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https://ceur-ws.org/Vol-3754/preface.pdf
Preface
SCSS 2024 is the 10th edition of the 10th International Symposium on Symbolic Computation in Software
Science. The symposium aims to promote research on the theoretical and practical aspects of symbolic
computation in software science in the context of modern computational and artificial intelligence
techniques. It will be held in Tokyo from August 28 to 30.
The symposium has three main types of presentations:
• the keynote and invited talks
• formal full papers
• works in progress.
This volume contains the record of the Work in Progress of SCSS 2024. The formal full papers and the
abstracts of the keynote and invited talks appear in the Springer Lecture Notes series as LNAI 14991.
What is the meaning of the symposium name “symbolic computation in software science”? Symbolic
computation is the science of computing with symbolic objects (terms, formulae, programs, represen-
tations of algebraic objects, and so on). Powerful algorithms have been developed during the past
decades for the significant subareas of symbolic computation: computer algebra and computational logic.
These include resolution proving, model checking, provers for various inductive domains, rewriting
techniques, cylindrical algebraic decomposition, Gröbner bases, characteristic sets, and telescoping for
recurrence relations. These algorithms and methods have been successfully applied in various fields.
Software science has the goal of applying scientific principles in the development of software and
covers a broad range of topics in software construction and analysis. One of the main objectives is to
enhance software quality. The SCSS meetings bring these fields together, allowing the ideas from each
to enhance the other.
Over the years, the scope of SCSS has evolved, incorporating new research themes that drive progress
in symbolic computation in software science. Some of the recurring topics in the SCSS meetings have
been:
• Theorem proving methods and techniques
• Algorithm synthesis and verification
• Formal methods, including for the analysis of network security
• Complexity analysis and termination analysis of algorithms
• Extraction of specifications from algorithms
• Generation of inductive assertions for algorithms
• Algorithm transformations
• Component-based programming
• Symbolic methods for semantic web and cloud computing.
The present instance of SCSS builds on these themes.
The abstracts and papers presented here emphasize symbolic computation, formal systems, and appli-
cations of formal methods. After fifteen years, the foundational framework stands firm, continually
incorporating innovative developments in SCSS domains.
August 2024 Katsusuke Nabeshima
Stephen M. Watt
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Organization
SCSS Steering Committee as of August 2023
Adel Bouhoula Arabian Gulf University, Bahrain
Bruno Buchberger RISC Johannes Kepler University, Austria
Hoon Hong North Carolina State University, USA
Tetsuo Ida University of Tsukuba, Japan
Laura Kovács TU Wien, Austria
Temur Kutsia RISC Johannes Kepler University, Austria
Mohamed Mosbah LABRI, France
Michael Rusinowitch INRIA, France
Masahiko Sato Kyoto University, Japan
Carsten Schneider RISC Johannes Kepler University, Austria
Dongming Wang Beihang University, China, and CNRS, France
SCSS 2024 Organizing Committee
General Chair Tetsuo Ida U. Tsukuba
Program Committee Chair Stephen Watt U. Waterloo
Local Arrangements Chair Katsusuke Nabeshima Tokyo U. of Science
Program Committee
David Cerna Czech Academy of Sciences, Czechia
Changbo Chen Chinese Academy of Sciences, China
Rachid Echahed CNRS and University of Grenoble, France
David Jeffrey University of Western Ontario, Canada
Cezary Kaliszyk University of Innsbruck, Austria
Yukiyoshi Kameyama University of Tsukuba, Japan
Laura Kovács TU Wien, Austria
Temur Kutsia RISC Johannes Kepler University, Austria
Christopher Lynch Clarkson University, USA
Yasuhiko Minamide Tokyo Institute of Technology
Julien Narboux CNRS and Université de Strasbourg, France
Wolfgang Schreiner RISC Johannes Kepler University, Austria
Sofiène Tahar Concordia University, Canada
Stephen Watt (chair) University of Waterloo, Canada
Lihong Zhi AMSS Chinese Academy of Sciences, China
Local Arrangements Committee
Yuki Ishihara Nihon University, Japan
Katsusuke Nabeshima (chair) Tokyo University of Science, Japan
Yosuke Sato Tokyo University of Science, Japan
Hiroshi Sekigawa Tokyo University of Science, Japan
Akira Terui University of Tsukuba, Japan
Sponsors
SCSS 2024 gratefully acknowledges the support of our sponsors,
the Kayamori foundation of informational science advancement and Maplesoft.
Table of Contents
Improving LLM-based code completion using LR parsing-based candidates
Atique, Choi, Sasano, Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Faster bivariate lexicographic Groebner bases modulo 𝑥𝑘
Dahan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Some applications of Chinese Remainder Theorem codes with error-correction
Elliott, Schost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Functional decomposition of sparse polynomials (short talk abstract)
Giesbrecht . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Towards trajectory planning of a robot manipulator with computer algebra using Bézier curves for obstacle
avoidance
Hatakeyama, Terui, Mikawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Algebraic (non) relations among polyzetas
Hoang Ngoc Minh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
An e-origami artwork of a big wing crane
Ida . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
The geometry of 𝑁 -body orbits and the DFT (extended abstract)
Ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Gröbner basis computation via learning
Kera, Ishihara, Vaccon, Yokoyama . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Solving estimation problems using minimax polynomials and Gröbner bases
Kuramochi, Terui, Mikawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
First-order theorem proving with power maps in semigroups
Lin, Padmanabhan, Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Software for indefinite integration
Norman, Jeffrey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Towards trajectory planning for a 6-degree-of-freedom robot manipulator considering the orientation of the
end-effector Using computer algebra
Okazaki, Terui, Mikawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Methods for solving the Post correspondence problem and certificate generation
Omori, Minamide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A stable computation of multivariarte apporximate GCD based on SVD and lifting technique
Sanuki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
An optimized path planning of manipulator with spline curves using real quantifier elimination based on
comprehensive Gröbner systems
Shirato, Oka, Terui, Mikawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Reasoning about the embedded shape of a qualitatively represented curve
Takahashi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113