Automata-based Quantitative Verification

TL;DR

This paper introduces a novel automata-theoretic framework called comparator automata that generalizes quantitative verification across various cost models, integrating structural and numerical analysis for improved scalability and efficiency.

Contribution

The paper presents comparator automata, a new automata-based framework that unifies structural and numerical phases in quantitative analysis, overcoming limitations of specialized and disparate techniques.

Findings

Generalizes across multiple cost models

Improves complexity-theoretic bounds

Enhances scalability and robustness

Abstract

Quantitative analysis of computing systems is an emerging area in automated formal analysis. Such properties address aspects such as costs and rewards, quality measures, resource consumption, distance metrics, etc. Existing solutions for problems in quantitative analysis face two challenges, namely lack of generalizability and separation-of-techniques. Lack of generalizability refers to the issue that solution approaches are specialized to cost model. Different cost models deploy such disparate algorithms that there is no transfer of knowledge from one cost model to another. Separation-of-techniques refers to the inherent dichotomy in solving problems in quantitative analysis. Most algorithms comprise of a structural phase which reasons about the structure of the quantitative system(s) using techniques from automata or graphs, and a numerical phase, which reasons about the quantitative dimension/cost model using numerical methods. The techniques used in both phases are so unlike each other that they are difficult to combine, thereby impacting scalability. This thesis contributes to a novel framework that addresses these challenges. The introduced framework, called comparator automata or comparators in short, builds on automata-theoretic foundations to generalize across a variety of cost models. Comparators enable automata-based methods in the numerical phase, hence eradicating the dependence on numerical methods. In doing so, comparators are able to integrate the structural and numerical phases. On the theoretical front, we demonstrate that these have the advantage of generalizable results, and yield complexity-theoretic improvements over a range of problems in quantitative analysis. On the empirical front, we demonstrate that comparator-based solutions render more efficient, scalable, and robust performance, and are able to integrate quantitative with qualitative objectives.