How does a Post machine operate with a two-way tape?

A Post machine, as proposed by E.L. Post, operates using a finite sequence of instruction pairs. Each pair consists of a step number and an associated instruction, which governs the machine's behavior on a two-way tape.1

The machine functions through the following mechanisms:

• Movement and Printing: The machine can be instructed to move the two-way tape one square to the right or left, or to print a symbol (including a blank) from a finite alphabet onto the current square.1
• Sequential Execution: Starting at step 1, the machine executes the instruction associated with the current step and proceeds to the next step ($n+1$) by default.1
• Conditional Branching: If an instruction is an integer $m$, the machine performs a conditional check: if the square currently being scanned is marked, the machine jumps to step $m$; if the square is blank, it proceeds to the next step ($n+1$).1

These machines are computationally equivalent to Turing machines and are capable of computing any partial recursive function.1