Abstract
Automata 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.
Research supported by the Polish Ministry of Science and Higher Education under grant N N206 492638 2010-2012.
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Bala, S., Jackowski, D. (2013). Limited Non-determinism Hierarchy of Counter Automata. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_10
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DOI: https://doi.org/10.1007/978-3-642-37064-9_10
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