THE VERY IDEA OF TURING MACHINE A Turing machine is a device that manipulates symbols on a strip of tape to simulatethe logic of any computer algorithm, an dis particularly useful ip% mated according to a table of rules. Despite its simplicity, a Turing machine can be explaining the functions of a CPU inside a computer. The "turing washe Turingmachine is not intended as a practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation Turing gave a succinct definition of the experiment in his 1948 essay, Intelligent Machinery. Referring to his 1936 publication, Turing wrote that the Turing machine, here called a Logical Computing Machine, consisted of: an infinite memory capacity obtained in the form of an infinite tape marked out into squares, on each of which a symbol could be printed. At any moment there is one symbol in the machine; it is called the scanned symbol The machine can alte the scanned symbol and its behavior is in part determined by that symbol, but the symbols on the tape elsewhere do not affect the behaviour of the machine. However the tape can be moved back and forth through the machine, this being one of the elementary operations of the machine. Any symbol on the tape may therefore eventually have an innings. (Turing 1948, p. 61)
THE VERY IDEA OF TURING MACHINE A Turing machine is a device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer. The "Turing" machine was described by Alan Turing in 1936,[1] who called it an "a(utomatic)-machine". The Turing machine is not intended as a practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation. Turing gave a succinct definition of the experiment in his 1948 essay, "Intelligent Machinery". Referring to his 1936 publication, Turing wrote that the Turing machine, here called a Logical Computing Machine, consisted of: ...an infinite memory capacity obtained in the form of an infinite tape marked out into squares, on each of which a symbol could be printed. At any moment there is one symbol in the machine; it is called the scanned symbol. The machine can alter the scanned symbol and its behavior is in part determined by that symbol, but the symbols on the tape elsewhere do not affect the behaviour of the machine. However, the tape can be moved back and forth through the machine, this being one of the elementary operations of the machine. Any symbol on the tape may therefore eventually have an innings.[2] (Turing 1948, p. 61)
More precisely, a Turing machine consists of A tape which is divided into cells, one next to the other. Each cell contains a symbol from some finite alphabet. The alphabet contains a special blank symbol (here written as 'B) and one or more other symbols. The tape is assumed to be arbitrarily extendable to the left and to the right, ie, the Turing machine is always supplied with as much tape as it needs for its computation. Cells that have not been written to before are assumed to be filled with the blank symbol. In some models the tape has a left end marked with a special symbol; the tape extends or is indefinitely extensible to the right A head that can read and write symbols on the tape and move the tape left and right one (and only one) cell at a time In some models the head moves and the tape is stationary. A finite table(occasionally called an action table or transition function) of instructions(usually quintuples [5 tuples]: qia; dk, but sometimes 4-tuples)that, given the state( qi) the machine is currently in and the symbol(a )it is reading on the tape(symbol currently under the head) tells the machine to do the following in sequence(for the 5 tuple models) o Either erase or write a symbol (instead of ai, write ai1), and then o Move the head (which is described by dk and can have values: ' L' for one step left or'R' for one step rightor N for staying in the same place), and then o Assume the same or a new state as prescribed (go to state qin) In the 4-tuple models, erase or write a symbol (ain )and move the head left or right (dk)are specified as separate instructions. Specifically, the table tells the machine to (ia)erase or write a symbol or (ib)move the head left or machine v rill halt; other models require all entries to be filled. A state register that stores the state of the Turing machine, one of finitely many. There is one specialstart state with which the state register is initialized. These states, writes Turing, replace the"state of mind"a person performing computations would ordinarily be in
More precisely, a Turing machine consists of: A tape which is divided into cells, one next to the other. Each cell contains a symbol from some finite alphabet. The alphabet contains a special blank symbol (here written as 'B') and one or more other symbols. The tape is assumed to be arbitrarily extendable to the left and to the right, i.e., the Turing machine is always supplied with as much tape as it needs for its computation. Cells that have not been written to before are assumed to be filled with the blank symbol. In some models the tape has a left end marked with a special symbol; the tape extends or is indefinitely extensible to the right. A head that can read and write symbols on the tape and move the tape left and right one (and only one) cell at a time. In some models the head moves and the tape is stationary. A finite table (occasionally called an action table or transition function) of instructions (usually quintuples [5- tuples] : qiaj→qi1aj1dk , but sometimes 4-tuples) that, given the state(qi ) the machine is currently in and the symbol(aj ) it is reading on the tape (symbol currently under the head) tells the machine to do the following in sequence (for the 5- tuple models): Either erase or write a symbol (instead of aj , write aj1 ),and then Move the head (which is described by dk and can have values: 'L' for one step left or 'R' for one step rightor 'N' for staying in the same place), and then Assume the same or a new state as prescribed (go to state qi1 ). In the 4-tuple models, erase or write a symbol (aj1 ) and move the head left or right (dk) are specified as separate instructions. Specifically, the table tells the machine to (ia) erase or write a symbol or (ib) move the head left or right, and then (ii) assume the same or a new state as prescribed, but not both actions (ia) and (ib) in the same instruction. In some models, if there is no entry in the table for the current combination of symbol and state then the machine will halt; other models require all entries to be filled. A state register that stores the state of the Turing machine, one of finitely many. There is one specialstart state with which the state register is initialized. These states, writes Turing, replace the "state of mind" a person performing computations would ordinarily be in