Rational equivalence relations
Theoretical Computer Science
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata Theory and Its Applications
Automata Theory and Its Applications
Automatic Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Automatic structures: overview and future directions
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)
Elements of Automata Theory
Complexity classes of equivalence problems revisited
Information and Computation
Iterating invertible binary transducers
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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We study natural computational problems associated with iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata are known to be free Abelian groups and the orbits of words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show how to compute the associated coordinates of words in quadratic time and how to apply coordinates to the problem of deciding whether two words generate the same orbit under a given transduction. In some special cases our algorithms can be implemented on finite state machines.