Test: The Language of Turing Machine - Computer Science Engineering (CSE) MCQ

A more mathematically oriented definition with the same universal nature was introduced by church and turing together called the Church-Turing thesis(formal theory of computation).

Alan turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.

 state register is one which stores the state of the turing machine, one of the finitely many. Among these is the special start state with which the state register is initialized.

The 7-tuple definition of turing machine: (Q, S, G, d, q0, B, F)
where Q= The finite set of states of finite control
S= The finite set of input symbols
G= The complete set of tape symbols
d= The transition function
q0= The start state, a member of Q, in which the finite control is found initially.
B= The blank symbol
F= The set of final or accepting states, a subset of Q.

 If we reach h_A or h_R, we say TM halts. Once it has halted, it cannot move further, since d is not defined at any pair (h_A,X) or (h_R,X) where h_A = accept halting state and h_R = reject halting state.

Inorder to describe formally what a Turing machine does, we need to develop a notation for configurations or Instantaneous descriptions(ID).

Many machines that might be thought to have more computational capability than a simple UTM can be shown to have no more power. They might compute faster or use less memory but cannot compute more powerfully i.e. more mathematical questions.

In automata theory, an o- machine or oracle machine is a abstract machine used to study decision problems. The problem the oracle solves can be of any complexity class. Even undecidable problems like halting problems can be used.

RASP or Random access stored program is an abstract machine that has instances like modern stored computers.

In theoretical computer science, the random access stored program( RASP ) machine model is an abstract machine used for the purpose of algorithm development and algorithm complexity theory.