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Abstract rewriting system and Binary relation

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Abstract rewriting system and Binary relation

Abstract rewriting system vs. Binary relation

In mathematical logic and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviation ARS) is a formalism that captures the quintessential notion and properties of rewriting systems. In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

Similarities between Abstract rewriting system and Binary relation

Abstract rewriting system and Binary relation have 13 things in common (in Unionpedia): Binary relation, Closure (mathematics), Composition of relations, Confluence (abstract rewriting), Converse relation, Equality (mathematics), Equivalence relation, Preorder, Reflexive relation, Set (mathematics), Transitive closure, Transitive relation, Well-founded relation.

Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Closure (mathematics)

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.

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Composition of relations

In the mathematics of binary relations, the composition relations is a concept of forming a new relation from two given relations R and S. The composition of relations is called relative multiplication in the calculus of relations.

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Confluence (abstract rewriting)

In computer science, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result.

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Converse relation

In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation.

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Equality (mathematics)

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

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Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

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Preorder

In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive.

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Reflexive relation

In mathematics, a binary relation R over a set X is reflexive if every element of X is related to itself.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Transitive closure

In mathematics, the transitive closure of a binary relation R on a set X is the smallest relation on X that contains R and is transitive.

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Transitive relation

In mathematics, a binary relation over a set is transitive if whenever an element is related to an element and is related to an element then is also related to.

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Well-founded relation

In mathematics, a binary relation, R, is called well-founded (or wellfounded) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is an element m not related by sRm (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.

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The list above answers the following questions

Abstract rewriting system and Binary relation Comparison

Abstract rewriting system has 41 relations, while Binary relation has 110. As they have in common 13, the Jaccard index is 8.61% = 13 / (41 + 110).

References

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