In this lecture we will discuss introduction to #theory of #automata which is nearly equal to thoery of #computation. We start from definition of thoery of automata in urdu.
Furthur more we will be studying thoery of automata and formal languages, automata language and basics of thoery of computation and basics of automata thoery and what is automata thoery and automata language, automata theory languages and computation and automata and formal languages.
Automata theory: Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science and discrete mathematics (a subject of study in both mathematics and computer science). The word automata (the plural of automaton) comes from the Greek word αὐτόματα, which means "self-acting".
Automata theory is closely related to formal language theory. An automaton is a finite representation of a formal language that may be an infinite set. Automata are often classified by the class of formal languages they can recognize, typically illustrated by the Chomsky hierarchy, which describes the relations between various languages and kinds of formalized logic.
Automata play a major role in theory of computation, compiler construction, artificial intelligence, parsing and formal verification.
Very informal description: An automaton is a construct made of states designed to determine if the input should be accepted or rejected. It looks a lot like a basic board game where each space on the board represents a state. Each state has information about what to do when an input is received by the machine (again, rather like what to do when you land on the Jail spot in a popular board game). As the machine receives a new input, it looks at the state and picks a new spot based on the information on what to do when it receives that input at that state. When there are no more inputs, the automaton stops and the space it is on when it completes determines whether the automaton accepts or rejects that particular set of inputs.
Informal description: An automaton runs when it is given some sequence of inputs in discrete (individual) time steps or steps. An automaton processes one input picked from a set of symbols or letters, which is called an alphabet. The symbols received by the automaton as input at any step are a finite sequence of symbols called words. An automaton has a finite set of states. At each moment during a run of the automaton, the automaton is in one of its states. When the automaton receives new input it moves to another state (or transitions) based on a function that takes the current state and symbol as parameters. This function is called the transition function. The automaton reads the symbols of the input word one after another and transitions from state to state according to the transition function until the word is read completely. Once the input word has been read, the automaton is said to have stopped. The state at which the automaton stops is called the final state. Depending on the final state, it's said that the automaton either accepts or rejects an input word. There is a subset of states of the automaton, which is defined as the set of accepting states. If the final state is an accepting state, then the automaton accepts the word. Otherwise, the word is rejected. The set of all the words accepted by an automaton is called the language recognized by the automaton.
In short, an automaton is a mathematical object that takes a word as input and decides whether to accept it or reject it. Since all computational problems are reducible into the accept/reject question on inputs, (all problem instances can be represented in a finite length of symbols)
Formal definition: A deterministic finite automaton is represented formally 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 alphabet of the automaton. δ is the transition function, that is, δ: Q × Σ → Q. q0 is the start state, that is, the state of the automaton before any input has been processed, where q0∈ Q. F is a set of states of Q (i.e. F⊆Q) called accept states.
Input word: An automaton reads a finite string of symbols a1,a2,...., an , where ai ∈ Σ, which is called an input word. The set of all words is denoted by Σ*.
Accepting word A word w ∈ Σ* is accepted by the automaton if qn ∈ F.