239 research outputs found
Bisimulation for quantum processes
In this paper we introduce a novel notion of probabilistic bisimulation for
quantum processes and prove that it is congruent with respect to various
process algebra combinators including parallel composition even when both
classical and quantum communications are present. We also establish some basic
algebraic laws for this bisimulation. In particular, we prove uniqueness of the
solutions to recursive equations of quantum processes, which provides a
powerful proof technique for verifying complex quantum protocols.Comment: Journal versio
Lifted Relax, Compensate and then Recover: From Approximate to Exact Lifted Probabilistic Inference
We propose an approach to lifted approximate inference for first-order
probabilistic models, such as Markov logic networks. It is based on performing
exact lifted inference in a simplified first-order model, which is found by
relaxing first-order constraints, and then compensating for the relaxation.
These simplified models can be incrementally improved by carefully recovering
constraints that have been relaxed, also at the first-order level. This leads
to a spectrum of approximations, with lifted belief propagation on one end, and
exact lifted inference on the other. We discuss how relaxation, compensation,
and recovery can be performed, all at the firstorder level, and show
empirically that our approach substantially improves on the approximations of
both propositional solvers and lifted belief propagation.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
Toward Automatic Verification of Quantum Cryptographic Protocols.
Several quantum process algebras have been proposed and successfully applied
in verification of quantum cryptographic protocols. All of the bisimulations
proposed so far for quantum processes in these process algebras are
state-based, implying that they only compare individual quantum states, but not
a combination of them. This paper remedies this problem by introducing a novel
notion of distribution-based bisimulation for quantum processes. We further
propose an approximate version of this bisimulation that enables us to prove
more sophisticated security properties of quantum protocols which cannot be
verified using the previous bisimulations. In particular, we prove that the
quantum key distribution protocol BB84 is sound and (asymptotically) secure
against the intercept-resend attacks by showing that the BB84 protocol, when
executed with such an attacker concurrently, is approximately bisimilar to an
ideal protocol, whose soundness and security are obviously guaranteed, with at
most an exponentially decreasing gap.Comment: Accepted by Concur'1
Symbolic bisimulation for quantum processes
With the previous notions of bisimulation presented in literature, to check
if two quantum processes are bisimilar, we have to instantiate the free quantum
variables of them with arbitrary quantum states, and verify the bisimilarity of
resultant configurations. This makes checking bisimilarity infeasible from an
algorithmic point of view because quantum states constitute a continuum. In
this paper, we introduce a symbolic operational semantics for quantum processes
directly at the quantum operation level, which allows us to describe the
bisimulation between quantum processes without resorting to quantum states. We
show that the symbolic bisimulation defined here is equivalent to the open
bisimulation for quantum processes in the previous work, when strong
bisimulations are considered. An algorithm for checking symbolic ground
bisimilarity is presented. We also give a modal logical characterisation for
quantum bisimilarity based on an extension of Hennessy-Milner logic to quantum
processes.Comment: 30 pages, 7 figures, comments are welcom
A Simple Approach for State-Action Abstraction using a Learned MDP Homomorphism
Animals are able to rapidly infer from limited experience when sets of state
action pairs have equivalent reward and transition dynamics. On the other hand,
modern reinforcement learning systems must painstakingly learn through trial
and error that sets of state action pairs are value equivalent -- requiring an
often prohibitively large amount of samples from their environment. MDP
homomorphisms have been proposed that reduce the observed MDP of an environment
to an abstract MDP, which can enable more sample efficient policy learning.
Consequently, impressive improvements in sample efficiency have been achieved
when a suitable MDP homomorphism can be constructed a priori -- usually by
exploiting a practioner's knowledge of environment symmetries. We propose a
novel approach to constructing a homomorphism in discrete action spaces, which
uses a partial model of environment dynamics to infer which state action pairs
lead to the same state -- reducing the size of the state-action space by a
factor equal to the cardinality of the action space. We call this method
equivalent effect abstraction. In a gridworld setting, we demonstrate
empirically that equivalent effect abstraction can improve sample efficiency in
a model-free setting and planning efficiency for modelbased approaches.
Furthermore, we show on cartpole that our approach outperforms an existing
method for learning homomorphisms, while using 33x less training data.Comment: Previously Presented at the Multi-disciplinary Conference on
Reinforcement Learning and Decision Making (RLDM) 202
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