science

Wang B-machine

Wang B-machine is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Wang B-machine rather than just read about it. In short: As presented by Hao Wang (1954, 1957), his basic machine B is an extremely simple computational model equivalent to the Turing machine. It is "the first formulation of a Turing-machine theory in terms of computer-like models" (Minsky, 1967: 200).

Key takeaways

Wang B-machine belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Wang B-machine to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Wang B-machine from memory before moving on to harder problems.

Reference excerpt

As presented by Hao Wang (1954, 1957), his basic machine B is an extremely simple computational model equivalent to the Turing machine. It is "the first formulation of a Turing-machine theory in terms of computer-like models" (Minsky, 1967: 200). With only 4 sequential instructions it is very similar to, but even simpler than, the 7 sequential instructions of the Post–Turing machine. In the same paper, Wang introduced a variety of equivalent machines, including what he called the W-machine, which is the B-machine with an "erase" instruction added to the instruction set.

Description As defined by Wang (1954) the B-machine has at its command only 4 instructions:

→ : Move tape-scanning head one tape square to the right (or move tape one square left), then continue to next instruction in numerical sequence; ← : Move tape-scanning head one tape square to the left (or move tape one square right), then continue to next instruction in numerical sequence; * : In scanned tape-square print mark * then go to next instruction in numerical sequence; Cn: Conditional "transfer" (jump, branch) to instruction "n": If scanned tape-square is marked then go to instruction "n" else (if scanned square is blank) continue to next instruction in numerical sequence. A sample of a simple B-machine instruction is his example:

1. *, 2. →, 3. C2, 4. →, 5. ← He rewrites this as a collection of ordered pairs:

{ ( 1, * ), ( 2, → ), ( 3, C2 ), ( 4, → ), ( 5, ← ) } Wang's W-machine is simply the B-machine with the one additional instruction

5. E : In scanned tape-square erase the mark * (if there is one) then go to next instruction in numerical sequence.

See also Codd's cellular automaton Counter-machine model

Notes

References

Worked examples

Example 1 — a first encounter with Wang B-machine

Start with the simplest possible case. Write down what Wang B-machine claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Wang B-machine before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Wang B-machine ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Wang B-machine

In research: Wang B-machine appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Wang B-machine in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Wang B-machine is common in secondary-school and first-year university syllabi. It links to neighbouring topics Turing machine, so understanding it makes those chapters shorter.
In everyday life: Look for Wang B-machine outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Wang B-machine” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Wang B-machine in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Wang B-machine means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Wang B-machine out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Wang B-machine in simple terms?

Why does Wang B-machine matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Wang B-machine?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Wang B-machine.