My two previous posts looked at experiments with ChatGPT and Google Bard. This post will look at redoing the same experiments with Microsoft’s Bing Chat: looking for mnemonic encodings and simplifying Boolean expressions.

When you open up Bing chat you can select a conversational style:

- More creative
- More balanced
- More precise

I chose “more precise” for my experiments.

## Mnemonic encodings

Bing seems to “know” more about the Major mnemonic system. In response to my first question about the system it gave a link to the Wikipedia article on the Major system and a couple other relevant links. It gives a more complete table of encodings than ChatGPT did:

- 0: s, z
- 1: t, d, th
- 2: n
- 3: m
- 4: r
- 5: l
- 6: j, ch, sh
- 7: c, k, g, q, ck
- 8: v, f, ph
- 9: p, b

### Directly asking for encodings

It seems to do pretty well when I ask for an encoding of a two-digit number, and when I ask for an encoding of a three-digit number it encodes the first two digits correctly but ignores the third digit. However, when I asked it to encode 345 it did very well:

Using the Major System, the number 345 can be encoded as “molar” or “mailer” or “miller” or “mural” or “marl”, among others.

ChatGPT and Google Bard said that no English word can encode 345, though Google Bard came up with Merlin anyway. (Strictly speaking “Merlin” encodes 3452, but it’s a common practice to just pay attention the first three consonants in words with more than three consonants.)

### Asking for sounds

When I asked “Find a word with the sounds g, r, and f” Bing came back with

One word that contains the sounds g, r, and f is “giraffe” 🦒

When I asked for the sounds l, f, and b, Bard came up with “belief.” When I added “in that order” to my prompt it came back with “bluff” and “flyby,” ignoring the order requirement.

In general Bing AI seems to do better that ChatGPT and Bard at word game questions.

## Boolean minimization

Next I tried the Boolean minimization problem that I’d tried with ChatGPT and Bard using the prompt

Minimize the boolean expression ¬AB¬C¬D + A¬B¬C¬D + A¬B¬CD + A¬BC¬D + A¬BCD + AB¬C¬D + ABC¬D + ABCD

ChatGPT tried a Karnaugh map approach, but botched it. Bard tried an algebraic approach, but also botched it.

Bing tried something different:

The given boolean expression can be simplified using the **consensus theorem**. The consensus theorem states that for any three variables A, B, and C: `AB + AC + BC = AB + AC`

. Applying this theorem to the given expression, we get

¬AB¬C¬D + A¬B¬C¬D + A¬B¬CD + A¬BC¬D + A¬BCD + AB¬C¬D + ABC¬D + ABCD

= ¬AB¬C¬D + A¬B¬C¬D + A¬B¬CD + A¬BC¬D + A¬BCD + AB¬C¬D + ABC

= ¬AB¬C¬D + A( ¬B¬C¬D + ¬B¬CD + ¬BC¬D + ¬BCD) + AB( ¬C¬D) + ABC

= ¬AB( ¬C) ( ¬D) + A( ¬B) ( ¬C( ¬D) + ¬CD) + AB( ¬C( ¬D)) + ABC

= ¬AB( ¬C) ( ¬D) + A( ¬B) ( ¬CD) + AB( ¬C( ¬D)) + ABC

= (A+B)(A+C)(A+D)(B+C)(B+D)(C+D)

This derivation starts out correctly but goes astray about halfway through.