# Deque Automata for All Classes of Formal Languages

**Topics:**Automata theory, Formal language, Regular expression

**Pages:**10 (1939 words)

**Published:**February 18, 2013

Deque Automata for all classes of Formal languages

B. Asha latha1

Department of computers

SRKIT Engineering

Vijayawada Andhra Pradesh (India)

T.Vishnupriya2

Department of Electronics

SRKIT Vijayawada, Andhra Pradesh (India)

N.Himabindu3

Department of computers

KBN College of Vijayawada, Andhra Pradesh (India)

Abstract: The purpose of computation involves solving problems by communicating them to a computational model by means of a suitable language .A number of languages have been developed for this purpose. To recognize these languages some computational models has been developed and they are finite state machine, push down automata, queue automata and turing machines. But these machines are restricted to only one specific formal languages like regular, context free ,etc. In this paper we proposed a machine called a Dequeue automaton that is capable of recognizing different classes of automata. We also shown that the simulation results from the Deque automata.

Keywords: Formal languages, Finite automata, PDA ,TM.

I. Introduction

A finite automaton was the first abstract model as well as the mathematical model of digital computers. It is very powerful model of computation. It can recognize and accept regular languages. But finite automata have limited memory(states) which prevents them accepting Context free languages .Since memory is a limitation of finite automata ,a memory element is added as a stack, in order to made finite automata a powerful machine and to accept Context free languages. That new type of computational model is known as a Push down automata.PDA is similar to finite automata except that it has an extra memory unit stack. Stack is defined as a data structure where insertion and deletion of any element is possible only at one end called top of the stack.[1].

The automata with queue memory was constructed in a similar way as the PDA, however the new type of memory of QA is queue. The definition of queue automata is similar to that of PDA. The difference concerns the type of memory. The main advantage of QA is it is equivalent to Turing machine. That is a TM can be simulated by a QA that keep a copy of the TM‘s contents in its queue at all times with two special marks. One for the end of TM’s head position and one for the end of the tape. Its transitions simulate those of the TM by running through the whole queue, popping off each of its symbols and re-enqueing either the popped symbol or near the head position. A queue machine can be simulated by a TM but more easily by a multi tape TM which is known to be equivalent to a normal single-tape machine.

But the PDA is not able to recognize the Context sensitive languages and Recursively Enumerable languages. To recognize the Context sensitive languages and Recursively Enumerable languages another automaton that is Turing machine was developed. The following table summarizes each class of the formal language and its corresponding automaton that recognizes it.

II. Categories of languages and Automaton

|S.NO |Formal language |Automaton | |1 |Regular language |Finite automaton | |2 |Context free language |Non deterministic Push down automaton | |3 |Context sensitive and Recursively enumerable languages |Turing machine | |4 |Context free languages |Queue Automaton |

Table: 1 Different types of Automaton

Every regular language is Context free, every context free language, not containing empty string is context sensitive and every recursive language is recursively enumerable. These are all proper inclusions, meaning...

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