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- W243230860 abstract "AbstractAutomata with weights on edges, especially automata with counters, have been studied extensively in recent years, both because of to their interesting theory and due to their practical applications in data analysis. One of the most significant differences between weighted and classical automata concerns determinization: while every classical automaton can be determinized, this is not the case for weighted automata. Still, obtaining an equivalent automaton as close to a sequential (deterministic) one as possible is crucial in many practical applications, as unbounded non-determinism incurs large computational costs. There exist a few ways to limit the non-determinism of a counter automaton. For each word, one can require that only k runs are accepting (k-ambiguous automata), that there are only k possible runs at all (k-path automata), or one can restrict the automaton itself to be a disjoint sum of k sequential ones (k-sequential automata). Moreover, there are different types of automata with counters: distance automata that cannot reset, desert automata, and R-automata with many counters. In this paper, we establish a hierarchy for all these possibilities. First, we show that the parameter k induces a hierarchy in all cases. Then, we prove that k-path automata can be made 2k − 1-sequential and that this bound is strict. Finally, we show an unambiguous automaton which is not finitely sequential at all.KeywordsMinimal WeightDeterministic ComponentCounter OperationNondeterministic ChoiceStrict HierarchyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W243230860 created "2016-06-24" @default.
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- W243230860 date "2013-01-01" @default.
- W243230860 modified "2023-10-16" @default.
- W243230860 title "Limited Non-determinism Hierarchy of Counter Automata" @default.
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- W243230860 doi "https://doi.org/10.1007/978-3-642-37064-9_10" @default.
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