Experimental Study on CTL model checking using Machine Learning

TL;DR

This paper explores machine learning techniques to improve CTL model checking by achieving high accuracy and significantly increasing efficiency, addressing the state explosion problem in existing tools.

Contribution

It identifies optimal ML algorithms for CTL model checking, achieving near 99% accuracy and over 450 times efficiency improvement.

Findings

LR-based approach achieves 98.8% accuracy

BT-based approach achieves 98.7% accuracy

Efficiency is 459 to 639 times higher than existing methods

Abstract

The existing core methods, which are employed by the popular CTL model checking tools, are facing the famous state explode problem. In our previous study, a method based on the Machine Learning (ML) algorithms was proposed to address this problem. However, the accuracy is not satisfactory. First, we conduct a comprehensive experiment on Graph Lab to seek the optimal accuracy using the five machine learning algorithms. Second, given the optimal accuracy, the average time is seeked. The results show that the Logistic Regressive (LR)-based approach can simulate CTL model checking with the accuracy of 98.8%, and its average efficiency is 459 times higher than that of the existing method, as well as the Boosted Tree (BT)-based approach can simulate CTL model checking with the accuracy of 98.7%, and its average efficiency is 639 times higher than that of the existing method.

Tables

Table 1. Table 1: Graphlab experiment where length of each CTL formula is 500 What are the values of the parameters if the illustrations of Fig.1(a) occur

Names of parameters	Meaning of parameters	Values of parameters
seed	Seed for the random number generator used to split	459
fraction	For determining the proportion of the records of training set in the total records of data set	0.8

Table 2. Table 2: Graphlab experiment where length of each CTL formula is 500 What are the values of the parameters if the illustrations of Fig.1(b) occur

Names of parameters	Meaning of parameters	Values of parameters
seed	Seed for the random number generator used to split	536
fraction	For determining the proportion of the records of training set in the total records of data set	0.8

Table 3. Table 3: Graphlab experiment where length of each CTL formula is 500 What are the values of the parameters if the illustrations of Fig.1(c) occur

Names of parameters	Meaning of parameters	Values of parameters
seed	Seed for the random number generator used to split	399
fraction	For determining the proportion of the records of training set in the total records of data set	0.86

Table 4. Table 4: Graphlab experiment where length of each CTL formula is 500 What are the values of the parameters if the illustrations of Fig.1(d) occur

Names of parameters	Meaning of parameters	Values of parameters
seed	Seed for the random number generator used to split	536
fraction	For determining the proportion of the records of training set in the total records of data set	0.8

Table 5. Table 5: Graphlab experiment where length of each CTL formula is 500 What are the values of the parameters if the illustrations of Fig.1(e) occur

Names of parameters	Meaning of parameters	Values of parameters
seed	Seed for the random number generator used to split	2077
fraction	For determining the proportion of the records of training set in the total records of data set	0.8

Table 6. Table 6: The new method improves the efficiency

ML algorithms	Average running time $t_1$ (in Seconds) of NuSMV for one pair of Kripke structure and formula	Average predictive time $t_2$ (in Seconds) of ML for one record	$t_1$/$t_2$
RF	0.0147	0.000026	565
BT	0.0147	0.000023	639
KNN	0.0147	0.3056	0.05
DT	0.0147	0.000028	525
LR	0.0147	0.000032	459

Full text

Experimental Study on CTL model checking using Machine Learning

Weijun ZHU

School of Information Engineering, Zhengzhou University, Zhengzhou City,450001, China

**Abstract: The existing core methods, which are employed by the popular CTL model checking tools, are facing the famous state explode problem. In our previous study, a method based on the Machine Learning (ML) algorithms was proposed to address this problem. However, the accuracy is not satisfactory. First, we conduct a comprehensive experiment on Graph Lab to seek the optimal accuracy using the five machine learning algorithms. Second, given the optimal accuracy, the average time is seeked. The results show that the Logistic Regressive (LR)-based approach can simulate CTL model checking with the accuracy of 98.8%, and its average efficiency is 459 times higher than that of the existing method, as well as the Boosted Tree (BT)-based approach can simulate CTL model checking with the accuracy of 98.7%, and its average efficiency is 639 times higher than that of the existing method. **

