arXiv subjects

Predrag Janičić

Publications and source records attributed to Predrag Janičić.

6 recordsLinked to original sources

arXiv2026

A SAT-based Approach for Specification, Analysis, and Justification of Reductions between NP-complete Problems

We propose a novel framework for developing, analyzing, and validating reductions between NP-complete problems. Powered by the SAT-based constraint solver URSA, our methodology introduces several distinct features that set it apart from other related approaches. The proposed workflow effectively bridges the crucial gap between informal, high-level reduction descriptions and formalized mathematical proofs. By supplementing rather than replacing human intuition, this interactive methodology serves as an aid for exploring relationships between NP-complete problems.

cs.LO↗

arXiv2024

Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn a conjecture with missing assumptions and with an under-specified goal into a proper theorem. Also, the proposed framework can help in completing a proof sketch into a human-readable and machine-checkable proof. Our approach is focused on synthetic geometry, and uses coherent logic and constraint solving. The proposed approach is uniform for all three kinds of tasks, flexible and, to our knowledge, unique such approach.

cs.AI↗

arXiv2022

Automated Generation of Illustrations for Synthetic Geometry Proofs

We report on a new, simple, modular, and flexible approach for automated generation of illustrations for (readable) synthetic geometry proofs. The underlying proofs are generated using the Larus automated prover for coherent logic, and corresponding illustrations are generated in the GCLC language. Animated illustrations are also supported.

cs.LO↗

arXiv2021

Proceedings of the 13th International Conference on Automated Deduction in Geometry

Automated Deduction in Geometry (ADG) is a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction. Relevant topics include (but are not limited to): polynomial algebra, invariant and coordinate-free methods; probabilistic, synthetic, and logic approaches, techniques for automated geometric reasoning from discrete mathematics, combinatorics, and numerics; interactive theorem proving in geometry; symbolic and numeric methods for geometric computation, geometric constraint solving, automated generation/reasoning and manipulation with diagrams; design and implementation of geometry software, automated theorem provers, special-purpose tools, experimental studies; applications of ADG in mechanics, geometric modelling, CAGD/CAD, computer vision, robotics and education. Traditionally, the ADG conference is held every two years. The previous editions of ADG were held in Nanning in 2018, Strasbourg in 2016, Coimbra in 2014, Edinburgh in 2012, Munich in 2010, Shanghai in 2008, Pontevedra in 2006, Gainesville in 2004, Hagenberg in 2002, Zurich in 2000, Beijing in 1998, and Toulouse in 1996. The 13th edition of ADG was supposed to be held in 2020 in Hagenberg, Austria, but due to the COVID-19 pandemic, it was postponed for 2021, and held online (still hosted by RISC Institute, Hagenberg, Austria), September 15-17, 2021 (https://www.risc.jku.at/conferences/adg2021).

cs.AI↗

arXiv2019

Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to $n \times n$ board (for natural $n$ greater than $3$). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs.

cs.LO↗

arXiv2012

Formalization and Implementation of Algebraic Methods in Geometry

We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, open-source Java implementation of the algebraic methods. The project should fill-in some gaps still existing in this area (e.g., the lack of formal links between algebraic methods and synthetic geometry and the lack of self-contained implementations of algebraic methods suitable for integration with dynamic geometry tools) and should enable new applications of theorem proving in education.

cs.SC↗