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Descriptive complexity for minimal time of cellular automata

Etienne Grandjean 1 Théo Grente 1 
1 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
Abstract : Descriptive complexity may be useful to design programs in a natural declarative way. This is important for parallel computation models such as cellular automata, because designing parallel programs is considered difficult. Our paper establishes logical characterizations of the three classical complexity classes that model minimal time, called real-time, of one-dimensional cellular automata according to their canonical variants. Our logics are natural restrictions of the existential second-order Horn logic. They correspond to the three ways of deciding a language on a square grid circuit of side n according to the three canonical placements of an input word of length n on the grid. Our key tool is a normalization method that transforms a formula into an equivalent formula that literally mimics a grid circuit.
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Submitted on : Thursday, March 7, 2019 - 5:56:09 PM
Last modification on : Saturday, June 25, 2022 - 9:53:15 AM
Long-term archiving on: : Sunday, June 9, 2019 - 10:13:05 AM


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  • HAL Id : hal-02020180, version 3


Etienne Grandjean, Théo Grente. Descriptive complexity for minimal time of cellular automata. 2019. ⟨hal-02020180v3⟩



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