Bibliographic Details
| Title: |
Logical Zonotopes: A Set Representation for the Formal Verification of Boolean Functions |
| Authors: |
Alanwar, Amr, Jiang, Frank J., Amin, Samy, Johansson, Karl H. |
| Publication Year: |
2022 |
| Collection: |
Computer Science |
| Subject Terms: |
Electrical Engineering and Systems Science - Systems and Control, Computer Science - Computational Complexity, Computer Science - Cryptography and Security, Computer Science - Logic in Computer Science |
| More Details: |
A logical zonotope, which is a new set representation for binary vectors, is introduced in this paper. A logical zonotope is constructed by XOR-ing a binary vector with a combination of other binary vectors called generators. Such a zonotope can represent up to 2^n binary vectors using only n generators. It is shown that logical operations over sets of binary vectors can be performed on the zonotopes' generators and, thus, significantly reduce the computational complexity of various logical operations (e.g., XOR, NAND, AND, OR, and semi-tensor products). Similar to traditional zonotopes' role in the formal verification of dynamical systems over real vector spaces, logical zonotopes can efficiently analyze discrete dynamical systems defined over binary vector spaces. We illustrate the approach and its ability to reduce the computational complexity in two use cases: (1) encryption key discovery of a linear feedback shift register and (2) safety verification of a road traffic intersection protocol.
Comment: This paper is accepted at the 62nd IEEE Conference on Decision and Control (CDC 2023) |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2210.08596 |
| Accession Number: |
edsarx.2210.08596 |
| Database: |
arXiv |
