566 research outputs found
Thermodynamic graph-rewriting
We develop a new thermodynamic approach to stochastic graph-rewriting. The
ingredients are a finite set of reversible graph-rewriting rules called
generating rules, a finite set of connected graphs P called energy patterns and
an energy cost function. The idea is that the generators define the qualitative
dynamics, by showing which transformations are possible, while the energy
patterns and cost function specify the long-term probability of any
reachable graph. Given the generators and energy patterns, we construct a
finite set of rules which (i) has the same qualitative transition system as the
generators; and (ii) when equipped with suitable rates, defines a
continuous-time Markov chain of which is the unique fixed point. The
construction relies on the use of site graphs and a technique of `growth
policy' for quantitative rule refinement which is of independent interest. This
division of labour between the qualitative and long-term quantitative aspects
of the dynamics leads to intuitive and concise descriptions for realistic
models (see the examples in S4 and S5). It also guarantees thermodynamical
consistency (AKA detailed balance), otherwise known to be undecidable, which is
important for some applications. Finally, it leads to parsimonious
parameterizations of models, again an important point in some applications
Reversing Single Sessions
Session-based communication has gained a widespread acceptance in practice as
a means for developing safe communicating systems via structured interactions.
In this paper, we investigate how these structured interactions are affected by
reversibility, which provides a computational model allowing executed
interactions to be undone. In particular, we provide a systematic study of the
integration of different notions of reversibility in both binary and multiparty
single sessions. The considered forms of reversibility are: one for completely
reversing a given session with one backward step, and another for also
restoring any intermediate state of the session with either one backward step
or multiple ones. We analyse the costs of reversing a session in all these
different settings. Our results show that extending binary single sessions to
multiparty ones does not affect the reversibility machinery and its costs
On paths-based criteria for polynomial time complexity in proof-nets
Girard's Light linear logic (LLL) characterized polynomial time in the
proof-as-program paradigm with a bound on cut elimination. This logic relied on
a stratification principle and a "one-door" principle which were generalized
later respectively in the systems L^4 and L^3a. Each system was brought with
its own complex proof of Ptime soundness.
In this paper we propose a broad sufficient criterion for Ptime soundness for
linear logic subsystems, based on the study of paths inside the proof-nets,
which factorizes proofs of soundness of existing systems and may be used for
future systems. As an additional gain, our bound stands for any reduction
strategy whereas most bounds in the literature only stand for a particular
strategy.Comment: Long version of a conference pape
Which graph states are useful for quantum information processing?
Graph states are an elegant and powerful quantum resource for measurement
based quantum computation (MBQC). They are also used for many quantum protocols
(error correction, secret sharing, etc.). The main focus of this paper is to
provide a structural characterisation of the graph states that can be used for
quantum information processing. The existence of a gflow (generalized flow) is
known to be a requirement for open graphs (graph, input set and output set) to
perform uniformly and strongly deterministic computations. We weaken the gflow
conditions to define two new more general kinds of MBQC: uniform
equiprobability and constant probability. These classes can be useful from a
cryptographic and information point of view because even though we cannot do a
deterministic computation in general we can preserve the information and
transfer it perfectly from the inputs to the outputs. We derive simple graph
characterisations for these classes and prove that the deterministic and
uniform equiprobability classes collapse when the cardinalities of inputs and
outputs are the same. We also prove the reversibility of gflow in that case.
The new graphical characterisations allow us to go from open graphs to graphs
in general and to consider this question: given a graph with no inputs or
outputs fixed, which vertices can be chosen as input and output for quantum
information processing? We present a characterisation of the sets of possible
inputs and ouputs for the equiprobability class, which is also valid for
deterministic computations with inputs and ouputs of the same cardinality.Comment: 13 pages, 2 figure
A feasible algorithm for typing in Elementary Affine Logic
We give a new type inference algorithm for typing lambda-terms in Elementary
Affine Logic (EAL), which is motivated by applications to complexity and
optimal reduction. Following previous references on this topic, the variant of
EAL type system we consider (denoted EAL*) is a variant without sharing and
without polymorphism. Our algorithm improves over the ones already known in
that it offers a better complexity bound: if a simple type derivation for the
term t is given our algorithm performs EAL* type inference in polynomial time.Comment: 20 page
Controlling Reversibility in Reversing Petri Nets with Application to Wireless Communications
Petri nets are a formalism for modelling and reasoning about the behaviour of
distributed systems. Recently, a reversible approach to Petri nets, Reversing
Petri Nets (RPN), has been proposed, allowing transitions to be reversed
spontaneously in or out of causal order. In this work we propose an approach
for controlling the reversal of actions of an RPN, by associating transitions
with conditions whose satisfaction/violation allows the execution of
transitions in the forward/reversed direction, respectively. We illustrate the
framework with a model of a novel, distributed algorithm for antenna selection
in distributed antenna arrays.Comment: RC 201
A rule-based kinetic model of RNA polymerase II C-terminal domain phosphorylation
The complexity ofmany RNA processing pathways is such that a conventional systemsmodelling approach is inadequate to represent all themolecular species involved. We demonstrate that rule-based modelling permits a detailed model of a complex RNA signalling pathway to be defined. Phosphorylation of the RNApolymerase II (RNAPII)C-terminal domain (CTD; a flexible tail-like extension of the largest subunit) couples pre-messenger RNA capping, splicing and 30 end maturation to transcriptional elongation and termination, and plays a central role in integrating these processes. The phosphorylation states of the serine residues of many heptapeptide repeats of the CTD alter along the coding region of genes as a function of distance from the promoter. From a mechanistic perspective, both the changes in phosphorylation and the location atwhich they take place on the genes are a function of the time spent byRNAPII in elongation as this interval provides the opportunity for the kinases and phosphatases to interactwith theCTD.On this basis,we synthesize the available data to create a kinetic model of the action of the known kinases and phosphatases to resolve the phosphorylation pathways and their kinetics.</p
Distribution-based bisimulation for labelled Markov processes
In this paper we propose a (sub)distribution-based bisimulation for labelled
Markov processes and compare it with earlier definitions of state and event
bisimulation, which both only compare states. In contrast to those state-based
bisimulations, our distribution bisimulation is weaker, but corresponds more
closely to linear properties. We construct a logic and a metric to describe our
distribution bisimulation and discuss linearity, continuity and compositional
properties.Comment: Accepted by FORMATS 201
Batalin-Vilkovisky Integrals in Finite Dimensions
The Batalin-Vilkovisky method (BV) is the most powerful method to analyze
functional integrals with (infinite-dimensional) gauge symmetries presently
known. It has been invented to fix gauges associated with symmetries that do
not close off-shell. Homological Perturbation Theory is introduced and used to
develop the integration theory behind BV and to describe the BV quantization of
a Lagrangian system with symmetries. Localization (illustrated in terms of
Duistermaat-Heckman localization) as well as anomalous symmetries are discussed
in the framework of BV.Comment: 35 page
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