Related papers: A syntactical proof of the operational equivalence…
We consider the following decision problem: given two simply typed $\lambda$-terms, are they $\beta$-convertible? Equivalently, do they have the same normal form? It is famously non-elementary, but the precise complexity - namely…
One takes advantage of some basic properties of every homotopic $\lambda$-model (e.g.\ extensional Kan complex) to explore the higher $\beta\eta$-conversions, which would correspond to proofs of equality between terms of a theory of…
In this paper, we prove an $L^2$ extension theorem with optimal estimate in a precise way, which implies optimal estimate versions of various well-known $L^2$ extension theorems. As applications, we give proofs of a conjecture of Suita on…
Since the very beginning of the theory of linear logic it is known how to represent the $\lambda$-calculus as linear logic proof nets. The two systems however have different granularities, in particular proof nets have an explicit notion of…
In the development of a presumed asymptotic expansion for lambda_d in previous work, a basic step involved extracting the asymptotic behavior of a sum as being dominated by the largest term in the sum. But this argument only is valid when…
We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment. While the reachability problem is…
This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for {\zeta}(s). We present here, after showing the first proof of Riemann, a new, simple and direct proof of…
In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…
An operator $T$ on a Hilbert space $\mathcal H$ is called expansive, if $\|Tx\|\geq \|x\|$ ($x\in\mathcal H$). Expansive operators $T$ quasisimilar to the unilateral shift $S_N$ of finite multiplicity $N$ are studied. It is proved that…
In this paper, we prove a version of the typed B\"ohm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a…
We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is…
Let $J$ be a Jacobi operator on $\ell^2\left(\mathbb{Z}\right)$. We prove an eigenfunction expansion theorem for the singular part of $J$ using subordinate solutions to the eigenvalue equation. We exploit this theorem in order to show that…
This article examines the interpretation of the LTL temporal operators over finite and infinite sequences. This is used as the basis for deriving a sound and complete axiomatization for Caret, a recent temporal logic for reasoning about…
Motivated by several conjectures posed in the paper " Completely monotonic degrees for a difference between the logarithmic and psi functions",we confirm in this work some conjectures on completely monotonic degrees of remainders of the…
The $\lambda$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional…
$J$-self-adjoint extensions of the Phillips symmetric operator $S$ are studied. The concepts of stable and unstable $C$-symmetry are introduced in the extension theory framework. The main results are the following: if ${A}$ is a…
Let $\beta>1$. For $x \in [0,\infty)$, we have so-called the $\beta$-expansion of $x$ in base $\beta$ as follows: $$x= \sum_{j \leq k} x_{j}\beta^{j} = x_{k}\beta^{k}+ \cdots + x_{1}\beta+x_{0}+x_{-1}\beta^{-1} + x_{-2}\beta^{-2} + \cdots$$…
We consider model-theoretic properties related to the expressive power of three analogues of $L_{\omega_1, \omega}$ for metric structures. We give an example showing that one of these infinitary logics is strictly more expressive than the…
This paper is a sequel to "Logical systems I: Lambda calculi through discreteness". It provides a general 2-categorical setting for extensional calculi and shows how intensional and extensional calculi can be related in logical systems. We…
We sketch a tentative proof of P-completeness for the $\beta$-convertibility problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.