5,482 research outputs found
Emulating Digital Logic using Transputer Networks (Very High Parallelism = Simplicity = Performance)
Modern VLSI technology has changed the economic rules by which the balance between processing
power, memory and communications is decided in computing systems. This will have a profound
impact on the design rules for the controlling software. In particular, the criteria for judging efficiency
of the algorithms will be somewhat different. This paper explores some of these implications through
the development of highly parallel and highly distributable algorithms based on occam and transputer
networks. The major results reported are a new simplicity for software designs, a corresponding ability
to reason (formally and informally) about their properties, the reusability of their components and some
real performance figures which demonstrate their practicality. Some guidelines to assist in these designs
are also given. As a vehicle for discussion, an interactive simulator is developed for checking the
functional and timing characteristics of digital logic circuits of arbitrary complexity
Interpolation Methods for Binary and Multivalued Logical Quantum Gate Synthesis
A method for synthesizing quantum gates is presented based on interpolation
methods applied to operators in Hilbert space. Starting from the diagonal forms
of specific generating seed operators with non-degenerate eigenvalue spectrum
one obtains for arity-one a complete family of logical operators corresponding
to all the one-argument logical connectives. Scaling-up to n-arity gates is
obtained by using the Kronecker product and unitary transformations. The
quantum version of the Fourier transform of Boolean functions is presented and
a Reed-Muller decomposition for quantum logical gates is derived. The common
control gates can be easily obtained by considering the logical correspondence
between the control logic operator and the binary propositional logic operator.
A new polynomial and exponential formulation of the Toffoli gate is presented.
The method has parallels to quantum gate-T optimization methods using powers of
multilinear operator polynomials. The method is then applied naturally to
alphabets greater than two for multi-valued logical gates used for quantum
Fourier transform, min-max decision circuits and multivalued adders
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An Efficient Algorithm for the Analysis of Cyclic Circuits
Compiling high-level hardware languages can produce circuits containing combinational cycles that can never be sensitized. Such circuits do have well-defined functional behavior, but wreak havoc with most logic synthesis and timing tools, which assume acyclic combinational logic. As such, some sort of cycle-removal step is usually necessary for handling these circuits. We present an algorithm able to quickly and exactly characterize all combinational behavior of a cyclic circuit. It iteratively examines the boundary between gates whose outputs are and are not defined and works backward to find additional input patterns that make the circuit behave combinationally. It produces a minimal set of sets of assignments to inputs that together cover all combinational behavior. This can be used to restructure the circuit into an acyclic equivalent, report errors, or as an optimization aid. Experiments show our algorithm runs several orders of magnitude faster than existing ones on real-life cyclic circuits, making it useful in practice
Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
The known Pfaffian structure of the boundary spin correlations, and more
generally order-disorder correlation functions, is given a new explanation
through simple topological considerations within the model's random current
representation. This perspective is then employed in the proof that the
Pfaffian structure of boundary correlations emerges asymptotically at
criticality in Ising models on with finite-range interactions.
The analysis is enabled by new results on the stochastic geometry of the
corresponding random currents. The proven statement establishes an aspect of
universality, seen here in the emergence of fermionic structures in two
dimensions beyond the solvable cases.Comment: 59 pages, 19 figure
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
Diagrammatic Semantics for Digital Circuits
We introduce a general diagrammatic theory of digital circuits, based on connections between monoidal categories and graph rewriting. The main achievement of the paper is conceptual, filling a foundational gap in reasoning syntactically and symbolically about a large class of digital circuits (discrete values, discrete delays, feedback). This complements the dominant approach to circuit modelling, which relies on simulation. The main advantage of our symbolic approach is the enabling of automated reasoning about parametrised circuits, with a potentially interesting new application to partial evaluation of digital circuits. Relative to the recent interest and activity in categorical and diagrammatic methods, our work makes several new contributions. The most important is establishing that categories of digital circuits are Cartesian and admit, in the presence of feedback expressive iteration axioms. The second is producing a general yet simple graph-rewrite framework for reasoning about such categories in which the rewrite rules are computationally efficient, opening the way for practical applications
5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal
We study two-dimensional rotation-symmetric number-conserving cellular
automata working on the von Neumann neighborhood (RNCA). It is known that such
automata with 4 states or less are trivial, so we investigate the possible
rules with 5 states. We give a full characterization of these automata and show
that they cannot be strongly Turing universal. However, we give example of
constructions that allow to embed some boolean circuit elements in a 5-states
RNCA
The Complexity of Satisfiability for Sub-Boolean Fragments of ALC
The standard reasoning problem, concept satisfiability, in the basic
description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the
presence of unrestricted axioms. Several fragments of ALC, notably logics in
the FL, EL, and DL-Lite family, have an easier satisfiability problem;
sometimes it is even tractable. All these fragments restrict the use of Boolean
operators in one way or another. We look at systematic and more general
restrictions of the Boolean operators and establish the complexity of the
concept satisfiability problem in the presence of axioms. We separate tractable
from intractable cases.Comment: 17 pages, accepted (in short version) to Description Logic Workshop
201
Modeling multi-valued biological interaction networks using Fuzzy Answer Set Programming
Fuzzy Answer Set Programming (FASP) is an extension of the popular Answer Set Programming (ASP) paradigm that allows for modeling and solving combinatorial search problems in continuous domains. The recent development of practical solvers for FASP has enabled its applicability to real-world problems. In this paper, we investigate the application of FASP in modeling the dynamics of Gene Regulatory Networks (GRNs). A commonly used simplifying assumption to model the dynamics of GRNs is to assume only Boolean levels of activation of each node. Our work extends this Boolean network formalism by allowing multi-valued activation levels. We show how FASP can be used to model the dynamics of such networks. We experimentally assess the efficiency of our method using real biological networks found in the literature, as well as on randomly-generated synthetic networks. The experiments demonstrate the applicability and usefulness of our proposed method to find network attractors
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