Inductive Invariants for Nested Recursion

2003 ◽  
pp. 253-269 ◽  
Author(s):  
Sava Krstić ◽  
John Matthews
Keyword(s):  
Nested Recursion ◽  
Inductive Invariants

Synthesizing Conjunctive & Disjunctive Linear Invariants by K-means++ and SVM

2020 ◽  
Vol 17 (6) ◽  
pp. 847-856
Author(s):  
Shengbing Ren ◽  
Xiang Zhang
Keyword(s):  
Software Verification ◽  
State Of The Art ◽  
Positive Sample ◽  
Machine Learning Algorithms ◽  
Support Vector ◽  
Hoare Logic ◽  
Excellent Performance ◽  
Automated Software ◽  
Inductive Invariants ◽  
Linear Invariants

The problem of synthesizing adequate inductive invariants lies at the heart of automated software verification. The state-of-the-art machine learning algorithms for synthesizing invariants have gradually shown its excellent performance. However, synthesizing disjunctive invariants is a difficult task. In this paper, we propose a method k++ Support Vector Machine (SVM) integrating k-means++ and SVM to synthesize conjunctive and disjunctive invariants. At first, given a program, we start with executing the program to collect program states. Next, k++SVM adopts k-means++ to cluster the positive samples and then applies SVM to distinguish each positive sample cluster from all negative samples to synthesize the candidate invariants. Finally, a set of theories founded on Hoare logic are adopted to check whether the candidate invariants are true invariants. If the candidate invariants fail the check, we should sample more states and repeat our algorithm. The experimental results show that k++SVM is compatible with the algorithms for Intersection Of Half-space (IOH) and more efficient than the tool of Interproc. Furthermore, it is shown that our method can synthesize conjunctive and disjunctive invariants automatically

Decidability of inferring inductive invariants

2016 ◽  
Author(s):  
Oded Padon ◽  
Neil Immerman ◽  
Sharon Shoham ◽  
Aleksandr Karbyshev ◽  
Mooly Sagiv
Keyword(s):  
Inductive Invariants

scholarly journals Bounded Quantifier Instantiation for Checking Inductive Invariants

2017 ◽  
pp. 76-95 ◽  
Author(s):  
Yotam M. Y. Feldman ◽  
Oded Padon ◽  
Neil Immerman ◽  
Mooly Sagiv ◽  
Sharon Shoham
Keyword(s):  
Quantifier Instantiation ◽  
Inductive Invariants

W. W. Tait. Nested recursion. Mathematische Annalen, Bd. 143 (1961), S. 236–250.

1963 ◽  
Vol 28 (1) ◽  
pp. 103-104
Author(s):  
Rózsa Péter
Keyword(s):  
Nested Recursion

scholarly journals Strengthening Model Checking Techniques With Inductive Invariants

2009 ◽  
Vol 28 (1) ◽  
pp. 154-158 ◽  
Author(s):  
Gianpiero Cabodi ◽  
Sergio Nocco ◽  
Stefano Quer
Keyword(s):  
Model Checking ◽  
Inductive Invariants

scholarly journals Inductive invariants of closed extensions of mappings

1972 ◽  
Vol 25 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Togo Nishiura
Keyword(s):  
Inductive Invariants
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