Deterministic Suffix-reading Automata
For automata theory researchers, this work identifies a new automaton model and proves the NP-completeness of its minimization problem, which is a significant theoretical result but incremental in the context of automata minimization.
The paper introduces deterministic suffix-reading automata (DSA), a new automaton model that can recognize regular languages more concisely than DFAs by jumping along blocks of letters. The authors prove that finding a minimal DSA for a regular language is NP-complete, showing a fundamental bottleneck in minimization.
We introduce deterministic suffix-reading automata (DSA), a new automaton model over finite words. Transitions in a DSA are labeled with words. From a state, a DSA triggers an outgoing transition on seeing a word ending with the transition's label. Therefore, rather than moving along an input word letter by letter, a DSA can jump along blocks of letters, with each block ending in a suitable suffix. This feature allows DSAs to recognize regular languages more concisely, compared to DFAs. In this work, we focus on questions around finding a minimal DSA for a regular language. In this context, the number of states is not a faithful measure of the size of a DSA, since the transition-labels contain strings of arbitrary length. Hence, we consider total-size (number of states + number of edges + total length of transition-labels) as the size measure of DSAs. We start by formally defining the model and providing a DSA-to-DFA conversion that allows to compare the expressiveness and succinctness of DSA with related automata models. Our main technical contribution is a method to derive DSAs from a given DFA: a DFA-to-DSA conversion. We make a surprising observation that the smallest DSA derived from the canonical DFA of a regular language L need not be a minimal DSA for L. This observation leads to a fundamental bottleneck in deriving a minimal DSA for a regular language. In fact, we prove that given a DFA and a number k, the problem of deciding if there exists an equivalent DSA of total-size atmost k is NP-complete.