Keywords: Machine Learning; Model Checking; Computational Tree Logic; Kripke Structure

1 Introduction

Model checking was presented by Turing Award winner Prof. Clarke et al [1]. It has been widely used in several fields such as CPU design, network protocols. The basic principle of model checking can be depicted as follows: (1) a Kripke structure is employed to construct a systematic model, while a formula of a temporal logic is employed to describe a property which should be satisfied by this system; (2) a model checking algorithm decides whether the Kripke structure satisfies the formula or no. In model checking, linear temporal logic [2] and computational tree logic (CTL) [3] are the two popular temporal logics. In other words, CTL model checking and LTL model checking are the two different problems which are related with each other.

The state explosion problem is always one of the important bottlenecks of CTL model checking. Unfortunately, the state explosion problem inherently originates from the gene of model checking. Thus, we proposed an approximate CTL model checking approach using machine learning in our previous study [4][5]. And we obtained the accuracy of 96% when we predict the result of CTL model checking via ML algorithms. Considering model checking is a formal method which is very accurate, the accuracy of 96% is not enough to formal computing. How to further improve the accuracy of ML-based approximate CTL model checking? Something more needs to be done. This is the motivation of this paper.

2 The principle of the approximate CTL model checking based on machine learning

Given a Kripke structure and a CTL formula, how to decide whether this Kripke structure satisfy this formula or not? This is a model checking problem, as well as a ML binary classification problem. If a model checking algorithm is used, the state explode will be inevitable. If a ML algorithm is employed, the state explode will not happen.

The principle of the ML-based approximate CTL model checking is as follows. (1) A number of records in a data set are inputted to a ML algorithm for training, where each record has the two features, one is Kripke structure and the other is CTL formula, as well as each record has only one label, i.e., the result of CTL model checking (yes or no). (2) If a record in a test set is inputted to the trained ML model M, the predictive result will be gotten.

See [4][5] for more details on the ML-based approximate CTL model checking.

3 Simulated experiments

3.1 Experimental objective

We will compare the ability and the efficiency between the ML-based approximate CTL model checking and the classic CTL model checking.

3.2 The simulation platform

1. (1)

CPU: Intel(R) Core(TM) i7-4790 CPU @3.60GHz. 2. (2)

RAM: 8.0G RAM. 3. (3)

OS: Windows 10. 4. (4)

NuSMV [6]: for performing CTL model checking. 5. (5)

Graph Lab [7]: for implementing Random Forest (RF), Boosted Tree (BT), K-Nearest Neighbor (KNN), Decision Tree (DT) and Logistic Regressive (LR) algorithms. 6. (6)

the raw data: same as the one in Ref.[4][5].

3.3 Experimental Procedures

Similar with that of Ref.[4][5].

3.4 Experimental Results

The same raw data with the one in Ref.[4][5] are inputted to Graphlab. Fig.1 illustrates the result of ML prediction including predictive accuracy and average time for predicting the model checking result for a pair of Kripke structure and a CTL formula. And Tab.1, Tab.2, Tab.3, Tab.4 and Tab.5 show the value of parameters when the above predictive results occur. Furthermore, Tab.6 gives a comparison between the ML-based approaches and a typical CTL model checking approach, i.e., NuSMV.

As shown in these figures and tables, the accuracy of the LR-based approach is 98.8%, and the accuracy of the BT-based approach is 98.7%. It indicates that predictions are very accurate using the ML-based method to simulate CTL model checking.

4 Conclusions

In this study, we obtain a comprehensive experimental result on the ML-based approximate CTL model checking. This method has a high accuracy of approximate CTL model checking which has declined slightly (1.2%-1.3% only) from that of actual CTL model checking, in exchange for a substantial increase in efficiency of CTL model checking (639 times).

Acknowledgements

This work has been supported by the National Natural Science Foundation of China (No.U1204608).