Quantitative Automata under Probabilistic Semantics

TL;DR

This paper explores automata with monitor counters and nested weighted automata under probabilistic semantics, establishing their equivalence and analyzing decidability and complexity of related problems.

Contribution

It is the first to study these automata under probabilistic semantics, showing decidability results and complexity classifications for various problems.

Findings

Automata with monitor counters and nested weighted automata are equivalent.

Decidability of emptiness and universality problems changes under probabilistic semantics.

Provided a comprehensive classification of decidability and complexity for probabilistic questions.

Abstract

Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent. We study for the first time such quantitative automata under probabilistic semantics. We show that several problems that are undecidable for the classical questions of emptiness and universality become decidable under the probabilistic semantics. We present a complete picture of decidability for such automata, and even an almost-complete picture of computational complexity, for the probabilistic questions we consider.