Extending QuAK with Nested Quantitative Automata

TL;DR

This paper enhances the QuAK tool to support nested quantitative automata, enabling analysis of more complex properties like average response time by reducing NQAs to QAs.

Contribution

It implements flattening procedures in QuAK to support NQAs, preserving decision problem answers and expanding property specification capabilities.

Findings

Successfully extended QuAK to handle NQAs.

Demonstrated effectiveness on response-time benchmarks.

Supported all decidable combinations of parent and child automata.

Abstract

Quantitative automata (QAs) extend finite-state automata on infinite words with weighted transitions to specify quantitative system properties. However, their finite weight sets rule out properties like average response time, where response times can be arbitrarily large. Nested quantitative automata (NQAs) overcome this limitation: a parent automaton spawns child automata to compute unbounded values over finite infixes and aggregates them into a final result. Despite this expressiveness, NQAs have lacked practical tool support to date. We close this gap by extending the Quantitative Automata Kit (QuAK), a software tool for QA analysis, to support NQAs. Our core contribution is implementing a suite of flattening procedures that reduce NQAs to QAs, leveraging QuAK's existing decision procedures. These reductions preserve the answers to threshold decision problems, while allowing users to specify properties in the more expressive NQA formalism. The tool handles all combinations of parent aggregators (including limits and averages) and child functions (extrema and monotonic or bounded summations) for which emptiness and universality are known to be decidable. Experiments on response-time and resource-consumption benchmarks demonstrate QuAK's effectiveness.