We show that the satisfiability problem for the two-variable first-order logic, FO2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO2l...

It has previously been shown that transitive verbs are more difficult to recall than intransitive. Experiment I replicated this finding. Experiment II examined the associations to, and response latencies of, transitive and intransitive verbs. Latencies of responses did not differ, but the form class of responses was significantly different. Transitive verbs elicited more noun responses. It is s...

A graph is called cubic and tetravalent if all of its vertices have valency 3 and 4, respectively. It is called vertex-transitive and arc-transitive if its automorphism group acts transitively on its vertex-set and on its arcset, respectively. In this paper, we combine some new theoretical results with computer calculations to construct all cubic vertex-transitive graphs of order at most 1280. ...

The complementary prism of a graph Γ is the ΓΓ̄, which formed from union and its complement Γ̄ by adding an edge between each pair identical vertices in Γ̄. Vertex-transitive self-complementary graphs provide vertex-transitive prisms. It was recently proved author that ΓΓ̄ core, i.e. all endomorphisms are automorphisms, whenever vertex-transitive, self-complementary, either core or complete graph. ...

General transitive closures are a convenient operation for process ing recursive structures with relational languages because they are easy to understand e ciently to implement and expressive enough to support a broad range of practical applications To further extend the expressiveness of general transitive closures we study the use of aggregate functions together with general transitive closur...

Transitive signature, motivated by signing vertices and edges of a dynamically growing, transitively closed graph, was first proposed by Micali and Rivest. The general designing paradigm proposed there involved a underlying standard signature scheme, which is required to be existentially unforgeable against adaptive chosen message attacks. We show that the requirement for the underlying signatu...

A Boolean function is called vertex-transitive, if the partition of the Boolean cube into the preimage of 0 and the preimage of 1 is invariant under a vertex-transitive group of isometric transformations of the Boolean cube. The logarithm of the number of the vertex-transitive functions of n variables is at least Ω(n) and at most O(n logn). There is a polynomial over F2 of any given degree, whi...

A cycle decomposition of a graph Γ is a set C of cycles of Γ such that every edge of Γ belongs to exactly one cycle in C. Such a decomposition is called arc-transitive if the group of automorphisms of Γ that preserve C setwise acts transitively on the arcs of Γ . In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining an...