Iterating Invertible Binary Transducers

Iterating Inverse Binary Transducers

We study iterated transductions defined by a class of inverse transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.

On stabilizers of infinite words

The stabilizer of an infinite word w over a finite alphabet Σ is the monoid of morphisms over Σ that fix w. In this paper we study various problems related to stabilizers and their generators. We show that over a binary alphabet, there exist stabilizers with at least n generators for all n. Over a ternary alphabet, the monoid of morphisms generating a given infinite word by iteration can be inf...

Iterating Transducers

Languages in AC de ned by iterating nite transducers

We present an explicit construction of AC circuits that simulate nite state transducer iteration. Our approach yields circuits with only Θ(n log(n)) linear fan-in gates, whereas the circuits built from standard proof of L ⊆ AC use matrix multiplication and hence have Θ(n log(n)) such gates.

Computational results on invertible matrices with the maximum number of invertible 2×2 submatrices

A linear 2-All-or-Nothing Transform can be considered as an invertible matrix with all 2 × 2 submatrices invertible. It is known [P. D’Arco, N. Nasr Esfahani and D.R. Stinson, Electron. J. Combin. 23(4) (2016), #P4.10] that there is no binary s×s matrix that satisfies these conditions, for s > 2. In this paper, different computational methods for generating invertible binary matrices with close...