The Incompleteness of State-Based Model Checking for Trace-Based Semantics

Title: The Incompleteness of State-Based Model Checking for Trace-Based Semantics

Abstract: This research paper investigates the relationship between state-based and trace-based model checking in the context of the /archleftdownµ⋆-calculus, a general temporal specification language with a natural time-symmetric trace-based semantics. The classical state-based model checking is found to be incomplete, i.e., trace-incomplete, even for finite systems. This is based on a number of results that characterize the structure of models, i.e., transition systems, whose state-based model checking is trace-complete. The paper also explores the possibility of finding some approximation A of the trace-based model checking problem that is related to states and induces an approximated model checking that is logically equivalent to the trace-based checking.

Research Question: Can we find some approximation A of the trace-based model checking problem that is related to states and induces an approximated model checking that is logically equivalent to the trace-based checking?

Methodology: The research uses the /archleftdownµ⋆-calculus, a general temporal specification language with a natural time-symmetric trace-based semantics. The paper investigates the relationship between state-based and trace-based model checking and explores the possibility of finding an approximation A of the trace-based model checking problem that is related to states and induces an approximated model checking that is logically equivalent to the trace-based checking.

Results: The main result is that the classical state-based model checking is incomplete, i.e., trace-incomplete, even for finite systems. This is based on a number of results that characterize the structure of models, i.e., transition systems, whose state-based model checking is trace-complete. The paper also explores the possibility of finding some approximation A of the trace-based model checking problem that is related to states and induces an approximated model checking that is logically equivalent to the trace-based checking.

Implications: The incompleteness of state-based model checking for trace-based semantics has important implications for the design of model checking algorithms and tools. It suggests that these algorithms may not provide exact information when viewed through a trace-based interpretation. Moreover, it opens the question of whether it is possible to find some approximation A of the trace-based model checking problem that is related to states and induces an approximated model checking that is logically equivalent to the trace-based checking. If such an approximation can be found, it could potentially lead to more meaningful and accurate model checking results.

Link to Article: https://arxiv.org/abs/0404048v1 Authors: arXiv ID: 0404048v1