Kuich, W., Droste, M., & Dziadek, S. (2019). Greibach Normal Form for omega-Algebraic Systems and Weighted Simple omega-Pushdown Automata. In A. Chattopadhyay & P. Gastin (Eds.), 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019) (pp. 38:1-38:14). Schloss Dagstuhl–Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2019.38
In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of omega-context-free languages (Cohen, Gold 1977) and an extension of weighted context-free languages of finite words (Chomsky, Schützenberger 1963). As in the theory of formal grammars, these weighted languages, or omega-algebraic series, can be represented as solutions of mixed omega-algebraic systems of equations and by weighted omega-pushdown automata. In our first main result, we show that mixed omega-algebraic systems can be transformed into Greibach normal form. Our second main result proves that simple omega-reset pushdown automata recognize all omega-algebraic series that are a solution of an omega-algebraic system in Greibach normal form. Simple reset automata do not use epsilon-transitions and can change the stack only by at most one symbol. These results generalize fundamental properties of context-free languages to weighted languages.
