# Flat Model Checking for Counting LTL Using Quantifier-Free Presburger Arithmetic

## TL;DR

This paper introduces a method for approximate verification of counter systems against expressive counting temporal logic properties using flat model checking and Presburger arithmetic, enabling scalable analysis.

## Contribution

It presents a novel approximation approach employing flat under-approximations and Presburger arithmetic for verifying counting LTL properties, extending recent frequency property techniques.

## Key findings

- Prototype implementation with z3 SMT solver shows effectiveness.
- Approach handles expressive counting properties in counter systems.
- Trade-off between analysis completeness and computational effort.

## Abstract

This paper presents an approximation approach to verifying counter systems with respect to properties formulated in an expressive counting extension of linear temporal logic. It can express, e.g., that the number of acknowledgements never exceeds the number of requests to a service, by counting specific positions along a run and imposing arithmetic constraints. The addressed problem is undecidable and therefore solved on flat under-approximations of a system. This provides a flexibly adjustable trade-off between exhaustiveness and computational effort, similar to bounded model checking. Recent techniques and results for model-checking frequency properties over flat Kripke structures are lifted and employed to construct a parametrised encoding of the (approximated) problem in quantifier-free Presburger arithmetic. A prototype implementation based on the z3 SMT solver demonstrates the effectiveness of the approach based on problems from the RERS Challange.