On the Comparison of Discounted-Sum Automata with Multiple Discount Factors
Udi Boker, Guy Hefetz · Lecture notes in computer science · 2023
Abstract We look into the problems of comparing nondeterministic discounted-sum automata on finite and infinite words. That is, the problems of checking for automata $${\mathcal {A}}$$ A and $${\mathcal {B}}$$ B whether or not it holds that for all words w , $${\mathcal {A}}(w)={\mathcal {B}}(w), {\mathcal {A}}(w)\le {\mathcal {B}}(w)$$ A ( w ) = B ( w ) , A ( w ) ≤ B ( w ) , or $${\mathcal {A}}(w) {\mathcal {D}}(w)$$ N ( w ) > D ( w ) for all words w .