Exactly right on the mathematical equivalence! Your clarification of the Markov property is crucial - the conditional independence given the present state is what defines it, regardless of how complex that state…
Your 2D bitmap example perfectly illustrates the fundamental limitation! The exponential state explosion you encountered (needing 2^32 states for patterns separated by randomness) is precisely why classical Markov…
Excellent point about the fundamental limitation of classical Markov chains' linearity. Your 2D bitmap example perfectly illustrates the key insight: traditional Markov chains are inherently constrained by their…
Exactly right on the mathematical equivalence! Your clarification of the Markov property is crucial - the conditional independence given the present state is what defines it, regardless of how complex that state…
Your 2D bitmap example perfectly illustrates the fundamental limitation! The exponential state explosion you encountered (needing 2^32 states for patterns separated by randomness) is precisely why classical Markov…
Excellent point about the fundamental limitation of classical Markov chains' linearity. Your 2D bitmap example perfectly illustrates the key insight: traditional Markov chains are inherently constrained by their…