Quadratic Automata

From Bidirectionality to Alternation

We describe an explicit simulation of 2-way nondeterministic automata by 1-way alternating automata with quadratic blow-up. We first describe the construction for automata on finite words, and extend it to automata on infinite words.

Synchronizing Automata on Quasi-Eulerian Digraph

In 1964 Černý conjectured that each n-state synchronizing automaton posesses a reset word of length at most (n − 1). From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in n. Thus the main problem here is to prove quadratic (in n) upper bounds. Since 1964, this problem has been solved for few special classes of synchronizing automata. One ...

Optimal Clock Allocation for a Class of Timed Automata

We address the problem of allocating a minimal number of clocks to timed automata. To make the problem tractable we assume that all locations are reachable. We identify a fairly general class of timed automata, TADS , for which there is an algorithm whose complexity is quadratic in the size of the graph.

On the Average Size of Glushkov's Automata

Glushkov’s algorithm builds an ε-free nondeterministic automaton from a given regular expression. In the worst case, its number of states is linear and its number of transitions is quadratic in the size of the expression. We show in this paper that in average, the number of transitions is linear.

Dynamics of Real Quadratic Cellular Automata