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Algebraic systems and pushdown automata. (English) Zbl 1251.68135
Kuich, Werner (ed.) et al., Algebraic foundations in computer science. Essays dedicated to Symeon Bozapalidis on the occasion of his retirement. Berlin: Springer (ISBN 978-3-642-24896-2/pbk). Lecture Notes in Computer Science 7020, 228-256 (2011).
Summary: This survey paper serves two purposes: Firstly, we consider cycle-free algebraic systems (with respect to a given strong convergence) as a generalization of the usually considered proper systems (with respect to the discrete convergence). Secondly, we develop in a parallel manner the theory of these cycle-free algebraic systems over an arbitrary semiring and the theory of arbitrary algebraic systems over a continuous semiring. In both cases we prove that algebraic systems and weighted pushdown automata are mechanisms of equal power. For the entire collection see [Zbl 1225.68022].
68Q45Formal languages and automata
68Q42Grammars and rewriting systems
68Q70Algebraic theory of languages and automata
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