Related papers: Transcendence Certificates for D-finite Functions
Formal software verification uses mathematical techniques to establish that software has certain properties. For example, that the behaviour of a software system satisfies certain logically-specified properties. Formal methods have a long…
G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…
We prove that $ZF+DC+"$there exists a transcendence basis for the reals$"+"$there is no well-ordering of the reals$"$ is consistent relative to $ZFC$. This answers a question of Larson and Zapletal.
We consider the decidability of the verification problem of programs \emph{modulo axioms} --- that is, verifying whether programs satisfy their assertions, when the functions and relations it uses are assumed to interpreted by arbitrary…
The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints :…
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…
The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…
System integration testing is the process of testing a system by the stepwise integration of sub-components. Usually these sub-components are already verified to guarantee their correct functional behavior. By integration of these verified…
A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous…
In this paper we propose a sequence of tests which gives a definitive test for checking $2\times M$ separability. The test is definitive in the sense that each test corresponds to checking membership in a cone, and that the closure of the…
It is not uncommon in analysis that existence of extremal objects is obtained via an iterative procedure: we start from a given admissible object, then modify it, then modify again etc... If being extremal means maximimizing a real valued…
When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods…
Let $f$ be a transcendental entire function. For $n \in \mathbb{N},$ let $ f^{n}$ denote the $n^{th}$ iterate of $f$. Let $ I(f) = \{z \in \mathbb{C} : f^n \rightarrow \infty $ as $ n \rightarrow \infty \} $ and $ K(f) = \{z: \textrm{ there…
With the aid of the concept of stable independence we can construct, in an efficient way, a compact representation of a semi-graphoid independence relation. We show that this representation provides a new necessary condition for the…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
Supersinglets are states of spin-zero of $d \ge 3$ particles of $d$ levels. They are invariant under unitary transformations of the form $U^{\otimes d}$ and have applications in metrology, error protection, and communication. They also…
We study satisfiability for HyperLTL with a $\forall^*\exists^*$ quantifier prefix, known to be highly undecidable in general. HyperLTL can express system properties that relate multiple traces (so-called hyperproperties), which are often…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…
All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…
We show that all--instances termination of chase is undecidable. More precisely, there is no algorithm deciding, for a given set $\cal T$ consisting of Tuple Generating Dependencies (a.k.a. Datalog$^\exists$ program), whether the $\cal…