On every n-long input, every two-way finite automaton (fa) can reverse its head O(n) times before halting. A fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2) states on every deterministic fa with few reversals, but only h states on a nondeterministic fa with few reversals.

We propose an algebraic model for hybrid systems and illustrate its usefulness by proving theorems in realization theory using this viewpoint. By a hybrid system, we mean a collection of continuous nonlinear control systems associated with a discrete finite state automaton. The automaton switches between the continuous control systems, and this switching is a function of the discrete input symb...

We introduce two series of finite automata starting from the socalled Aleshin and Bellaterra automata. We prove that each automaton in the first series defines a free non-Abelian group while each automaton in the second series defines the free product of groups of order 2. Furthermore, these properties are shared by disjoint unions of any number of distinct automata from either series.

This paper describes non-deterministic finite-state automaton based on DNA strands. The automaton uses massive parallel processing offered by molecular approach for computation and exhibits a number of advantages over traditional electronic implementations. This device is used to analyze DNAmolecules, whether they are described by specified regular expression. Presented ideas are confirmed by e...

We present a new incremental algorithm for minimising deterministic finite automata. It runs in quadratic time for any practical application and may be halted at any point, returning a partially minimised automaton. Hence, the algorithm may be applied to a given automaton at the same time as it is processing a string for acceptance. We also include some experimental comparative results.

A cellular automaton collider is a finite state machine build of rings of onedimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings. 1.

We consider the problem of learning a finite automaton with recurrent neural networks, given a training set of sentences in a language. We train Elman recurrent neural networks on the prediction task and study experimentally what these networks learn. We found that the network tends to encode an approximation of the minimum automaton that accepts only the sentences in the training set.

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.

We improve a recent result [A. Badr: Hyper-Minimization in O(n). In Proc. CIAA, LNCS 5148, 2008] for hyper-minimized finite automata. Namely, we present an O(n logn) algorithm that computes for a given finite deterministic automaton (dfa) an almost equivalent dfa that is as small as possible—such an automaton is called hyper-minimal. Here two finite automata are almost equivalent if and only if...