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arXiv 2018年

作者： Ospina, Juan Logic and Computation Group Mathematics Engineering Program Department of Mathematics School of Sciences EAFIT University Medellín Colombia

A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the anyonic engineering will provide the anyonic devices from which the topological quantum computers will be constructed. From other side the string anyons are interesting topological phases of matter which can be described using mathematical constructions such as Frobenius algebras and open-closed string topological quantum field theories which are based on cobordism categories. Recently was proposed that is possible to obtain representations of cobordism categories using modular categories. In the present work, the modular categories resulting as representations of the 3-dimensional bordism 2-category are used with the aim to construct a new model of topological quantum computation. Such new model is named "Sanyon Topological Quantum computation" and it is is theoretically performed by evolving non-abelian string- anyons (sanyons) using the Loop Braid Group and the open-closed cobordism category. The output of the computation uniquely depends on how the sanyons have been braided by the Loop Braid Group and operated by the generators of the cobordism category. Small disturbances do not unravel the loop braids and the cobordisms, making the computation resistant to errors and decoherence. Copyright © 2018, The Authors. All rights reserved.

关键词： Quantum computers

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A new game equivalence and its modal logic

arXiv

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arXiv 2017年

作者： Van Benthem, Johan Bezhanishvili, Nick Enqvist, Sebastian Institute for Logic Language and Computation University of Amsterdam Netherlands Department of Philosophy Stanford University United States Changjiang Scholar Program Tsinghua University China Department for Philosophy Stockholm University Sweden

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal bisimulation. Concretely, we propose a more finegrained notion of equality of 'basic powers' which record what players can force plus what they leave to others to do, a crucial feature of interaction. This notion is closer to game-theoretic strategic form, as we explain in detail, while remaining amenable to logical analysis. We determine the properties of basic powers via a new representation theorem, find a matching 'instantial neighborhood game logic', and show how our analysis can be extended to a new game algebra and dynamic game logic. Copyright © 2017, The Authors. All rights reserved.

关键词： Game theory

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Moving up and down in the generic multiverse

Moving up and down in the generic multiverse

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5th Indian Conference on logic and Its Applications, ICLA 2013

作者： Hamkins, Joel David Löwe, Benedikt Mathematics Program Graduate Center City University of New York 365 Fifth Avenue New York NY 10016 United States Department of Mathematics College of Staten Island of CUNY Staten Island NY 10314 United States Institute for Logic Language and Computation Universiteit Van Amsterdam Postbus 94242 1090 GE Amsterdam Netherlands Department Mathematik Universität Hamburg Bundesstrasse 55 20146 Hamburg Germany

ISBN: (纸本)9783642360381

We investigate the modal logic of the generic multiverse which is a bimodal logic with operators corresponding to the relations "is a forcing extension of" and "is a ground model of". The fragment of the first relation is the modal logic of forcing and was studied by the authors in earlier work. The fragment of the second relation is the modal logic of grounds and will be studied here for the first time. In addition, we discuss which combinations of modal logics are possible for the two fragments. © 2013 Springer-Verlag Berlin Heidelberg.

关键词： Computer circuits

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Generalizations in mathematical epidemiology: Using computer algebra and intuitive mechanized reasoning

Generalizations in mathematical epidemiology: Using computer...

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International Conference on Advances in Machine Learning and Systems Engineering

作者： Cano, Davinson Castaño Logic and Computation Group Engineering Physics Program EAFIT University Carrera 49 N 7 Sur 50 Medellín Suramérica Colombia

ISBN: (纸本)9789048194186

We are concerned by imminent future problems caused by biological dangers, here we think of a way to solve them. One of them is analyzing endemic models, for this we make a study supported by Computer Algebra Systems (CAS) and Mechanized Reasoning (MR). Also we show the advantages of the use of "CAS" and "MR" to obtain in that case, an epidemic threshold theorem. We prove a previously obtained theorem for SnIR endemic model. Moreover using "CAS+MR" we obtain a new epidemic threshold theorem for the SnImR epidemic model and for the staged progressive SImR model. Finally we discuss the relevance of the theorems and some future applications. © 2010 Springer Science+Business Media B.V.

关键词： Algebra

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LQR control for a multi - inverted pendulum using maple

LQR control for a multi - inverted pendulum using maple

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2008 International Conference on Scientific Computing, CSC 2008

作者： Castaño, Leidy Marcela Giraldo Logic and Computation Group Program of Physical Engineering EAFIT University Medellín Colombia

ISBN: (纸本)1601320590

This article will describe a system for obtaining a LQR controller for a multi-inverted pendulum. The theoretical model of that, it will implement using Maple. The equations are constructed with the Euler-Lagrange mechanical and from them are possible to analyze the stability, controllability and observability matrixes of that system. Finally, this paper presents the LQR controller which is obtained as linear combination of dynamics variables, so that system will be implemented in analogue and computational form to achieve that the system remains stable.

关键词： Inverted pendulum

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Termination of abstract reduction systems

Termination of abstract reduction systems

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13th Computing: The Australasian Theory Symposium, CATS2007

作者： Dawson, Jeremy E. Goré, Rajeev Logic and Computation Program NICTA Automated Reasoning Group Australian National University Canberra ACT 0200 Australia

ISBN: (纸本)1920682465

We present a general theorem capturing conditions required for the termination of abstract reduction systems. We show that our theorem generalises another similar general theorem about termination of such systems. We apply our theorem to give interesting proofs of termination for typed combinatory logic. Thus, our method can handle most path-orderings in the literature as well as the reducibility method typically used for typed combinators. Finally we show how our theorem can be used to prove termination for incrementally defined rewrite systems, including an incremental general path ordering. All proofs have been formally machine-checked in Isabelle/HOL. Copyright 2007, Australian Computer Society, Inc.

