POWERS OF REGULAR LANGUAGES

In this paper we prove that it is decidable whether the set pow (L), which we get by taking all the powers of all the words in some regular language L, is regular or not. The problem was originally posed by Calbrix and Nivat in 1995. Partial solutions have been given by Cachat for unary languages and by Horváth et al. for various kinds of exponent sets for the powers and regular languages which have primitive roots satisfying certain properties. We show that the regular languages which have a regular power are the ones which are 'almost' equal to their Kleene-closure.

Uniform quality constrained gaussian basis sets

Uniformly balanced (6S3P), (7S3P), and (8S4P) gaussian basis sets with identical exponent sets for functions describing the 2s and 2p subshells have been obtained for the first row atoms. The basis sets have been determined using a direct optimization technique; they are thoroughly balanced and satisfy a rigorous quality criterion. These uniform quality constrained basis sets were designed for applications in ab initio programs of the type of the GAUSSIAN 70 program system, that may utilize the integration-time saving constraint α2s = α2p.