1,038 research outputs found
Relativistic wave equations with fractional derivatives and pseudo-differential operators
The class of the free relativistic covariant equations generated by the
fractional powers of the D'Alambertian operator is studied.
Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac
equations) are local in their nature, the multicomponent equations for
arbitrary n>2 are non-local. It is shown, how the representation of generalized
algebra of Pauli and Dirac matrices looks like and how these matrices are
related to the algebra of SU(n) group. The corresponding representations of the
Poincar\'e group and further symmetry transformations on the obtained equations
are discussed. The construction of the related Green functions is suggested.Comment: 29 pages, Tex. In the corrected version a small bug in
cross-references to some equations is removed. Minor text corrections are
done and some references are adde
GLC actors, artificial chemical connectomes, topological issues and knots
Based on graphic lambda calculus, we propose a program for a new model of
asynchronous distributed computing, inspired from Hewitt Actor Model, as well
as several investigation paths, concerning how one may graft lambda calculus
and knot diagrammatics
Refactoring pattern matching
Defining functions by pattern matching over the arguments is advantageous for understanding and reasoning, but it tends to expose the implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to program refactoring based on a right-invertible language rinv—every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation, while maintaining simple and sound reasoning
Semantics of a Typed Algebraic Lambda-Calculus
Algebraic lambda-calculi have been studied in various ways, but their
semantics remain mostly untouched. In this paper we propose a semantic analysis
of a general simply-typed lambda-calculus endowed with a structure of vector
space. We sketch the relation with two established vectorial lambda-calculi.
Then we study the problems arising from the addition of a fixed point
combinator and how to modify the equational theory to solve them. We sketch an
algebraic vectorial PCF and its possible denotational interpretations
A Simple Attack on Some Clock-Controlled Generators
We present a new approach to edit distance attacks on certain
clock-controlled generators, which applies basic concepts of Graph Theory to
simplify the search trees of the original attacks in such a way that only the
most promising branches are analyzed. In particular, the proposed improvement
is based on cut sets defined on some graphs so that certain shortest paths
provide the edit distances. The strongest aspects of the proposal are that the
obtained results from the attack are absolutely deterministic, and that many
inconsistent initial states of the target registers are recognized beforehand
and avoided during search
Dual-Context Calculi for Modal Logic
We present natural deduction systems and associated modal lambda calculi for
the necessity fragments of the normal modal logics K, T, K4, GL and S4. These
systems are in the dual-context style: they feature two distinct zones of
assumptions, one of which can be thought as modal, and the other as
intuitionistic. We show that these calculi have their roots in in sequent
calculi. We then investigate their metatheory, equip them with a confluent and
strongly normalizing notion of reduction, and show that they coincide with the
usual Hilbert systems up to provability. Finally, we investigate a categorical
semantics which interprets the modality as a product-preserving functor.Comment: Full version of article previously presented at LICS 2017 (see
arXiv:1602.04860v4 or doi: 10.1109/LICS.2017.8005089
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