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Cellular Automata, Decidability and Phasespace
 FUNDAMENTA INFORMATICAE
"... Cellular automata have rich computational properties and, at the same time, provide plausible models of physicslike computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first or ..."
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Cited by 3 (2 self)
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Cellular automata have rich computational properties and, at the same time, provide plausible models of physicslike computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first order theory is decidable but the addition of an orbit predicate results in undecidability. We comment on connections between this “what you see is what you get” model and the lack of natural intermediate degrees.
DECIDABILITY AND COMPUTABILITY OF CERTAIN TORSIONFREE ABELIAN GROUPS
"... Abstract. We study completely decomposable torsionfree abelian groups of the form GS: = ⊕n∈SQpn for sets S ⊆ ω. We show that GS has a decidable copy if and only if S is Σ0 2 and has a computable copy if and only if S is Σ0 3. 1. ..."
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Cited by 2 (2 self)
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Abstract. We study completely decomposable torsionfree abelian groups of the form GS: = ⊕n∈SQpn for sets S ⊆ ω. We show that GS has a decidable copy if and only if S is Σ0 2 and has a computable copy if and only if S is Σ0 3. 1.
RESEARCH ARTICLE Computational Classification of Cellular Automata
"... We discuss attempts at the classification of cellular automata, in particular with a view towards decidability. We will see that a large variety of properties relating to the shortterm evolution of configurations is decidable in principle, but questions relating to the longterm evolution are typic ..."
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We discuss attempts at the classification of cellular automata, in particular with a view towards decidability. We will see that a large variety of properties relating to the shortterm evolution of configurations is decidable in principle, but questions relating to the longterm evolution are typically undecidable. Even in the decidable case, computational hardness poses a major obstacle for the automatic analysis of cellular automata.