For example ( q, aab abb ) shows that the Turing machine isĬurrently in state q, the taper contents are the string aababb and the head is reading To describe the operation of Turing machine we use configuration.Ī configuration for a Turing machine is an ordered pairĪnd the tape contents with the symbol currently under the head marked with underscore. It is assumed that the tape has at the left endĪnd the head is initially at the left end of the tape. Is drawn with label ( X/Y, D ) indicating that the state is changed from q to r, the symbol XĬurrently being read is changed to Y and the tape head is moved as directed by D.Ī transition diagram of this Turing machine is given below. ( q, X ) = ( r, Y, D ), where D represents R, L or S, an arc from q to r The states are represented by vertices and for a transition A transition diagram can also be drawn for a Turing machine. Here denotes the blank and R, L and S denote move the head right, Is the transition function but its value may not be defined Is a finite set of symbols and it is the input alphabet.Īs its subset and it is the set of tape symbols. The symbol h is used to denote the halt state. Q is a finite set of states, which is assumed not to contain the symbol h. One of its states is the halt state and when the Turing machine goes into the halt state,įormally a Turing machine is a 5-tuple T = , It then moves the head to left or right orĭoes not move it and goes to the next state which may be the same as the current state. With a symbol (possibly the same symbol). Given a string of symbols on the tape, a Turing machine starts at the initial state.Īt any state it reads the symbol under the head, either erases it or replaces it However, unlike finite automata, its head is a read-writeĬan move left, right or stay at the same square after a read or write.
The tape has the leftĮnd but it extends infinitely to the right.Ī symbol can be written in each square. At any time it is in one of the finite number of states. We are going to study Turing machines here and through that limitations of computers and computationĬonceptually a Turing machine, like finite automata, consists of a finite control andĪ tape. While Turing machines have infinite memory. This conjecture is known as Church's thesis and today it is generally accepted as true.Ĭomputers we use today are as powerful as Turing machines except that computers have finite memory That any computation done by humans or computers can be carried out by some Turing machine. Turing machines were conceived of by the English mathematician Alan Turing as a model Hierarchy, the phrase structure languages (also called Type 0 languages), and the machines
In this chapter we are going to study the most general of the languages in Chomsky They are, however, of limited capability and there are many languages that they can Systems and so they are heavily used in practice. These languages can describe many practically important We have studied two types of languages from the Chomsky hierarchy: regular languagesĪnd context-free languages.
0 kommentar(er)
