Corrigendum to “Completeness results for graph isomorphism” [J. Comput. System Sci. 66 (2003) 549–566]

Completeness results for graph isomorphism

Corrigendum to "Shifting: One-inclusion mistake bounds and sample compression" [J. Comput. System Sci 75 (1) (2009) 37-59]

Article history: Received 8 February 2010 Available online 11 March 2010 H. Simon and B. Szörényi have found an error in the proof of Theorem 52 of “Shifting: One-inclusion mistake bounds and sample compression”, Rubinstein et al. (2009) [3]. In this note we provide a corrected proof of a slightly weakened version of this theorem. Our new bound on the density of one-inclusion hypergraphs is aga...

Graph Isomorphism Completeness for Trapezoid Graphs

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability graphs of partially ordered sets with interval dimension 2 and height 3. In contrast, the problem is known to be solvable in polynomial time for comparabilit...

Erratum to: "A new framework for declarative programming": [Theoret. Comput. Sci. 300 (2003) 91-160]

We propose a new framework for the syntax and semantics of Weak Hereditarily Harrop logic programming with constraints, based on resolution over -categories: 9nite product categories with canonical structure. Constraint information is directly built-in to the notion of signature via categorical syntax. Many-sorted equational constraints are a special case of the formalism which combines feature...

Completeness results for metrized rings and lattices

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...