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PSOP decomposition for EXOR-based synthesis

  • Anna Bernasconi received the Laurea degree in Physics from the University of Pavia in 1992, and the Ph.D. in Computer Science from the University of Pisa in 1998. Her dissertation “Mathematical techniques for the analysis of Boolean functions” received the Doctoral Dissertation Thesis Award 1998 from the Italian Chapter of the European Association for Theoretical Computer Science (EATCS). She is currently an Associate Professor with the Department of Computer Science of the University of Pisa, where she teaches fundamental courses in the Computer Science Program (Algorithms and Data Structures, Cryptography, Quantum Computing). Her research interests include algorithms and complexity, authenticated data structures, Boolean function complexity, and logic synthesis for emerging technologies. Recently, she got interested in quantum computing, and in particular in quantum Machine Learning techniques and in the synthesis of quantum logic circuits. She has authored or coauthored many research papers, published in international journals, conference proceedings, books and books chapters.

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    Valentina Ciriani received the Ph.D. degree in Computer Science from the University of Pisa, Italy. She is currently a Full Professor with the Department of Computer Science of the University of Milano (Italy). Her research interests include algorithms and data structures, as well as combinational logic synthesis for classical and emerging technologies. She has authored more than 100 research papers, published in international journals, conference proceedings, and books chapters.

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    Gianmarco Cuciniello received his Laurea degree in Computer Systems and Networks Security from the University of Milan in 2022. He is currently a master student in Computer Science and Security at the University of Milan. His research interests include quantum computing and cybersecurity.

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    Asma Taheri Monfared received the Ph.D. degree in computer science from the University of Milano, Italy, in 2024. She is currently a researcher at the University of Bergamo, Italy. Her research interests include logic synthesis, reversible and multiple-valued logic, quantum circuits, emerging technologies, and circuit design. She serves as a reviewer for prestigious journals, including IEEE Access, IET Quantum Communication, and Journal of Computational Electronics, as well as major international conferences.
Published/Copyright: January 24, 2025
it - Information Technology
From the journal it - Information Technology Volume 66 Issue 4-5

Abstract

In the classical CMOS technology, EXOR gates are considered expensive and impractical. Recently, the growing relevance of cryptography-related applications and emerging technologies has revived the interest in EXOR gates. In this contexts, it is therefore important to consider network representations that assume EXOR gates explicitly, since the non-EXOR gates have, in general, a higher cost than EXOR ones. As a result, the widely adopted And-Inverter Graph (AIG) logic networks, have recently evolved into the new XOR-AND Graph (XAG) multi-level logic representation, and the logic synthesis on XAGs mainly aims at reducing the number of AND nodes. In general, we call EXOR-based synthesis the synthesis methods that minimize the non-EXOR gates in a Boolean circuit. Projected Sum Of Product, PSOP, decomposition is an EXOR based technique that can be applied to any Boolean function as a very fast pre-processing step for further minimizing the circuit area in standard logic synthesis. In this paper, we exploit PSOP decomposition in EXOR-based synthesis. The experimental results validate the proposed pre-processing method in EXOR-based synthesis, showing an interesting gain in area, within the same time limit.

Keywords: circuit decomposition; reversible logic; secure multiparty computation
Corresponding author: Valentina Ciriani, Dipartimento di Informatica, Università degli Studi di Milano, Milan, Italy, E-mail: 

About the authors

Anna Bernasconi

Anna Bernasconi received the Laurea degree in Physics from the University of Pavia in 1992, and the Ph.D. in Computer Science from the University of Pisa in 1998. Her dissertation “Mathematical techniques for the analysis of Boolean functions” received the Doctoral Dissertation Thesis Award 1998 from the Italian Chapter of the European Association for Theoretical Computer Science (EATCS). She is currently an Associate Professor with the Department of Computer Science of the University of Pisa, where she teaches fundamental courses in the Computer Science Program (Algorithms and Data Structures, Cryptography, Quantum Computing). Her research interests include algorithms and complexity, authenticated data structures, Boolean function complexity, and logic synthesis for emerging technologies. Recently, she got interested in quantum computing, and in particular in quantum Machine Learning techniques and in the synthesis of quantum logic circuits. She has authored or coauthored many research papers, published in international journals, conference proceedings, books and books chapters.

Valentina Ciriani

Valentina Ciriani received the Ph.D. degree in Computer Science from the University of Pisa, Italy. She is currently a Full Professor with the Department of Computer Science of the University of Milano (Italy). Her research interests include algorithms and data structures, as well as combinational logic synthesis for classical and emerging technologies. She has authored more than 100 research papers, published in international journals, conference proceedings, and books chapters.

Gianmarco Cuciniello

Gianmarco Cuciniello received his Laurea degree in Computer Systems and Networks Security from the University of Milan in 2022. He is currently a master student in Computer Science and Security at the University of Milan. His research interests include quantum computing and cybersecurity.

Asma Taheri Monfared

Asma Taheri Monfared received the Ph.D. degree in computer science from the University of Milano, Italy, in 2024. She is currently a researcher at the University of Bergamo, Italy. Her research interests include logic synthesis, reversible and multiple-valued logic, quantum circuits, emerging technologies, and circuit design. She serves as a reviewer for prestigious journals, including IEEE Access, IET Quantum Communication, and Journal of Computational Electronics, as well as major international conferences.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: This work was supported in part by project SERICS (PE00000014) under the NRRP MUR program funded by the EU – NGEU. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the Italian MUR. Neither the European Union nor the Italian MUR can be held responsible for them. This work has also been supported by the National Recovery and Resilience Plan (NRRP), Mission 4, Component 2, Investment 1.1, under Call No. 104 (2.2.2022) by the Italian Ministry of University and Research (MUR), funded by the EU – NextGenerationEU – SAFEST project (CUP F53D23004230006), Grant Decree n. 861 (16-6-2023) by MUR. The first two authors are members of the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (GNCS-INdAM), which provided partial support for this work.

  7. Data availability: Not applicable.

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Received: 2024-08-10
Accepted: 2024-12-16
Published Online: 2025-01-24
Published in Print: 2024-08-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Solving Boolean Problems and Beyond
  4. Research Articles
  5. PSOP decomposition for EXOR-based synthesis
  6. Structural bias in synthesis of sparsely-specified functions
  7. Two approaches of arithmetic units design
  8. EnR: extend and reduce methodology to enable formal verification of truncated adders
  9. Approximate synthesis for LUT count reduction via probabilistic error propagation
  10. Detailed insight into approximate circuits with error-responsive information flow tracking
  11. Rectangle-free four-colored square grids realized by cyclic-rotated reusable patterns
  12. Why less is sometimes more
https://doi.org/10.1515/itit-2024-0073
Keywords for this article
circuit decomposition; reversible logic; secure multiparty computation

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Solving Boolean Problems and Beyond
  4. Research Articles
  5. PSOP decomposition for EXOR-based synthesis
  6. Structural bias in synthesis of sparsely-specified functions
  7. Two approaches of arithmetic units design
  8. EnR: extend and reduce methodology to enable formal verification of truncated adders
  9. Approximate synthesis for LUT count reduction via probabilistic error propagation
  10. Detailed insight into approximate circuits with error-responsive information flow tracking
  11. Rectangle-free four-colored square grids realized by cyclic-rotated reusable patterns
  12. Why less is sometimes more
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