相关论文: Quantifier Elimination for Normal Cone Computation…

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…

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre…

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order…

The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for…

Quantifier elimination theorems show that each formula in a certain theory is equivalent to a formula of a specific form -- usually a quantifier-free one, sometimes in an extended language. Model theoretic embedding tests are a frequently…

Quantifier elimination (QE) is an important problem that has numerous applications. Unfortunately, QE is computationally very hard. Earlier we introduced a generalization of QE called $\mathit{partial}$ QE (or PQE for short). PQE allows to…

We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…

Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF…

We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a…

The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical…

Quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by the theory of complete discrimination systems, function \RealTriangularize in Maple15 and the so-called…

A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness…

We examine two natural operations to create numerical semigroups. We say that a numerical semigroup $\mathcal{S}$ is $k$-normalescent if it is the projection of the set of integer points in a $k$-dimensional polyhedral cone, and we say that…

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance.…

We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation. This unifies the same known results for algebraically closed valued fields and real closed valued fields.

A simple model of a relativistic open string with a point mass attached at one end is quantized. The normal modes are derived and used to construct expressions for the operator commutators. Light cone gauge is used to find the mass squared…

We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…

We characterize normalization by evaluation as the composition of a self-interpreter with a self-reducer using a special representation scheme, in the sense of Mogensen (1992). We do so by deriving in a systematic way an untyped…

This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…