Turing’s Bold Claim He could design a simple computer that could solve anything that was computable. He postulated that whatever fancy new computers were invented in the future, and whatever problems they could solve, his machine could also solve them. And he could simulate it using paper and pencil.

Note The Connection The Turing Test from week 1 is related to Turing’s claim: If his Turing Machine can mimic any computer, then it can mimic an intelligent computer. In other words, his Turing Machine can pass the Turing Test if computer intelligence is possible. If you can write “smart software”, his TM can run it!

The Turing Machine and Logic Circuits We could build a TM out of logic circuits we have seen, with one important exception: The TM requires memory to keep track of what state it is in. Can we build computer memory out of logic circuits? Yes! [I’ll demonstrate with xLogicCircuits tool.]

A Couple Artist Conceptions

What Does a TM Program Look Like?  First, you have to know what symbols can appear on the tape.  Theoretically, you can get away with just 0 and 1.  But for convenience, often have a few more, e.g.,

Now We Know Symbols – What Next? We need a set of “rules” of the following form: If you are in state s and read symbol p then write symbol q and move direction. Where p and q are in the Symbols set and direction is left or right.

Often Easiest to Program in Excel In State ReadingWriteMove New State 0xyR0 0yxR1 1xxL2 ……………

Let’s Try A Program In State ReadingWriteMove New State ????? ##101001## Your program:  Always starts at left-most digit (for simplicity).  Places a 0 after right-most digit and halts in next blank.

Let’s Try Another Program In State ReadingWriteMove New State ????? ##111111## Your program:  Always starts at left-most 1 (for simplicity).  If even number of 1’s, places an x after right-most 1 and halts in next blank.  If odd number of 1’s, places a y after right-most 1 and halts in next blank.

We Can Use A Tool To Test This is interesting. Tool allows you to provide a default rule for each state, only one per state. “other” will match any other symbol not named in another rule for that state. “same” refers to the symbol matched by “other”. Can save lots of rule writing!