Assertion: predicate | /r/HasProperty | regular
Facets:
value: defined in the language of congruence
type: OTHER
Source sentences:
text: A predicate is said to be regular if the formal language is regular:25.
text: Predicates are encoded into languages in a different way, and the predicate is said to be regular if and only if the language is
text: A predicate is regular if and only if it can be defined by a monadic second order formula ϕ ( x 0 , … , x
text: A predicate is regular if and only if it can be defined by a first order logic formula ϕ ( x 0 , … , x
text: A predicate is regular if and only if it can be defined in the language of congruence arithmetic.
text: A predicate P {\displaystyle P} of arity r ≥ 1 {\displaystyle r\geq 1} is regular if it satisfies the two following conditions:
text: The predicate P {\displaystyle P} is regular if and only if for each increasing sequence of set s {\displaystyle \mathbf {s} } , P s {\displaystyle P_{\mathbf {s} }} is a recognizable submonoid of N p {\displaystyle \mathbb {N} ^{p}} .
text: The predicate P {\displaystyle P} is regular if and only if all languages which can be defined in first order logic with atomic predicates for letters and the atomic predicate P {\displaystyle P} are regular.
text: The predicate P {\displaystyle P} is non regular if and only if there exists a formula in F O [ ≤ , R ] {\displaystyle \mathbf {FO} [\leq ,R]} which defines the multiplication by a rational p q ∉ { 0 , 1 } {\displaystyle {\frac {p}{q}}
text: It is decidable whether a predicate defined in Presburger arithmetic is regular.