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L/poly

L/poly is a computer 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 L/poly rather than just read about it. In short: In computational complexity theory, L/poly is the complexity class of logarithmic space machines with a polynomial amount of advice. L/poly is a non-uniform logarithmic space class, analogous to the non-uniform polynomial time class P/poly.

Key takeaways

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

Reference excerpt

In computational complexity theory, L/poly is the complexity class of logarithmic space machines with a polynomial amount of advice. L/poly is a non-uniform logarithmic space class, analogous to the non-uniform polynomial time class P/poly. Formally, for a formal language L to belong to L/poly, there must exist an advice function f that maps an integer n to a string of length polynomial in n, and a Turing machine M with two read-only input tapes and one read-write tape of size logarithmic in the input size, such that an input x of length n belongs to L if and only if machine M accepts the input x, f(n). Alternatively and more simply, L is in L/poly if and only if it can be recognized by branching programs of polynomial size. One direction of the proof that these two models of computation are equivalent in power is the observation that, if a branching program of polynomial size exists, it can be specified by the advice function and simulated by the Turing machine. In the other direction, a Turing machine with logarithmic writable space and a polynomial advice tape may be simulated by a branching program the states of which represent the combination of the configuration of the writable tape and the position of the Turing machine heads on the other two tapes. In 1979, Aleliunas et al. showed that symmetric logspace is contained in L/poly. However, this result was superseded by Omer Reingold's result that SL collapses to uniform logspace. BPL is contained in L/poly, which is a variant of Adleman's theorem.

References

Worked examples

Example 1 — a first encounter with L/poly

Start with the simplest possible case. Write down what L/poly claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer 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 L/poly 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 L/poly 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 L/poly

In research
L/poly appears in computer 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 L/poly 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
L/poly is common in secondary-school and first-year university syllabi. It links to neighbouring topics Complexity classes, Theoretical computer science stubs, so understanding it makes those chapters shorter.
In everyday life
Look for L/poly 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.

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How to study L/poly in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what L/poly means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain L/poly out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is L/poly in simple terms?

In computational complexity theory, L/poly is the complexity class of logarithmic space machines with a polynomial amount of advice. L/poly is a non-uniform logarithmic space class, analogous to the non-uniform polynomial time class P/poly.

Why does L/poly matter?

Because it connects several computer 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 L/poly?

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 L/poly.

Tags

  • Complexity classes
  • Theoretical computer science stubs

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