Related papers: On reduction and normalization in the computationa…
Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…
A famous result by Milner is that the lambda-calculus can be simulated inside the pi-calculus. This simulation, however, holds only modulo strong bisimilarity on processes, i.e. there is a slight mismatch between beta-reduction and how it…
This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambda-calculus can simulate each other within a polynomial…
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
We introduce a call-by-name lambda-calculus $\lambda Jn$ with generalized applications which is equipped with distant reduction. This allows to unblock $\beta$-redexes without resorting to the standard permutative conversions of generalized…
I distinguish two types of reduction within the context of quantum-classical relations, which I designate "formal" and "empirical". Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two…
Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation,…
This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de…
The paper demonstrates how a 2-dimensional recurrence problem can be reduced to a mono-dimensional recurrence problem where the Kogge and Stone algorithm is applicable, with the computation time - excluding the reduction step - becoming…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation…
Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between…
We review and investigate the general theory of thermodynamics of computation, and derive the fundamental inequalities that set the lower bounds of the work requirement and the heat emission during a computation. These inequalities…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…