Related papers: On a logical model of combinatorial problems
We introduce an algorithm that exploits a combinatorial symmetry of an arrangement in order to produce a geometric reflection between two disconnected components of its moduli space. We apply this method to disqualify three real examples…
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown…
We give a polynomial-time dynamic programming algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. We briefly review three known tractable matrix classes and show that none of…
This paper proves that there does not exist a polynomial-time algorithm to the the subset sum problem. As this problem is in NP, the result implies that the class P of problems admitting polynomial-time algorithms does not equal the class…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
This paper proposes seven combinatorial problems around formulas for the characteristic polynomial and the spectral numbers of a quasihomogeneous singularity. One of them is a new conjecture on the characteristic polynomial. It is an…
We study the computational complexity of fundamental problems over the $p$-adic numbers ${\mathbb Q}_p$ and the $p$-adic integers ${\mathbb Z}_p$. Gu\'epin, Haase, and Worrell proved that checking satisfiability of systems of linear…
The asymmetric May-Leonard model is a prototypical system of 3 nonlinearly coupled first-order Ordinary Differential Equations with second-degree polynomial right-hand sides. In this short paper we identify a class of special solutions of…
We present an untyped linear lambda calculus with braids, the corresponding combinatory logic, and the semantic models given by crossed G-sets.
We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
We discuss some diverse open problems in the dimer model, motivated by a geometric viewpoint. This is part of a conference proceedings for the OPAC 2022 conference.
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…