Semirings, automata, languages
Semirings, automata, languages
Rational series and their languages
Rational series and their languages
Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Pushdown tree automata, algebraic tree systems, and algebraic tree series
Information and Computation
Information and Computation
Algebraic Semantics
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Greibach Normal Form in Algebraically Complete Semirings
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
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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.