TL;DR
This paper determines the exact number of states in the minimal DFA that recognizes base-b numbers divisible by k, providing a theoretical foundation for automata-based divisibility testing.
Contribution
It introduces and proves a theorem that precisely characterizes the state complexity of minimal DFAs for divisibility recognition.
Findings
Exact state count for minimal DFA recognizing divisibility by k
Theoretical proof of the state complexity theorem
Provides a basis for automata-based divisibility testing
Abstract
We present and prove a theorem answering the question "how many states does a minimal deterministic finite automaton (DFA) that recognizes the set of base-b numbers divisible by k have?"
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