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A complete characterization of primitive recursive intensional behaviours

P. Valarcher (2008)

RAIRO - Theoretical Informatics and Applications

We give a complete characterization of the class of functions that are the intensional behaviours of primitive recursive (PR) algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers.

A Finite Characterization and Recognition of Intersection Graphs of Hypergraphs with Rank at Most 3 and Multiplicity at Most 2 in the Class of Threshold Graphs

Yury Metelsky, Kseniya Schemeleva, Frank Werner (2017)

Discussiones Mathematicae Graph Theory

We characterize the class [...] L32 L 3 2 of intersection graphs of hypergraphs with rank at most 3 and multiplicity at most 2 by means of a finite list of forbidden induced subgraphs in the class of threshold graphs. We also give an O(n)-time algorithm for the recognition of graphs from [...] L32 L 3 2 in the class of threshold graphs, where n is the number of vertices of a tested graph.

A geometrical method in combinatorial complexity

Jaroslav Morávek (1981)

Aplikace matematiky

A lower bound for the number of comparisons is obtained, required by a computational problem of classification of an arbitrarily chosen point of the Euclidean space with respect to a given finite family of polyhedral (non-convex, in general) sets, covering the space. This lower bound depends, roughly speaking, on the minimum number of convex parts, into which one can decompose these polyhedral sets. The lower bound is then applied to the knapsack problem.

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