2,919 research outputs found
Free Theorems In The Presence Of seq
Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, the standard parametricity theorem fails for nonstrict languages supporting a polymorphic strict evaluation primitive like Haskell’s seq. Contrary to the folklore surrounding seq and parametricity, we show that not even quantifying only over strict and bottom-reflecting relations in the - clause of the underlying logical relation — and thus restricting the choice of functions with which such relations are instantiated to obtain free theorems to strict and total ones — is sufficient to recover from this failure. By addressing the subtle issues that arise when propagating up the type hierarchy restrictions imposed on a logical relation in order to accommodate the strictness primitive, we provide a parametricity theorem for the subset of Haskell corresponding to a Girard-Reynolds-style calculus with fixpoints, algebraic datatypes, and seq. A crucial ingredient of our approach is the use of an asymmetric logical relation, which leads to “inequational” versions of free theorems enriched by preconditions guaranteeing their validity in the described setting. Besides the potential to obtain corresponding preconditions for standard equational free theorems by combining some new inequational ones, the latter also have value in their own right, as is exemplified with a careful analysis of seq’s impact on familiar program transformations
A Procedure for Splitting Processes and its Application to Coordination
We present a procedure for splitting processes in a process algebra with
multi-actions (a subset of the specification language mCRL2). This splitting
procedure cuts a process into two processes along a set of actions A: roughly,
one of these processes contains no actions from A, while the other process
contains only actions from A. We state and prove a theorem asserting that the
parallel composition of these two processes equals the original process under
appropriate synchronization.
We apply our splitting procedure to the process algebraic semantics of the
coordination language Reo: using this procedure and its related theorem, we
formally establish the soundness of splitting Reo connectors along the
boundaries of their (a)synchronous regions in implementations of Reo. Such
splitting can significantly improve the performance of connectors.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432
Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
The rate of entropy production in a classical dynamical system is
characterized by the Kolmogorov-Sinai entropy rate given by
the sum of all positive Lyapunov exponents of the system. We prove a quantum
version of this result valid for bosonic systems with unstable quadratic
Hamiltonian. The derivation takes into account the case of time-dependent
Hamiltonians with Floquet instabilities. We show that the entanglement entropy
of a Gaussian state grows linearly for large times in unstable systems,
with a rate determined by the Lyapunov exponents and
the choice of the subsystem . We apply our results to the analysis of
entanglement production in unstable quadratic potentials and due to periodic
quantum quenches in many-body quantum systems. Our results are relevant for
quantum field theory, for which we present three applications: a scalar field
in a symmetry-breaking potential, parametric resonance during post-inflationary
reheating and cosmological perturbations during inflation. Finally, we
conjecture that the same rate appears in the entanglement growth of
chaotic quantum systems prepared in a semiclassical state.Comment: 50+17 Pages, 11 figure
How long, O Bayesian network, will I sample thee? A program analysis perspective on expected sampling times
Bayesian networks (BNs) are probabilistic graphical models for describing
complex joint probability distributions. The main problem for BNs is inference:
Determine the probability of an event given observed evidence. Since exact
inference is often infeasible for large BNs, popular approximate inference
methods rely on sampling.
We study the problem of determining the expected time to obtain a single
valid sample from a BN. To this end, we translate the BN together with
observations into a probabilistic program. We provide proof rules that yield
the exact expected runtime of this program in a fully automated fashion. We
implemented our approach and successfully analyzed various real-world BNs taken
from the Bayesian network repository
NEW SMARANDACHE SEQUENCES: THE FAMILY OF METALLIC MEANS
The family of Metallic Means comprises every quadratic irrational number that is
the positive solution of algebraic equations, where n is a natural number. The most prominent member of this family is the Golden Mean, then it comes the Silver Mean, the Bronze Mean, the NIckel Mean, the Copper Mean, etc. All of them are closely related to quasi-periodic dynamics, being therefore important clues in the study of the onset to chaos
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