Blum–Shub–Smale model of computation

E537367

complexity theory framework computational model theoretical model

The Blum–Shub–Smale model of computation is a theoretical framework for analyzing algorithms over real numbers, extending classical complexity theory beyond discrete computation.

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All labels observed (2)

Label	Occurrences
Blum–Shub–Smale model of computation canonical	1
Blum–Shub–Smale model of real computation	1

Statements (47)

Predicate	Object
instanceOf	complexity theory framework ⓘ computational model ⓘ theoretical model ⓘ
alsoKnownAs	BSS model NERFINISHED ⓘ real RAM model NERFINISHED ⓘ
assumes	unit-cost arithmetic operations on real numbers ⓘ
characterizedBy	focus on algebraic operations rather than bit operations ⓘ unit-time cost for each arithmetic operation ⓘ
contrastsWith	bit-level Turing machine model ⓘ
defines	NP_R NERFINISHED ⓘ P_R NERFINISHED ⓘ complexity classes over the reals ⓘ decision problems over the reals ⓘ
extends	classical Turing machine model NERFINISHED ⓘ discrete complexity theory ⓘ
field	computational complexity theory ⓘ numerical analysis ⓘ real computation ⓘ theoretical computer science ⓘ
formalizedIn	"On a theory of computation and complexity over the real numbers" NERFINISHED ⓘ
hasApplication	computational geometry ⓘ optimization over the reals ⓘ real algebraic geometry ⓘ
hasFeature	branching based on sign of real-valued tests ⓘ infinite precision real arithmetic ⓘ random-access memory of real registers ⓘ
namedAfter	Lenore Blum NERFINISHED ⓘ Mike Shub NERFINISHED ⓘ Steve Smale NERFINISHED ⓘ
operatesOn	real numbers ⓘ vectors of real numbers ⓘ
purpose	analyze algorithms over real numbers ⓘ generalize computation beyond discrete structures ⓘ study complexity of real-valued computations ⓘ
relatedTo	Turing machine NERFINISHED ⓘ algebraic complexity theory ⓘ computable analysis ⓘ real RAM NERFINISHED ⓘ
supportsOperation	addition on real numbers ⓘ comparison of real numbers ⓘ division on real numbers ⓘ multiplication on real numbers ⓘ subtraction on real numbers ⓘ
usedFor	analyzing geometric algorithms ⓘ analyzing numerical algorithms abstractly ⓘ studying feasibility of systems of polynomial equations ⓘ
yearProposed	late 1980s ⓘ

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Instruction

You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10.

# Requirements
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- If the subject is not a named entity, return an empty list.
- Include at least one triple where predicate is "instanceOf".
- Do not get too wordy.
- Separate several objects into multiple triples with one object.

Input

Subject: Blum–Shub–Smale model of computation
Description of subject: The Blum–Shub–Smale model of computation is a theoretical framework for analyzing algorithms over real numbers, extending classical complexity theory beyond discrete computation.

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Lenore Blum → notableWork → Blum–Shub–Smale model of computation ⓘ

Lenore Blum → knownFor → Blum–Shub–Smale model of computation ⓘ

this entity surface form: Blum–Shub–Smale model of real computation