scholarly journals On characterizations of the basic feasible functionals, Part I

2001 ◽  
Vol 11 (1) ◽  
pp. 117-153 ◽  
Author(s):  
ROBERT J. IRWIN ◽  
JAMES S. ROYER ◽  
BRUCE M. KAPRON
Keyword(s):  
Polynomial Time ◽  
Theoretic Characterization

We introduce a typed programming formalism, type-2 inflationary tiered loop programs or ITLP2, that characterizes the type-2 basic feasible functionals. ITLP2 is based on Bellantoni and Cook's (1992) and Leivant's (1995) type-theoretic characterization of polynomial-time, and turns out to be closely related to Kapron and Cook's (1991; 1996) machine-based characterization of the type-2 basic feasible functionals.

LINDSTRÖM QUANTIFIERS AND LEAF LANGUAGE DEFINABILITY

1998 ◽  
Vol 09 (03) ◽  
pp. 277-294 ◽  
Author(s):  
HANS-JÖRG BURTSCHICK ◽  
HERIBERT VOLLMER
Keyword(s):  
Polynomial Time ◽  
Second Order ◽  
New Model ◽  
First Order ◽  
Theoretic Characterization ◽  
Polynomial Time Hierarchy ◽  
The Way

We introduce second-order Lindström quantifiers and examine analogies to the concept of leaf language definability. The quantifier structure in a second-order sentence defining a language and the quantifier structure in a first-order sentence characterizing the appropriate leaf language correspond to one another. Under some assumptions, leaf language definability and definability with second-order Lindström quantifiers may be seen as equivalent. Along the way we tighten the best up to now known leaf language characterization of the classes of the polynomial time hierarchy and give a new model-theoretic characterization of PSPACE.

CHARACTERISTIC PROPERTIES AND RECOGNITION OF GRAPHS IN WHICH GEODESIC AND MONOPHONIC CONVEXITIES ARE EQUIVALENT

2012 ◽  
Vol 04 (04) ◽  
pp. 1250063 ◽  
Author(s):  
FRANCESCO M. MALVESTUTO ◽  
MAURO MEZZINI ◽  
MARINA MOSCARINI
Keyword(s):  
Polynomial Time ◽  
Connected Graph ◽  
Convex Set ◽  
State Characteristic ◽  
Theoretic Characterization

Let G be a connected graph. A subset X of V(G) is g-convex (m-convex) if it contains all vertices on shortest (induced) paths between vertices in X. We state characteristic properties of graphs in which every g-convex set is m-convex, based on which we show that such graphs can be recognized in polynomial time. Moreover, we state a new convexity-theoretic characterization of Ptolemaic graphs.

scholarly journals A lattice-theoretic characterization of pure subgroups of Abelian groups

2021 ◽  
Author(s):  
M. Ferrara ◽  
M. Trombetti
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
General Definition ◽  
Short Paper ◽  
Theoretic Characterization ◽  
Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

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