What are the DFA configurations for L={w:${n}_{a}$(w) mod3 < 1} on $\sum$={a,b}?

In summary, a DFA is a mathematical model used to recognize patterns in strings of characters. It has a finite set of states, a starting state, and transition rules based on input symbols. The main purpose of a DFA is to recognize whether a given input belongs to a specific language and has applications in pattern matching, lexical analysis, and compiler design. It differs from an NFA in that it only accepts deterministic languages, while an NFA can have multiple transitions and states. A DFA is also different from a regular expression, which is a simpler sequence of characters used for search patterns. DFAs have more complex pattern recognition capabilities and can be used in various fields such as computer science, natural language processing, and DNA sequencing.
  • #1
comfortablynumb
3
0
Find dfa's for the following language on
$\sum$={a,b};

c)
L={w:${n}_{a}$(w) mod3 < 1;
 
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  • #2
You need three states $\{0,1,2\}$ that will correspond to the remainder when the number of read symbols $a$ is divided by 3. When the automaton reads a $b$, it remains in the same state. When the automaton reads an $a$, it moves to the next state. Can you figure out which states should be accepting?
 
  • #3
Thank you, Evgeny.Makarov, I figured it out. I treated mod3<1 as mod3=0 and did it. I was okay figuring out accepting states.
 

FAQ: What are the DFA configurations for L={w:${n}_{a}$(w) mod3 < 1} on $\sum$={a,b}?

What is a DFA?

A DFA (Deterministic Finite Automaton) is a mathematical model used to recognize and accept or reject strings of symbols. It consists of a finite set of states, a finite alphabet of input symbols, a transition function, a start state, and a set of accept states.

What is the purpose of a DFA?

The purpose of a DFA is to determine whether a given input string belongs to a specific language or not. It can also be used to validate or recognize patterns in data, such as in lexical analysis or parsing.

What is the difference between DFA and NFA?

DFA (Deterministic Finite Automaton) and NFA (Nondeterministic Finite Automaton) are two types of finite automata used in the theory of computation. The main difference between them is that in DFA, for each input symbol, there is exactly one transition to a next state, while in NFA, there can be multiple transitions for the same input symbol.

What are the limitations of a DFA?

One of the main limitations of a DFA is that it can only recognize regular languages, which are languages that can be expressed by a regular expression. It cannot recognize more complex languages, such as context-free or context-sensitive languages. Additionally, DFAs can become very large and complex for certain languages, making it difficult to design and analyze them.

How is a DFA constructed?

A DFA can be constructed using various methods, such as state elimination, state minimization, or the subset construction algorithm. The basic steps involve defining the states, alphabet, and transition function of the DFA based on the language it needs to recognize, and then determining the start state and accept states. A diagram, called a state transition diagram, is often used to represent the DFA.

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