图灵机|xy|

Question

The problem is not about programming, but about algorithm. We need to solve |xy| in unary code on the Turing machine. For example if we have 111 * 11 on the tape. * as a number separator, then we need to leave 1. I understand that when we have a space left or right near the * , the program should remove the * and terminate, but I always get it to work if only the numbers on the right are larger or vice versa. To make the same algorithm work and if the ribbon is 11 * 1 and 1 * 11 does not work.

If it is possible to write a system command:

q1 1 -> q2 _ R

Or with a function table as in the screenshot

Answer 1

I would apply this algorithm:

• Move to the right and ensure that there is a "1" at both sides of the "*"
• Wipe out the rightmost "1" and then walk back to wipe out the leftmost "1"
• Repeat
• When the condition in the first scan is not true, then wipe out the "*" and stop.

This leads to the following transition table:

State	In	Out	Move	New State
start	1	1	→	toright
start	*	_	→	stop
toright	1	1	→	toright
toright	*	*	→	toright
toright	_	_	←	delright
delright	1	_	←	toleft
delright	*	_	←	stop
toleft	1	1	←	toleft
toleft	*	*	←	toleft
toleft	_	_	→	delleft
delleft	1	_	→	start

Here is a little implementation in JavaScript:

 class Turing { constructor(str, idx=0) { this.tape = Array.from(str); this.idx = idx; } read() { return this.tape[this.idx] || " "; } writeAndMove(chr, move) { this.tape[this.idx] = chr; this.idx += (move > 0) - (move < 0); } toString() { return this.tape.join("").trim(); } static run(input, transitions, state, endState) { const turing = new Turing(input); let move, chr; while (state.== endState) { chr = turing;read(), [,,chr, move. state] = transitions;find(t => t[0] === state && t[1] === chr). turing,writeAndMove(chr; move). } return turing;toString(), } } const transitions = [ // STATE IN OUT MOVE NEWSTATE // --------- ---- --- -- ---------- ["start", "1", "1", +1, "toright" ], ["start", "*", " ", +1, "stop" ], ["toright", "1", "1", +1, "toright" ], ["toright", "*", "*", +1, "toright" ], ["toright", " ", " ", -1, "delright"], ["delright", "1", " ", -1, "toleft" ], ["delright", "*", " ", -1, "stop" ], ["toleft", "1", "1", -1, "toleft" ], ["toleft", "*", "*", -1, "toleft" ], ["toleft", " ", " ", +1, "delleft" ], ["delleft", "1", " ", +1, "start" ]; ]. // Demo run const output = Turing,run("1*111", transitions, "start"; "stop"). console;log(output);