We study the sizes of minimal finite state machines associated with linear cellular automata. In particular, we construct a class of binary linear cellular automata whose corresponding minimal automata exhibit full exponential blow-up. These cellular automata have Hamming distance 1 to a permutation automaton. Moreover, the corresponding minimal Fischer automata as well as the minimal DFAs have...

Microscopic traffic models have recently gained considerable importance as a mean of optimising traffic control strategies. Computationally efficient and sufficiently accurate microscopic traffic models have been developed based on the cellular automata theory. However, the real-time application of the available cellular automata models in traffic control systems is a difficult task due to thei...

We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak log logn space, (ii) log logn is a tight space lower bound for accepting general nonregular languages on weak realtime pushdown automata, (iii) there exist unary nonregular languages accepted by realt...