma ∑ = {0, 1} for the language accepting strings containing at most two ‘0’.


DFA Example: 

Design a DFA with sigma ∑ = {0, 1} for the language accepting strings containing an odd number of total zeros (or odd binary numbers strings).

DFA Example: 

Design a DFA for the Language (L) that accepts only the strings where every “00” is Immediately Followed by 1 over the input alphabet ∑= {0,1}



Comments

Post a Comment

Popular posts from this blog

Theory Of Computation PCCST302 KTU Semester 3 BTech 2024 Scheme

About Me Course Details and Syllabus Module-1 Foundations of Finite Automata Motivation-Computability Need for Mathematical Modelling and automata Introducing automata     on-off switch     coffee vending machine Alphabet, Strings, and Languages Formal Definition of Finite Automata Deterministic Finite Automata - DFA Dead state in DFA Categories of DFA      Category 1: Accept Only the Given Input      Category 2: Starts and ends with      Category 3: Contains substring      Category 4: Specific length     Category 5: Divisibility ( Binary Numbers) Examples  DFA( University Questions) DFA Implementation C Program Non Deterministic Finite Automata - NFA Epsilon NFA  (∈-NFA) Examples NFA( University Questions) Regular Languages Epsilon Closure of NFA Eliminating Epsilon Transitions from NFA Epsilon Free NFA to DFA Conversion - Examples DFA state minimization DFA vs NFA Applications of Fini...
Read more

Non deterministic Finite Automata NFA

Image
  🤖 Formal Definition of NFA An NFA (Nondeterministic Finite Automaton) is a theoretical machine used to recognize regular languages , like a DFA, but it allows multiple transitions for the same input or even no input at all (ε-transitions) . 📘 An NFA is defined as a 5-tuple : M = ( Q , Σ , δ , q 0 , F ) M = (Q, \Sigma, \delta, q_0, F) Where: Symbol Description Q Q A finite set of states Σ \Sigma A finite set called the input alphabet δ \delta The transition function : δ : Q × ( Σ ∪ { ε } ) → 2 Q \delta: Q \times (\Sigma \cup \{\varepsilon\}) \rightarrow 2^Q  (a set of states) q 0 q_0 ​ The initial state , q 0 ∈ Q q_0 \in Q F F The set of accepting states , F ⊆ Q F \subseteq Q 💡 Key Differences from DFA: DFA NFA Only one transition per input                Multiple transitions possible No ε-transitions                ε-transitions allowed Deterministic      ...
Read more

Example DFAs University Questions

Image
 Even number of a's ab as a substring empty set All strings except the empty set over the alphabet {0.1} Accept empty string and 0 every odd position of the string w is 1 begins with 1 ends with 0 {w| w contains at least 3 ones }  {w|w contains the substring 0101 ie; w=x0101y for some x and y} {w|w has length at least 3 and its third symbol is a zero} {w|w starts with 0 and has odd length , or starts with 1 and has even length } construct a DFA which accepts the language L = {a^N | N ≥ 1} String in {a,b} with odd number of a's starting with 01 over the alphabet [1,0} Strings ending with abc Program to build a DFA that checks if a string ends with "01" or "10" build a DFA to accept strings that start and end with same character build DFA that starts and end with 'a' from input (a, b) build a DFA that accepts strings starting and ending with different character DFA of a string starting with 0 and ends with 10? DFA of a string of a's and b's  st...
Read more