Rational relations having a rational trace on each finite intersection of rational relations

Rational relations having a rational trace on each finite intersection of rational relations

We consider the family of rational relations on words, i.e., relations recognized by multitape automata, which have rational trace on any finite intersection of rational relations. We prove that this family consists of finite unions of relations which are of two types: stars of tuples possibly with an extra prefix and suffix and relations with all but one singleton set components.

Uniformization of Rational Relations

Rational tree relations

We investigate forests and relations on trees generated by grammars in which the non-terminals represent relations. This introduces some synchronization between productions. We show that these sets are also solutions of systems of equations, that they are described by rational expressions involving union, substitution and iterated substitution, and that they are preserved by residuals. We show ...

Graph Logics with Rational Relations

We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword or subse...

Rational Functions with Linear Relations

We find all polynomials f, g, h over a field K such that g and h are linear and f(g(x)) = h(f(x)). We also solve the same problem for rational functions f, g, h, in case the field K is algebraically closed.