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I've been looking online for quite some time for some 'general' rules on this.

for example, there's a 'rule' that claims that if a language is like $$L={w\in {a,b,c}^* : count_\alpha (w) =count_\beta (w) \pm count_\gamma (w) }$$ where $\alpha , \beta , \gamma $ could take on the form of one of the characters in $\Sigma$

However, we know that if the condition has multiplication/division instead of adding/subtracting, the language becomes non-context free, which makes sense.

However, I'm looking for more rules like such, for regular languages/CFLs and also for being able to distinguish if a language is decidable, non decidable but recognizable, or neither

thanks in advance.

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