2,923 research outputs found
Kleene Algebras, Regular Languages and Substructural Logics
We introduce the two substructural propositional logics KL, KL+, which use
disjunction, fusion and a unary, (quasi-)exponential connective. For both we
prove strong completeness with respect to the interpretation in Kleene algebras
and a variant thereof. We also prove strong completeness for language models,
where each logic comes with a different interpretation. We show that for both
logics the cut rule is admissible and both have a decidable consequence
relation.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Quantum and Braided Lie Algebras
We introduce the notion of a braided Lie algebra consisting of a
finite-dimensional vector space \CL equipped with a bracket $[\ ,\
]:\CL\tens\CL\to \CL\Psi:\CL\tens\CL\to
\CL\tens\CLU(\CL)R[\ ,\ ]c^{IJ}{}_KRU(\CL)=B(R)\CL\CLU_q(g)[\ ,\ ]\CL\subset
U_q(g)$ given by the quantum adjoint action.Comment: 56 page
Sound and complete axiomatizations of coalgebraic language equivalence
Coalgebras provide a uniform framework to study dynamical systems, including
several types of automata. In this paper, we make use of the coalgebraic view
on systems to investigate, in a uniform way, under which conditions calculi
that are sound and complete with respect to behavioral equivalence can be
extended to a coarser coalgebraic language equivalence, which arises from a
generalised powerset construction that determinises coalgebras. We show that
soundness and completeness are established by proving that expressions modulo
axioms of a calculus form the rational fixpoint of the given type functor. Our
main result is that the rational fixpoint of the functor , where is a
monad describing the branching of the systems (e.g. non-determinism, weights,
probability etc.), has as a quotient the rational fixpoint of the
"determinised" type functor , a lifting of to the category of
-algebras. We apply our framework to the concrete example of weighted
automata, for which we present a new sound and complete calculus for weighted
language equivalence. As a special case, we obtain non-deterministic automata,
where we recover Rabinovich's sound and complete calculus for language
equivalence.Comment: Corrected version of published journal articl
Hamiltonian Gravity and Noncommutative Geometry
A version of foliated spacetime is constructed in which the spatial geometry
is described as a time dependent noncommutative geometry. The ADM version of
the gravitational action is expressed in terms of these variables. It is shown
that the vector constraint is obtained without the need for an extraneous shift
vector in the action.Comment: 22 pages, AMS-LaTeX. Some improvements - mainly to sections 8 and 9.
Typographical errors to equations in appendix correcte
- …