CONSTRUCTING A -[omega]-REGULAR EXPRESSION SPECIFIED BY A GRAPH OF ELEMENTARY EXTENSIONS

In synthesis of a [SIGMA]-automaton specified in the LP language, the problem arises how to represent the set of -[omega]-words defined by a formula F (t) in the form of a -[omega]-regular expression. Constructing this representation is based on the correspondence between structural components of formulas and -[omega]-regular expressions. To provide such a correspondence, two additional operations on -[omega]-regular sets relating to the operation of quantification in the formulas are introduced. The problem is reduced to calculating the -[omega]-regular expressions defined by these operations. This calculation relies on the construction of a graph of elementary extensions, in which certain set of infinite paths corresponds to all -[omega]-words that belong to the -[omega]-set to be calculated. A method for constructing a-an-regular expression specified by such a graph is proposed in the paper. This method is based on solving a system of linear equations over -[omega]-regular sets.