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searching for Least fixed point 21 found (43 total)

Fixed-point logic (2,013 words) [view diff] no match in snippet view article find links to article

relationship to database query languages, in particular to Datalog. Least fixed-point logic was first studied systematically by Yiannis N. Moschovakis in

Bekić's theorem (1,182 words) [view diff] exact match in snippet view article find links to article

(componentwise order). By the Kleene fixed-point theorem, it has a least fixed point μ ( x , y ) . ( f , g ) ( x , y ) {\displaystyle \mu (x,y).(f,g)(x

Inductive set (334 words) [view diff] exact match in snippet view article find links to article

inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ1n formula, for some

Kleene's recursion theorem (3,163 words) [view diff] exact match in snippet view article find links to article

^{k})} be a recursive functional. Then Φ {\displaystyle \Phi } has a least fixed point f Φ : N k → N {\displaystyle f_{\Phi }:\mathbb {N} ^{k}\rightarrow

Theories of iterated inductive definitions (2,536 words) [view diff] exact match in snippet view article find links to article

LFP(\Gamma )=I} , where L F P ( f ) {\displaystyle LFP(f)} denotes the least fixed point of f {\displaystyle f} . The language of ID1, L I D 1 {\displaystyle

S2S (mathematics) (4,617 words) [view diff] no match in snippet view article

be defined from S in arithmetic μ-calculus (arithmetic formulas + least fixed-point logic) (4) T is in the least β-model (i.e. an ω-model whose set-theoretic

Fixed-point theorem (1,278 words) [view diff] exact match in snippet view article find links to article

meaning is the same: a recursive function can be described as the least fixed point of a certain functional, mapping functions to functions. The above

Reinhardt cardinal (787 words) [view diff] no match in snippet view article find links to article

{\displaystyle \lambda } holds, where λ {\displaystyle \lambda } is the least fixed-point above the critical point. J1: For every ordinal α {\displaystyle \alpha

P versus NP problem (7,720 words) [view diff] no match in snippet view article find links to article

expressible in first-order logic with the addition of a suitable least fixed-point combinator. Recursive functions can be defined with this and the order

LL parser (4,363 words) [view diff] exact match in snippet view article find links to article

steps 2 and 3 until all Fi sets stay the same. The result is the least fixed point solution to the following system: Fi(A) ⊇ Fi(w) for each rule A →

Complete partial order (1,425 words) [view diff] no match in snippet view article find links to article

category. Every order-preserving self-map f of a cpo (P, ⊥) has a least fixed-point. If f is continuous then this fixed-point is equal to the supremum

Tefkat (422 words) [view diff] no match in snippet view article find links to article

more imperative semantics of a Tefkat transformation is the iterated least fixed-point of the immediate consequence of each rule. Due to stratification,

Relational model (4,219 words) [view diff] no match in snippet view article find links to article

which cannot expressive recursive queries without introducing a least-fixed-point operator, recursive relations can be defined in Datalog, without introducing

Datalog (4,915 words) [view diff] exact match in snippet view article find links to article

the rules of the program in a single step. The least-fixed-point semantics define the least fixed point of T to be the meaning of the program; this coincides

Abstract interpretation (2,924 words) [view diff] no match in snippet view article find links to article

x ′ ) ≤ x ′ {\displaystyle f(x')\leq x'} is an abstraction of the least fixed-point of f {\displaystyle f} , which exists, according to the Knaster–Tarski

Closure operator (2,664 words) [view diff] exact match in snippet view article find links to article

Then such an operator is continuous and we can define cl(X) as the least fixed point for J greater or equal to X. In accordance with such a point of view

Ordinal number (6,711 words) [view diff] exact match in snippet view article find links to article

(1+\alpha )} . Since f {\displaystyle f} has ω ω {\displaystyle \omega ^{\omega }} as least fixed point, larger ordinal numbers cannot be represented.

Coinduction (1,896 words) [view diff] no match in snippet view article find links to article

"non-F-logical assumptions"). The Knaster–Tarski theorem tells us that the least fixed-point of F {\displaystyle F} (denoted μ F {\displaystyle \mu F} ) is given

Denotational semantics of the Actor model (3,346 words) [view diff] exact match in snippet view article find links to article

then ProgressionS(⊔iεω Mi) = ⊔iεω ProgressionS(Mi) Furthermore, the least fixed point of ProgressionS is given by the Concurrency Representation Theorem

Dependence logic (4,500 words) [view diff] no match in snippet view article find links to article

greatest fixed-point logic sentences; hence inclusion logic captures (least) fixed-point logic on finite models, and PTIME over finite ordered models. Exclusion

Syntax and semantics of logic programming (2,189 words) [view diff] exact match in snippet view article find links to article

subset inclusion on T. By the Knaster–Tarski theorem, this map has a least fixed point; by the Kleene fixed-point theorem the fixed point is the supremum