Symbolic Manipulation Techniques Research Articles

The Philosophising Machine – a Specification of the Turing Test

Block’s (The Philosophical Review, 90(1), 5–43 1981) anti-behaviourist attack of the Turing Test not only illustrates that the test is a non-sufficient criterion for attributing thought; I suggest that it also exemplifies the limiting case of the more general concern that a machine which has access to enormous amounts of data can pass the Turing Test by simple symbol-manipulation techniques. If the answers to a human interrogator are entailed by the machines’ data, the Turing Test offers no clear criterion to distinguish between a thinking machine and a machine that merely manipulates representations of words and sentences as it is found in contemporary Natural Language Processing models. This paper argues that properties about vagueness are accessible to any human-like thinker but do not normally display themselves in ordinary language use. Therefore, a machine that merely performs simple symbol manipulation from large amounts of previously acquired data – where this body of data does not contain facts about vagueness – will not be able to report on these properties. Conversely, a machine that has the capacity to think would be able to report on these properties. I argue that we can exploit this fact to establish a sufficient criterion of thought. The criterion is a specification of some of the questions that, as I explain, should be asked by the interrogator in a Turing Test situation.

Analytic Free-Molecular Aerodynamics for Rapid Propagation of Resident Space Objects

Aerodynamic forces and moments are significant perturbations on low-Earth-orbiting objects, second in magnitude to the nonspherical gravity field. Traditionally, the aerodynamic perturbations are calculated using a direct simulation Monte Carlo method. Under certain assumptions, these forces and moments can be described analytically via free-molecular flow theory. Using symbolic manipulation techniques, exact expressions for the free-molecular aerodynamics of analytic shapes can be derived. In this investigation, analytic expressions for the aerodynamic force and moment coefficients of primitive and composite parametric surfaces are derived, then validated against industry-standard direct simulation Monte Carlo techniques. A framework for the rapid and accurate calculation of free-molecular aerodynamics of composite geometries based on superposition is described. This framework is applied to axisymmetric composite geometries. Results within 6% of direct simulation Monte Carlo calculations are obtained in 0.05% of the time. The analytic aerodynamics models enable rapid trajectory and uncertainty propagation for low-Earth-orbiting objects. A case study on aerodynamic perturbations of a low-Earth-orbit nanosatellite is included to demonstrate application of these analytic models. The case study shows that these derived analytical free-molecular aerodynamics produce results that are applicable to inclusion in rapid trajectory propagation tools for orbit prediction and conceptual mission design.

Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

Abstract In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.

Three Solvable Matrix Models of a Quantum Catastrophe

Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies called quantum catastrophes are described in detail. Computer-assisted symbolic manipulation techniques are shown unexpectedly efficient for the purpose.

Symbolic computation of the Hartree–Fock energy from a chiral EFT three-nucleon interaction at N 2LO

We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree–Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N 2LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector–isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions. Program summary Program title: SymbHFNNN Catalogue identifier: AEGC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 96 666 No. of bytes in distributed program, including test data, etc.: 378 083 Distribution format: tar.gz Programming language: Mathematica 7.1 Computer: Any computer running Mathematica 6.0 and later versions Operating system: Windows Xp, Linux/Unix RAM: 256 Mb Classification: 5, 17.16, 17.22 Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2LO involves tremendous spin–isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector–isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Solution method: The HF energy from the chiral EFT three-nucleon interaction at N 2LO is cast into a form suitable for an automatic simplification of the spin–isospin traces. Several Mathematica functions and symbolic manipulation techniques are used to obtain the result in terms of the scalar/vector–isoscalar/isovector parts of the one-body density matrix. Running time: Several hours

Automatic modular abstractions for linear constraints

We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and containing linear assignments and tests. In addition to loop-free code, the same method also applies for obtaining least fixed points as functions of the precondition, which permits the analysis of loops and recursive functions. Our algorithms are based on new quantifier elimination and symbolic manipulation techniques. Given the specification of an abstract domain, and a program block, our method automatically outputs an implementation of the corresponding abstract transformer. It is thus a form of program transformation. The motivation of our work is data-flow synchronous programming languages, used for building control-command embedded systems, but it also applies to imperative and functional programming.

Tridiagonal -symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime

A generic -symmetric Hamiltonian is assumed tridiagonalized and truncated to N < ∞ dimensions, H → H(chain model), and all its up–down symmetrized special cases with J = [N/2] real couplings are considered, H(chain model) → H(N). Using symbolic manipulation and extrapolation techniques we find out that in the strongly non-Hermitian regime the secular equation gets partially factorized at all N. This enables us to reveal a fine-tuned alignment of the dominant couplings implying an asymptotically sharply spiked shape of the boundary of the J-dimensional quasi-Hermiticity domain in which all the spectrum of energies E(N)n remains real and observable.

