A Semigroup Characterization of Dot-Depth one Languages

Some Forbidden Patterns in Automata for Dot-Depth One Languages

We deal with the class B of dot-depth one languages which forms level one of the socalled dot-depth hierarchy. For some fixed alphabet A with jAj , a language L A is in the class B if and only if it can be expressed as a Boolean combination of languages u A u A u A A un A un, where ui A and n . This class is the highest level of the dot-depth hierarchy known to be decidable up to now and a numb...

Modular quantifiers

In the late nineteen-eighties much of our research concerned the application of semigroup-theoretic methods to automata and regular languages, and the connection between computational complexity and this algebraic theory of automata. It was during this period that we became aware of the work of Wolfgang Thomas. Thomas had undertaken the study of concatenation hierarchies of star-free regular la...

Languages of Dot-Depth

We prove an effective characterization of languages having dot-depth . To our knowledge, only the classes of levels , and of the dot-depth hierarchy were known to be decidable. Let B denote the class of languages having dot-depth , i.e., languages that can be written as finite unions of languages of the form u L u L u Lnun, where ui A and Li are languages of dot-depth one. 1. Let k . We define ...

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

Boolean Hierarchies inside Dot–Depth One

Let B denote the class of languages having dot–depth , i.e., the class of languages that can we written as finite unions of languages u A u A un A un, where ui A and n . A language has dot–depth one if and only if it is in the Boolean closure of B . We examine the structure of the class of dot–depth one languages with respect to Boolean operations and identify an infinite family of Boolean hier...