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The Firing Squad Synchronization Problem is one of the classical problems for cellular automata. In this paper we consider the case of more than one general. A synchronous and an asynchronous version of the problem are considered. In the latter case the generals may start their activities at different times. In the synchronous case there are optimumtime solutions. Very simple and elegant techniques for constructing one of them are the main contribution of this paper on the algorithmic side. For the asynchronous case an exact formula for the optimum synchronization time of each instance is derived. We prove that no CA can solve all instances in optimum time, but we describe a CA whose running time is very close to it; it only needs additional steps.

We study the computational capacity of self-verifying cellular automata with an emphasis on one-way information flow (SVOCA). A self-verifying device is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. We show that realtime SVOCA are strictly more powerful than realtime deterministic one-way cellular automata, since they can accept non-semilinear unary languages. It turns out that SVOCA can strongly be sped-up from lineartime to realtime. They are even capable to simulate any lineartime computation of deterministic two-way cellular automata. Closure properties and decidability problems are considered as well.

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