# Faster Algorithms for Weighted Recursive State Machines

## TL;DR

This paper introduces faster algorithms for analyzing recursive state machines using semiring-labeled transitions, improving complexity bounds and efficiency for interprocedural analysis, including concurrent RSMs, with practical speed-ups demonstrated.

## Contribution

It presents novel algorithms that improve complexity bounds for RSM analysis, especially for finite-height semirings, and extends these improvements to concurrent RSMs, with practical implementation results.

## Key findings

- Improved complexity bounds for RSM analysis algorithms.
- Efficient algorithms for extracting distance values and handling queries.
- Prototype implementation shows significant speed-up on benchmarks.

## Abstract

Pushdown systems (PDSs) and recursive state machines (RSMs), which are linearly equivalent, are standard models for interprocedural analysis. Yet RSMs are more convenient as they (a) explicitly model function calls and returns, and (b) specify many natural parameters for algorithmic analysis, e.g., the number of entries and exits. We consider a general framework where RSM transitions are labeled from a semiring and path properties are algebraic with semiring operations, which can model, e.g., interprocedural reachability and dataflow analysis problems. Our main contributions are new algorithms for several fundamental problems. As compared to a direct translation of RSMs to PDSs and the best-known existing bounds of PDSs, our analysis algorithm improves the complexity for finite-height semirings (that subsumes reachability and standard dataflow properties). We further consider the problem of extracting distance values from the representation structures computed by our algorithm, and give efficient algorithms that distinguish the complexity of a one-time preprocessing from the complexity of each individual query. Another advantage of our algorithm is that our improvements carry over to the concurrent setting, where we improve the best-known complexity for the context-bounded analysis of concurrent RSMs. Finally, we provide a prototype implementation that gives a significant speed-up on several benchmarks from the SLAM/SDV project.