Abstract
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.
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Kuich, W. (2011). Algebraic Systems and Pushdown Automata. In: Kuich, W., Rahonis, G. (eds) Algebraic Foundations in Computer Science. Lecture Notes in Computer Science, vol 7020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24897-9_11
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DOI: https://doi.org/10.1007/978-3-642-24897-9_11
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