Generic -Removal Algorithm for Weighted Automata

We present a new generic-removal algorithm for weighted automata and transducers deened over a semiring. The algorithm can be used with any semiring covered by our framework and works with any queue discipline adopted. It can be used in particular in the case of unweighted automata and transducers and weighted automata and transducers deened over the tropical semiring. It is based on a general shortest-distance algorithm that we brieey describe. We give a full description of the algorithm including its pseudocode and its running time complexity, discuss the more eecient case of acyclic automata, an on-they implementation of the algorithm and an approximation algorithm in the case of the semirings not covered by our framework. We also illustrate the use of the algorithm with several semirings.