Related papers: Quadratic type checking for objective type theory
It has recently been discovered that both quantum and classical propositional logics can be modelled by classes of non-orthomodular and thus non-distributive lattices that properly contain standard orthomodular and Boolean classes,…
We present a variant of ATL with distributed knowledge operators based on a synchronous and perfect recall semantics. The coalition modalities in this logic are based on partial observation of the full history, and incorporate a form of…
We demonstrate a simplification of some recent works on the classification of the Lie symmetries for a quadratic equation of Li\'{e}nard type. We observe that the problem could have been resolved more simply.
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
We give a definition of finitary type theories that subsumes many examples of dependent type theories, such as variants of Martin-L\"of type theory, simple type theories, first-order and higher-order logics, and homotopy type theory. We…
In this paper, we first propose a natural generalization of the well-known compare-and-swap object, one that replaces the equality comparison with an arbitrary comparator. We then present a simple wait-free universal construction using this…
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type…
In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We give a short constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix.
We study the problems of testing isomorphism of polynomials, algebras, and multilinear forms. Our first main results are average-case algorithms for these problems. For example, we develop an algorithm that takes two cubic forms $f, g\in…
Consider systems of equations $q_i(x)=0$, where $q_i: {\Bbb R}^n \longrightarrow {\Bbb R}$, $i=1, \ldots, m$, are quadratic forms. Our goal is to tell efficiently systems with many non-trivial solutions or near-solutions $x \ne 0$ from…
We found in Homotopy Type Theory (HoTT), a way of representing a first order version of intuitionistic logic (ICL), for intuitionistic calculational logic) where, instead of deduction trees, corresponding linear calculational formats are…
We present a novel automata-based approach to address linear temporal logic modulo theory (LTL-MT) as a specification language for data words. LTL-MT extends LTL_f by replacing atomic propositions with quantifier-free multi-sorted…
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…
We show that restricting the elimination principle of the natural numbers type in Martin-L\"of Type Theory (MLTT) to a universe of types not containing $\Pi$-types ensures that all definable functions are primitive recursive. This extends…
One clock alternating timed automata OCATA have been recently introduced as natural extension of (one clock) timed automata to express the semantics of MTL (Ouaknine, Worrell 2005). We consider the application of OCATA to problem of…
We present a new algorithm for refining a real interval containing a single real root: the new method combines characteristics of the classical Bisection algorithm and Newton's Iteration. Our method exhibits quadratic convergence when…