Related papers: Canonical for Automated Theorem Proving in Lean
The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…
Based on continued fractions with subtractions, we identify the set of real numbers with the set of infinite integer sequences with all terms but the first one greater or equal to two. Each such sequence produces in a canonical way a unique…
Automated theorem proving systems built on Lean 4 increasingly rely on parallel tactic search over partially specified proofs, such as those generated by Draft-Sketch-Prove (DSP) pipelines. In current systems, each search branch…
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…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Actually, they provide a uniform and semantic way to axiomatise all extensions of intuitionistic logic and all modal logics above K4. Although the method…
We study the concept of canonical characteristic set of a characterizable differential ideal. We propose an efficient algorithm that transforms any characteristic set into the canonical one. We prove the basic properties of canonical…
This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality…
Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…
We discuss the canonical quantization of systems formulated on discrete space-times. We start by analyzing the quantization of simple mechanical systems with discrete time. The quantization becomes challenging when the systems have…
This paper presents a canonical dual approach for solving a nonlinear population growth problem governed by the well-known logistic equation. Using the finite difference and least squares methods, the nonlinear differential equation is…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
It has been shown in literature that a possible mechanism of mass generation for gauge fields is through a topological coupling of vector and tensor fields. After integrating over the tensor degrees of freedom, one arrives at an effective…
NPN classification has many applications in the synthesis and verification of digital circuits. The canonical-form-based method is the most common approach, designing a canonical form as representative for the NPN equivalence class first…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…
We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using automata and a package for manipulating them. We illustrate our technique by solving, purely mechanically, an open problem of Currie…
We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a…
Propositional canonical Gentzen-type systems, introduced in 2001 by Avron and Lev, are systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a connective is…
Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as $p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field…