Weighted grammars and automata with threshold interpretation

Authors:
Carlos Martín-Vide;Victor Mitrana;Ralf Stiebe
Affiliations:
Research Group in Mathematical Linguistics, Rovira i Virgili University, Pça. Imperial Tárraco 1, E-43005 Tarragona, Spain;Faculty of Mathematics, University of Bucharest, Str. Academiei 14, R-70109, Bucharest, Romania;Fakultät fär Informatik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Venue:
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)
Year:
2003

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Abstract

We discuss a particular type of weighted grammars and automata over the partially ordered group of additive real vectors Rk, and its subgroups Zk and Qk, as well as over the partially ordered group of component-wise multiplicative vectors with positive rational components. Computational power of these devices is investigated in comparison with the computational power of valence grammars and blind multicounter automata. We show that all these families are either full principal semi-AFL or full semi-AFL. Finally, some decidability matters are discussed.