Characterizing Level One in Group-Based Concatenation Hierarchies

Bridges for Concatenation Hierarchies

In the seventies, several classification schemes for the rational languages were proposed, based on the alternate use of certain operators (union, complementation, product and star). Some thirty years later, although much progress has been done, several of the original problems are still open. Furthermore, their significance has grown considerably over the years, on account of the successive di...

Arbres et Hierarchies de Concatenation

Generic Results for Concatenation Hierarchies

In the theory of formal languages, the understanding of concatenation hierarchies of regular languages is one of the most fundamental and challenging topic. In this paper, we survey progress made in the comprehension of this problem since 1971, and we establish new generic statements regarding this problem.

Concatenation Hierarchies and Forbidden Patterns

We make the following progress on the dot–depth problem: (1) We introduce classes CB n and CL n of starfree languages defined via forbidden patterns in finite automata. It is shown for all n 0 that CB n (CL n) contains level n + 1=2 of the dot–depth hierarchy (Straubing–Thérien hierarchy, resp.). Since we prove that CB n and CL n have decidable membership problems, this yields a lower bound alg...

The forbidden pattern approach to concatenation hierarchies