关键词： Theorem proving

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Combining knowledge compilation and search for conformant probabilistic planning

Combining knowledge compilation and search for conformant pr...

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ICAPS 2006 - 16th International Conference on Automated Planning and Scheduling

作者： Huang, Jinbo Logic and Computation Program National ICT Australia Canberra ACT 0200 Australia

We present a new algorithm for conformant probabilistic planning, which for a given horizon produces a plan that maximizes the probability of success under quantified uncertainty about the initial state and action effects, and absence of sensory information. Recent work has studied systematic search in the space of all candidate plans as a feasible approach to conformant probabilistic planning, but the algorithms proposed require caching of intermediate computations in such a way that memory is often exhausted quickly except for small planning horizons. On the other hand, planning problems in typical formulations generally have treewidths that do not grow with the horizon, as connections between variables are local to the neighborhood of each time step. These existing planners, however, are unable to directly benefit from the bounded treewidth owing to a constraint on the variable ordering which is necessary for correct computation of the optimal plan. We show that lifting such constraint allows one to obtain a compact compilation of the planning problem, from which an upper bound can be efficiently computed on the value of any partial plan generated during search. Coupled with several optimizations, this results in a depth-first branchand-bound algorithm which on the tested domains runs an order of magnitude faster than its predecessors, and at the same time is able to solve problems for significantly larger horizons thanks to its minimal memory requirements. Copyright © 2006, American Association for Artificial Intelligence (***). All rights reserved.

关键词： Probabilistic logics

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The effect of restarts on the efficiency of clause learning

The effect of restarts on the efficiency of clause learning

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2006 AAAI Workshop

作者： Jinbo, Huang Logic and Computation Program National ICT Australia Canberra ACT 0200 Australia

ISBN: (纸本)1577352939

Given the common use of restarts in today's clause learning SAT solvers, the task of choosing a good restart policy appears to have attracted remarkably little interest. Many solvers, for example, restart once every k conflicts with such a diverse choice of k as to give the impression that one policy may be just as good as another. On the other hand, results have been reported on the use of different restart policies for combinatorial search algorithms. Such results are not directly applicable to clause learning SAT solvers, as the latter are now understood as performing a form of resolution, something fundamentally different from search. In this paper we provide strong evidence that the restart policy matters, and deserves to be chosen less arbitrarily, for a clause learning SAT solver. We begin by pointing out that other things held constant, it is the combination of the restart policy and decision heuristic that completely determines the sequence of resolution steps performed by the solver, and hence its efficiency. In this spirit we implement a prototype clause learning SAT solver that facilitates restarts at arbitrary points, and conduct experiments on an extensive set of industrial benchmarks using various restart policies, including those used by well-known SAT solvers as well as a universal policy proposed in 1993 by Luby et al. The results indicate a substantial impact of the restart policy on the efficiency of the solver, and provide motivation for the design of better restart policies.

关键词： Learning systems

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Multiple preprocessing for systematic SAT solvers

Multiple preprocessing for systematic SAT solvers

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6th International Workshop on the Implementation of logics, IWIL 2006 - Held at the 13th International Conference on logic for programming, Artificial Intelligence and Reasoning

作者： Anbulagan Slaney, John Logic and Computation Program National ICT Australia Ltd. Australia Computer Sciences Laboratory Australian National University Australia

High-performance SAT solvers based on systematic search generally use either conflict driven clause learning (CDCL) or lookahead techniques to gain efficiency. Both styles of reasoning can gain from a preprocessing phase in which some form of deduction is used to simplify the problem. In this paper we undertake an empirical examination of the effects of several recently proposed preprocessors on both CDCL and lookahead-based SAT solvers. One finding is that the use of multiple preprocessors one after the other can be much more effective than using any one of them alone, but that the order in which they are applied is significant. We intend our results to be particularly useful to those implementing new preprocessors and solvers.

关键词： Model checking

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Solving MAP exactly by searching on compiled arithmetic circuits

Solving MAP exactly by searching on compiled arithmetic circ...

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21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06

作者： Huang, Jinbo Chavira, Mark Darwiche, Adnan Logic and Computation Program National ICT Australia Canberra ACT 0200 Australia Computer Science Department University of California Los Angeles Los Angeles CA 90095 United States

ISBN: (纸本)1577352815

The MAP (maximum a posteriori hypothesis) problem in Bayesian networks is to find the most likely states of a set of variables given partial evidence on the complement of that set. Standard structure-based inference methods for rinding exact solutions to MAP, such as variable elimination and join-tree algorithms, have complexities that are exponential in the constrained treewidth of the network. A more recent algorithm, proposed by Park and Darwiche, is exponential only in the treewidth and has been shown to handle networks whose constrained treewidth is quite high. In this paper we present a new algorithm for exact MAP that is not necessarily limited in scalability even by the treewidth. This is achieved by leveraging recent advances in compilation of Bayesian networks into arithmetic circuits, which can circumvent treewidth-imposed limits by exploiting the local structure present in the network. Specifically, we implement a branch-and-bound search where the bounds are computed using linear-time operations on the compiled arithmetic circuit. On networks with local structure, we observe orders-of-magnitude improvements over the algorithm of Park and Darwiche. In particular, we are able to efficiently solve many problems where the latter algorithm runs out of memory because of high treewidth. Copyright © 2006, American Association for Artificial Intelligence (***). All rights reserved.

关键词： Digital arithmetic

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