The Online Space Complexity of Probabilistic Languages

摘要

In this paper, we define the online space complexity of languages, as the size of the smallest abstract machine processing words sequentially and able to determine at every point whether the word read so far belongs to the language or not. The first part of this paper motivates this model and provides examples and preliminary results. One source of inspiration for introducing the online space complexity of languages comes from a seminal paper of Rabin from 1963, introducing probabilistic automata, which suggests studying the online space complexity of probabilistic languages. This is the purpose of the second part of the current paper.