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Category Archives: Theory of Computation & Automata

Prerequisite – Chomsky Hierarchy, Regular Languages As we all are aware that languages accepted by finite automata are called regular languages and those which are… Read More
  Decidable Problems A problem is decidable if we can construct a Turing machine which will halt in finite amount of time for every input… Read More
Prerequisite – Pushdown Automata and Context Free Languages .  Suppose we have a context free grammar G with production rules: S->aSb|bSa|SS|ℇ   Left most derivation (LMD)… Read More
Moore Machines: Moore machines are finite state machines with output value and its output depends only on present state. It can be defined as (Q, q0, ∑, O, δ, λ) where: Q is finite set of states. q0 is the initial state. ∑ is the input alphabet. O is the output alphabet. δ is transition function which maps Q×∑ → Q. λ is the output function which maps Q → O. Figure 1 In the moore machine shown in Figure 1, the output is represented with each input state separated by /. The length of output for a moore machine is greater than input by 1. Input: 11 Transition: δ (q0,11)=> δ(q2,1)=>q2 Output: 000 (0 for q0, 0 for q2 and again 0 for q2)  Mealy Machines: Mealy machines are also finite state machines with output value and its output depends on present state and current input symbol. It can be defined as (Q, q0, ∑, O, δ, λ’) where: Q is finite set of states. q0 is the initial state. ∑ is the input alphabet. O is the output alphabet. δ is transition function which maps Q×∑ → Q. ‘λ’ is the output function which maps Q×∑→ O. Figure… Read More
The definition of context free grammars (CFGs) allows us to develop a wide variety of grammars. Most of the time, some of the productions of… Read More
Identifying languages (or problems*) as decidable, undecidable or partially decidable is a very common question in GATE. With correct knowledge and ample experience, this question… Read More
Turing Machine was invented by Alan Turing in 1936 and it is used to accept Recursive Enumerable Languages (generated by Type-0 Grammar).  A turing machine… Read More
Before reading this article, we recommend you to first read about Pushdown Automata and Context Free Languages.   Suppose we have a context free grammar… Read More
Recursive Enumerable (RE) or Type -0 Language RE languages or type-0 languages are generated by type-0 grammars. An RE language can be accepted or recognized… Read More
DFA minimization stands for converting a given DFA to its equivalent DFA with minimum number of states. DFA minimization is also called as Optimization of DFA… Read More
An NFA can have zero, one or more than one move from a given state on a given input symbol. An NFA can also have… Read More
Context Free Languages (CFLs) are accepted by pushdown automata. Context free languages can be generated by context free grammars, which have productions (substitution rules) of… Read More
We have already discussed finite automata. But finite automata can be used to accept only regular languages. Pushdown Automata is a finite automata with extra memory… Read More
As discussed in Chomsky Hierarchy, Regular Languages are the most restricted types of languages and are accepted by finite automata.   Regular Expressions Regular Expressions… Read More
In this article, we will see some popular regular expressions and how we can convert them to finite automata. Even number of a’s : The… Read More

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