Related papers: SMT Solving over Finite Field Arithmetic
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Large linear systems play an important role in high-energy theory, appearing in amplitude bootstraps and during integral reduction. This paper introduces FiniteFieldSolve, a general-purpose toolkit for exactly solving large linear systems…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
In this paper two algorithms solving circuit satisfiability problem over supernilpotent algebras are presented. The first one is deterministic and is faster than fastest previous algorithm presented by Aichinger. The second one is…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
This work discusses the reachability analysis (RA) of Max-Plus Linear (MPL) systems, a class of continuous-space, discrete-event models defined over the max-plus algebra. Given the initial and target sets, we develop algorithms to verify…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…
Whether LLMs can reason or write software is widely debated, but whether they can write software that itself reasons is largely unexplored. We present a case study in which an LLM coding agent builds a complete DPLL(T)-style SMT solver for…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Feature attribution methods are popular for explaining neural network predictions, and they are often evaluated on metrics such as comprehensiveness and sufficiency. In this paper, we highlight an intriguing property of these metrics: their…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
This paper presents a new framework for constructing congruence closure of a finite set of ground equations over uninterpreted symbols and interpreted symbols for the group axioms. In this framework, ground equations are flattened into…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve…
The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domain-restricted but supports extensions including built-in functions as well…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…
In this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular…
We consider systems of strict multivariate polynomial inequalities over the reals. All polynomial coefficients are parameters ranging over the reals, where for each coefficient we prescribe its sign. We are interested in the existence of…