20 Problems (Wolfram)
What overall classification of CA can be given?
What are the exact relations between entropies and Lyapunov exponents for CA?
What is the analogue of geometry for the configuration space of a CA?
What statistical quantities characterize CA behavior?
What invariants are there in CA evolution?
How does thermodynamics apply to CA? (broken time symmetry problem)
How is different behavior distributed in the space of CA rules?
What are the scaling properties of CA?
What is the correspondence between CA and continuous systems?
What is the correspondence between CA and stochastic systems?
How are CA affected by noise and other perturbations?
Is regular language complexity generically non-decreasing with time in 1-D CA?
What limit sets can CA produce?
What are the connections between the computational and statistical characteristics of CA?
How random are the sequences generated by CA?
How common are computational universality and undecidability in CA?
What is the nature of the infinite size limit of CA?
How common is computational irreducability in CA?
How common are computationally intractable problems about CA?
What higher level descriptions of information processing in CA can be given?