On delay and regret determinization of max-plus automata

Emmanuel Filiot, Ismael Jecker, Nathan Lhote, Guillermo A. Perez, Jean-Francois Raskin
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
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
more » ... 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 EXPtimecomplete. We also show that determining whether a WA is r-regret determinizable for some r is in EXPtime.
doi:10.1109/lics.2017.8005096 dblp:conf/lics/FiliotJLPR17 fatcat:labvfd5ghrdsji3n4n4ao4ueqe