Transition Function, Instantaneous Descriptions, and Moves

: Q Q {L, R}

This means:
When the machine is in a given state (Q) and reads a given symbol () from the tape, it replaces the symbol on the tape with some other symbol (), goes to some other state (Q), and moves the tape head one square left (L) or right (R).

An instantaneous description or configuration of a Turing machine requires (1) the state the Turing machine is in, (2) the contents of the tape, and (3) the position of the tape head on the tape. This can be summarized in a string of the form

where the x's are the symbols on the tape, q_m is the current state, and the tape head is on the square containing x_k (the symbol immediately following q_m).

A move of a Turing machine can therefore be represented as a pair of instaneous descriptions, separated by the symbol "". For example, if

(q₅, b) = (q₈, c, R)

abbabq₅babb abbabcq₈abb