Automata with Stochastic Resolvers for Verification

In automata theory, nondeterminism is a fundamental paradigm that can offer succinctness and expressivity, often at the cost of computational complexity. While determinisation offers a standard route to solving many common verification problems such as reactive synthesis and runtime verification, it often becomes a computational bottleneck. AuRora will study and build the theoretical foundation for automata with a limited degree of nondeterminism that can be resolved stochastically. This resolution uses a policy that combines randomness and memory to build a run on-the-fly while reading the input word letter-by-letter, i.e., in an online manner. These automata are particularly well-suited to represent specifications for reactive synthesis or to serve as monitors in runtime verification. We will study two natural settings: one in which the letters of the word are chosen adversarially, and another in which the word is selected non-adversarially and revealed letter-by-letter. On these automata, we will study the fundamental questions of their succinctness, the complexity of recognising them, and the feasibility of constructing them. These objectives will necessitate and be supplemented by furthering the theory of partial-observation games on graphs. The automata and game-theoretic tools developed will then be used to develop algorithms for the practical problems of synthesis and runtime verification. In particular, we will focus on the fragment of reactive synthesis where we restrict the user to be blind to the system's actions, as is frequently the case in practice. The tools developed will also be of high-relevance to open problems in automata theory, in particular, those concerning history-deterministic automata.