On delay and regret determinization of max-plus automata

Filiot, Emmanuel; Jecker, Ismaël; Lhote, Nathan; Pérez, Guillermo A.; Raskin, Jean-François

doi:10.1109/LICS.2017.8005096

Title

On delay and regret determinization of max-plus automata

Author

Filiot, Emmanuel

Jecker, Ismaël

Lhote, Nathan

Pérez, Guillermo A.

Raskin, Jean-François

Abstract

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.

Language

English

Source (journal)

Proceedings. - Washington, D.C, 1986, currens

Source (book)

32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 20-23 June 2017, Reykjavik, Iceland

Publication

Washington, D.C : IEEE , 2017

ISSN

1043-6871

ISBN

978-1-5090-3018-7