computer science

Recursive grammar

Recursive grammar 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 Recursive grammar rather than just read about it. In short: In computer science, a grammar is informally called a recursive grammar if it contains production rules that are recursive, meaning that expanding a non-terminal according to these rules can eventually lead to a string that includes the same non-terminal again. Otherwise it is called a non-recursive grammar.

Key takeaways

Recursive grammar 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 Recursive grammar to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Recursive grammar from memory before moving on to harder problems.

Reference excerpt

In computer science, a grammar is informally called a recursive grammar if it contains production rules that are recursive, meaning that expanding a non-terminal according to these rules can eventually lead to a string that includes the same non-terminal again. Otherwise it is called a non-recursive grammar. For example, a grammar for a context-free language is left recursive if there exists a non-terminal symbol A that can be put through the production rules to produce a string with A (as the leftmost symbol). All types of grammars in the Chomsky hierarchy can be recursive and it is recursion that allows the production of infinite sets of words.

Properties A non-recursive grammar can produce only a finite language; and each finite language can be produced by a non-recursive grammar. For example, a straight-line grammar produces just a single word. A recursive context-free grammar that contains no useless rules necessarily produces an infinite language. This property forms the basis for an algorithm that can test efficiently whether a context-free grammar produces a finite or infinite language.

References

Worked examples

Example 1 — a first encounter with Recursive grammar

Start with the simplest possible case. Write down what Recursive grammar 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 Recursive grammar 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 Recursive grammar 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 Recursive grammar

In research: Recursive grammar 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 Recursive grammar 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: Recursive grammar is common in secondary-school and first-year university syllabi. It links to neighbouring topics Formal languages, Theoretical computer science stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Recursive grammar 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.

Affiliate

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

How to study Recursive grammar in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Recursive grammar 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 Recursive grammar out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Recursive grammar in simple terms?

Why does Recursive grammar 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 Recursive grammar?

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 Recursive grammar.