相关论文: Efficient Interpolant Generation in Satisfiability…

Mathematical problem generation (MPG) is a significant research direction in the field of intelligent education. In recent years, the rapid development of large language models (LLMs) has enabled new technological approaches to…

Interpolation and smoothing using cubic and generalized splines are fundamental tools in data analysis and statistical modeling. Recently, fast computational algorithms were developed for natural $L$-splines of order four, which arise as…

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the…

We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…

In this paper we present a Mathematica notebook for computing nonsymmetric and interpolation Macdonald polynomials. We present the new recursive generation algorithm employed within the notebook and the theory required for its development.…

Normal modal logics extending the logic K4.3 of linear transitive frames are known to lack the Craig interpolation property, except some logics of bounded depth such as S5. We turn this `negative' fact into a research question and pursue a…

Modern SMT solvers have revolutionized the approach to constraint satisfaction problems by integrating advanced theory reasoning and encoding techniques. In this work, we evaluate the performance of modern SMT solvers in Z3, CVC5 and…

For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…

In this chapter, we present six different proofs of Craig interpolation for the modal logic K, each using a different set of techniques (model-theoretic, proof-theoretic, syntactic, automata-theoretic, using quasi-models, and algebraic). We…

A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…

Mathematical reasoning remains challenging for LLMs due to complex logic and the need for precise computation. Existing methods enhance LLM reasoning by synthesizing datasets through problem rephrasing, but face issues with generation…

Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…

The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…

Capturing the intricate multiscale features of turbulent flows remains a fundamental challenge due to the limited resolution of experimental data and the computational cost of high-fidelity simulations. In many practical scenarios only…

This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…

The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…

SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing…

Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…

We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…