Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Handbook of formal languages, vol. 1
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
Varieties Of Formal Languages
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Journal of Computer and System Sciences
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Building on the celebrated Krohn-Rhodes Theorem we characterize classes of regular languages in terms of the cascade decompositions of minimal DFA of languages in those classes. More precisely we provide characterizations for the classes of piecewise testable languages and commutative languages. To this end we use biased resets, which are resets in the classical sense, that can change their state at most once. Next, we introduce the concept of the scope of a cascade product of reset automata in order to capture a notion of locality inside a cascade product and show that there exist constant bounds on the scope for certain classes of languages. Finally we investigate the impact of biased resets in a product of resets on the dot-depth of languages recognized by this product. This investigation allows us to refine an upper bound on the dot-depth of a language, given by Cohen and Brzozowski.