Turing machine in automata, Summaries of Compiler Design

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TURING MACHINE

By Alan Turing

Definition:

■ (^) A Turing machine is a theoretical model of computation that consists of a tape, a read/write head, a set of states, and a set of transition rules. ■ It was introduced by Alan Turing in 1936 and serves as a foundation for the study of computability and computational complexity.

Components:

A TM can be formally described as a 7-tuple (Q, X, ∑, δ, q0, B, F) where −  (^) Q is a finite set of states  (^) X is the tape alphabet  (^) ∑ is the input alphabet  (^) δ is a transition function; δ : Q × X → Q × X × {Left shift, Right shift}.  (^) q0 is the initial state  (^) B is the blank symbol  (^) F is the set of final states

Process:

■ (^) The Turing machine operates in a cycle of reading a symbol, performing the corresponding transition, and moving the head. The transitions are determined by a transition function that maps the current state and symbol to the next state, symbol to write, and head movement direction. ■ (^) A Turing machine is said to accept an input if it halts in an accepting state, and it rejects the input if it halts in a rejecting state. If the machine never halts, it is said to loop or diverge on that input.

Example:

■ (^) Turing machine M = (Q, X, ∑, δ, q0, B, F) with Q = {q0, q1, q2, qf}, X = {a, b}, ∑ = {1}, q0 = {q0}, B = blank symbol, F = {qf } δ is given by − Tape alphabet symbol Present State ‘q0’ Present State ‘q1’ Present State ‘q2’ a 1Rq1 1Lq0 1Lqf b 1Lq2 1Rq1 1Rqf