Quadratic automata

Quadratic Automata

In this paper the notion of a quadratic automaton transformation is defined and studied. The automata considered transform infinite input sequences of elements from a finite commutative ring with identity to infinite output sequences. Results extending the linear automaton transformation theory of 4. Nerode are derived and two distinct approaches to machine realization arise depending upon whet...

Dynamics of Real Quadratic Cellular Automata

Handling Left-Quadratic Rules When Completing Tree Automata

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

A Quadratic Upper Bound on the Size of a Synchronizing Word in One-Cluster Automata

Černý’s conjecture asserts the existence of a synchronizing word of length at most (n− 1) for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p·a = q ·a for s...