Expressive power of digraph solvability

Expressive power of digraph solvability

A kernel of a directed graph is a set of vertices without edges between them, such that every other vertex has a directed edge to a vertex in the kernel. A digraph possessing a kernel is called solvable. We show that solvability of digraphs is equivalent to satisfiability of theories of propositional logic. Based on a new normal form for such theories, this equivalence relates finitely branchin...

Expressive Power of SQL

It is a folk result in database theory that SQL cannot express recursive queries such as reachability; in fact, a new construct was added to SQL3 to overcome this limitation. However, the evidence for this claim is usually given in the form of a reference to a proof that re-lational algebra cannot express such queries. SQL, on the other hand, in all its implementations has three features that f...

The Expressive Power of

The expressive power of parallelism

We explore an algebraic language for networks consisting of a xed number of reactive units, communicating synchronously over a xed linking structure. The language has only two operators: disjoint parallelism, where two networks are composed in parallel without any interconnections, and linking, where an interconnec-tion is formed between two ports. The intention is that these operators correspo...

Expressive Power of Grammatical Formalisms

We propose formalisms and concepts which allow to make precise the m'gmnents in controversies over the adequacy of competing models of language, and over their formal equivalence.