0000000000315794
AUTHOR
Rosa Montalbano
Deterministic generalized automata
A generalized automaton (GA) is a finite automaton where the single transitions are defined on words rather than on single letters. Generalized automata were considered by K. Hashiguchi who proved that the problem of calculating the size of a minimal GA is decidable.
Local automata and completion
The problem of completing a finite automata preserving its properties is here investigated in the case of deterministic local automata. We show a decision procedure and give an algorithm which complete a deterministic local automaton (if the completion exists) with another one, having the same number of states.
Block-Deterministic Regular Languages
We introduce the notions of blocked, block-marked and blockdeterministic regular expressions. We characterize block-deterministic regular expressions with deterministic Glushkov block automata. The results can be viewed as a generalization of the characterization of one-unambiguous regular expressions with deterministic Glushkov automata. In addition, when a language L has a block-deterministic expression E, we can construct a deterministic finite-state automaton for L that has size linear in the size of E.
ON THE STAR HEIGHT OF RATIONAL LANGUAGES
Two problems concerning the star height of a rational language are investigated: the star height one problem and the relationships between the unambiguity of an expression and its star height. For this purpose we consider the class of factorial, transitive and rational (FTR) languages. From the algebraic point of view a FTR language is the set of factors of a rational submonoid M. Two subclasses of FTR languages are introduced: renewal languages, corresponding to the case of M finitely generated, and unambiguous renewal languages, corresponding to the case of M finitely generated and free. We prove that a FTR language has star height one if and only if it is renewal. This gives a simple de…