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Neurons and symbols: a manifesto
We discuss the purpose of neural-symbolic integration including its principles, mechanisms and applications. We outline a cognitive computational model for neural-symbolic integration, position the model in the broader context of multi-agent systems, machine learning and automated reasoning, and list some of the challenges for the area of
neural-symbolic computation to achieve the promise of effective integration of robust learning and expressive reasoning under uncertainty
A tool for model-checking Markov chains
Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EÎMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EÎMC2
Solving Diophantine problems on curves via descent on the jacobian
We suggest that the following plan will provide a powerful tool for trying to find the set of Q-rational points C(Q) on a curve C of genus>1:\ud
(1) Attempt to find J(Q)/2J(Q) via descent on J, the Jacobian of C.\ud
(2) Deduce generators for J(Q) via an explicit theory of heights.\ud
(3). Apply local techniques to try to deduce C(Q) via an embedding of C(Q) inside J(Q).\ud
We describe work just completed, which gives versions of (1),(2),(3) which are often workable in practice for genus 2, and outline the potential for a computationally viable generalisation. We note that (1),(2),(3) (quite aside from being part of this plan) have their own independent applications to other branches of the Mathematics of Computation, such as the search for large rank, the higher dimensional testing of well known conjectures, and algorithms for symbolic integration
Symbolic Algebra and Renormalization of Gauge Theories
Symbolic algebra relevant to the renormalization of gauge theories can be
efficiently performed by machine using modern packages. We devise a scheme for
representing and manipulating the objects involved in perturbative calculations
of gauge theories. This scheme is readily implemented using the general purpose
package, Mathematica. The techniques discussed are used to calculate
renormalization group functions for a non-abelian gauge theory with
massless fermions in a representation R, in the two-loop approximation, and to
simplify some expressions arising in electroweak calculations at the two loop
level.Comment: 16 pages, LaTex, 2 diagrams drawn with FEYNMAN, uses cite.sty Entire
manuscript available as a ps file at
http://www.physics.adelaide.edu.au/theory/home.html Also available via
anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-41.T193.ps
Accepted for publication in Computer Physics Communicatio
A Reduced Semantics for Deciding Trace Equivalence
Many privacy-type properties of security protocols can be modelled using
trace equivalence properties in suitable process algebras. It has been shown
that such properties can be decided for interesting classes of finite processes
(i.e., without replication) by means of symbolic execution and constraint
solving. However, this does not suffice to obtain practical tools. Current
prototypes suffer from a classical combinatorial explosion problem caused by
the exploration of many interleavings in the behaviour of processes.
M\"odersheim et al. have tackled this problem for reachability properties using
partial order reduction techniques. We revisit their work, generalize it and
adapt it for equivalence checking. We obtain an optimisation in the form of a
reduced symbolic semantics that eliminates redundant interleavings on the fly.
The obtained partial order reduction technique has been integrated in a tool
called APTE. We conducted complete benchmarks showing dramatic improvements.Comment: Accepted for publication in LMC
Inference of termination conditions for numerical loops in Prolog
We present a new approach to termination analysis of numerical computations
in logic programs. Traditional approaches fail to analyse them due to non
well-foundedness of the integers. We present a technique that allows overcoming
these difficulties. Our approach is based on transforming a program in a way
that allows integrating and extending techniques originally developed for
analysis of numerical computations in the framework of query-mapping pairs with
the well-known framework of acceptability. Such an integration not only
contributes to the understanding of termination behaviour of numerical
computations, but also allows us to perform a correct analysis of such
computations automatically, by extending previous work on a constraint-based
approach to termination. Finally, we discuss possible extensions of the
technique, including incorporating general term orderings.Comment: To appear in Theory and Practice of Logic Programming. To appear in
Theory and Practice of Logic Programmin
A Markov Chain Model Checker
Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker ), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of )
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