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On delay and regret determinization of max-plus automata

par Filiot, Emmanuel ;Jecker, Ismaël Robin ;Lhote, Nathan ;Perez, Guillermo A. ;Raskin, Jean-François
Référence Proceedings - Symposium on Logic in Computer Science, 8005096
Publication Publié, 2017-08

Article révisé par les pairs

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Résumé :

Decidability of the determinization problem for weighted automata over the semiring (ℤ∪{-∞}, max; +), WA for short, is a long-standing open question. We propose two ways of approaching it by constraining the search space of deterministic WA: k-delay and r-regret. A WA N is k-delay determinizable if there exists a deterministic automaton D that defines the same function as N and for all words α in the language of N, the accepting run of D on α is always at most k-away from a maximal accepting run of N on α. That is, along all prefixes of the same length, the absolute difference between the running sums of weights of the two runs is at most k. A WA N is r-regret determinizable if for all words α in its language, its non-determinism can be resolved on the fly to construct a run of N such that the absolute difference between its value and the value assigned to α by N is at most r. We show that a WA is determinizable if and only if it is k-delay determinizable for some k. Hence deciding the existence of some k is as difficult as the general determinization problem. When k and r are given as input, the k-delay and r-regret determinization problems are shown to be EXPTIME-complete. We also show that determining whether a WA is r-regret determinizable for some r is in EXPTIME.