17,409 research outputs found
What's Decidable About Sequences?
We present a first-order theory of sequences with integer elements,
Presburger arithmetic, and regular constraints, which can model significant
properties of data structures such as arrays and lists. We give a decision
procedure for the quantifier-free fragment, based on an encoding into the
first-order theory of concatenation; the procedure has PSPACE complexity. The
quantifier-free fragment of the theory of sequences can express properties such
as sortedness and injectivity, as well as Boolean combinations of periodic and
arithmetic facts relating the elements of the sequence and their positions
(e.g., "for all even i's, the element at position i has value i+3 or 2i"). The
resulting expressive power is orthogonal to that of the most expressive
decidable logics for arrays. Some examples demonstrate that the fragment is
also suitable to reason about sequence-manipulating programs within the
standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl
On quantum symmetries of ADE graphs
The double triangle algebra(DTA) associated to an ADE graph is considered. A
description of its bialgebra structure based on a reconstruction approach is
given. This approach takes as initial data the representation theory of the DTA
as given by Ocneanu's cell calculus. It is also proved that the resulting DTA
has the structure of a weak *-Hopf algebra. As an illustrative example, the
case of the graph A3 is described in detail.Comment: 15 page
Nonequilibrium potential and fluctuation theorems for quantum maps
We derive a general fluctuation theorem for quantum maps. The theorem applies
to a broad class of quantum dynamics, such as unitary evolution, decoherence,
thermalization, and other types of evolution for quantum open systems. The
theorem reproduces well-known fluctuation theorems in a single and simplified
framework and extends the Hatano-Sasa theorem to quantum nonequilibrium
processes. Moreover, it helps to elucidate the physical nature of the
environment inducing a given dynamics in an open quantum system.Comment: 10 page
Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization
In this work, an effective construction, via Sch\"utzenberger's monoidal
factorization, of dual bases for the non commutative symmetric and
quasi-symmetric functions is proposed
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