Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Algebraic Automata Theory
Automata, Languages, and Machines
Automata, Languages, and Machines
Algebraic Theory of Automata Networks (SIAM Monographs on Discrete Mathematics and Applications, 11)
Algebraic Theory of Automata Networks (SIAM Monographs on Discrete Mathematics and Applications, 11)
The q-theory of Finite Semigroups
The q-theory of Finite Semigroups
Handbook of Weighted Automata
On the equivalence of Z-automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We consider weighted finite transition systems with weights from naturally ordered semirings. Such semirings comprise distributive lattices as well as the natural numbers with ordinary addition and multiplication, and the max-plus-semiring. For these systems we explore the concepts of covering and cascade product. We show a cascade decomposition result for such weighted finite transition systems using special partitions of the state set of the system. This extends a classical result of automata theory to the weighted setting.