computer science

Sentential decision diagram

Sentential decision diagram 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 Sentential decision diagram rather than just read about it. In short: In artificial intelligence, a sentential decision diagram (SDD) is a type of knowledge representation used in knowledge compilation to represent Boolean functions. SDDs can be viewed as a generalization of the influential ordered binary decision diagram (OBDD) representation, by allowing decisions on multiple variables at once.

Key takeaways

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

Reference excerpt

In artificial intelligence, a sentential decision diagram (SDD) is a type of knowledge representation used in knowledge compilation to represent Boolean functions. SDDs can be viewed as a generalization of the influential ordered binary decision diagram (OBDD) representation, by allowing decisions on multiple variables at once. Like OBDDs, SDDs allow for tractable Boolean operations, while being exponentially more succinct. For this reason, they have become an important representation in knowledge compilation.

Properties SDDs are defined with respect to a generalization of variable ordering known as a variable tree (vtree). Provided that they satisfy additional properties known as compression and trimming (which are analogous to ROBDDs), SDDs are a canonical representation of Boolean functions; that is, they are unique given a vtree. Like OBDDs, they allow for operations such as conjunction, disjunction and negation to be computed directly on the representation in polynomial time, while being potentially more compact. They also allow for polynomial-time model counting. SDDs are known to be exponentially more succinct than OBDDs.

Applications SDDs are used as a compilation target for probabilistic logic programs by the ProbLog 2 system since they support tractable (weighted) model counting as well as tractable negation, conjunction and disjunction while being more succinct than BDDs. SDDs have also been extended to model probability distributions, in which context they are known as probabilistic sentential decision diagrams (PSDD).

References

Worked examples

Example 1 — a first encounter with Sentential decision diagram

Start with the simplest possible case. Write down what Sentential decision diagram 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 Sentential decision diagram 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 Sentential decision diagram 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 Sentential decision diagram

In research: Sentential decision diagram 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 Sentential decision diagram 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: Sentential decision diagram is common in secondary-school and first-year university syllabi. It links to neighbouring topics Artificial intelligence stubs, Graph data structures, Knowledge compilation, so understanding it makes those chapters shorter.
In everyday life: Look for Sentential decision diagram 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 Sentential decision diagram in 20 minutes

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

Frequently asked questions

What is Sentential decision diagram in simple terms?

Why does Sentential decision diagram 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 Sentential decision diagram?

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 Sentential decision diagram.