Symbolic manipulation techniques for low order LFT-based parametric uncertainty modelling

Symbolic techniques are very useful in obtaining low order LFT-representations of linear parametric models. The main role of symbolic manipulations is to find, via suitable pre-processing steps, equivalent representations of rationally dependent parametric matrices, which automatically lead to lower order LFT-representations. In this paper we give an overview of symbolic processing methods and we propose some new techniques and several enhancements of existing methods. All proposed methods are implemented in the latest version of the LFR-toolbox and served to illustrate the strengths of symbolic processing in obtaining low order LFT-representations of two challenging parametric model examples.

Specification, verification, and synthesis of concurrency control components

Run-time errors in concurrent programs are generally due to the wrong usage of synchronization primitives such as monitors. Conventional validation techniques such as testing become ineffective for concurrent programs since the state space increases exponentially with the number of concurrent processes. In this paper, we propose an approach in which 1) the concurrency control component of a concurrent program is formally specified, 2) it is verified automatically using model checking, and 3) the code for concurrency control component is automatically generated. We use monitors as the synchronization primitive to control access to a shared resource by multipleconcurrent processes. Since our approach decouples the concurrency control component from the rest of the implementation it is scalable. We demonstrate the usefulness of our approach by applying it to a case study on Airport Ground Traffic Control.We use the Action Language to specify the concurrency control component of a system. Action Language is a specification language for reactive software systems. It is supported by an infinite-state model checker that can verify systems with boolean, enumerated and udbounded integer variables. Our code generation tool automatically translates the verified Action Language specification into a Java monitor. Our translation algorithm employs symbolic manipulation techniques and the specific notification pattern to generate an optimized monitor class by eliminating the context switch overhead introduced as a result of unnecessary thread notification. Using counting abstraction, we show that we can automatically verify the monitor specifications for arbitrary number of threads.

Study on laminar flow in helical circular pipes with Galerkin method

A set of fluid mechanics equations in an arbitrary curvilinear coordinate system are obtained. The fully developed laminar flow in helical circular pipes subject to the influence of both curvature and torsion is analyzed. The solutions are obtained by the Galerkin method which is realized with the aid of computerized symbolic manipulation technique. The results indicate that the Galerkin technique can effectively overcome the limitation of small parameters for perturbation method. Based on the high-order semi-analytical solutions presented, the characteristics of secondary flow in pipes are discussed.

Integrated environmental management process applying genetic algorithm

This study proposes a Total Environmental Management System using a Genetic Algorithm (TEMS-AGA), which takes into account the possible effects on the environment together with other management concerns such as quality, lead time, and cost. In TEMS-AGA, a problem is modeled by an AND–OR-type tree structure in its structural aspects and by a list of symbolic expressions in its quantitative aspects. TEMS-AGA evaluates the activity (policy, project) using a symbolic manipulation technique. GA is used to search a compromising better solution. Experiments showed that the determination of sub-optimal combinations of activities for a problem with multiple facet can be made by GA.

Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems

In the present work, techniques for the symbolic manipulation of general nonlinear differential algebraic equation (DAE) systems are presented, and used for model simplification purposes, to support efficient simulation of large scale continuous systems in an object-oriented modelling environment. The specific problems addressed are efficient elimination of trivial equations by means of substitution, system block lower triangular (BLT) partitioning, and tearing, i.e. hiding of algebraic variables. Moreover, the weakening heuristic criterion for decoupling of large systems, via dynamic approximation, is studied. All these techniques have been successfully implemented and tested in MOSES (modular object-oriented software environment for simulation), in order to define a complete model simplification process. The results achieved by applying the discussed algorithms and criteria on serial multibody systems are illustrated. A brief overview on further known symbolic manipulation techniques is also given, comparing them with the proposed ones, throughout the paper.

Automatic Rendering of Astrodynamics Expressions for Efficient Evaluation

In this paper, we describe the automatic rendering of expressions computed using symbolic manipulation. Computations from astrodynamics frequently can be put in a fixed hierarchy of polynomials and Fourier series. Once in this form, FORTRAN subprograms can be generated automatically in a form that lends itself to numerical evaluation. The goal of the current work is to present an approach for using symbolic manipulation techniques to produce a Fortran representation of the normalized Hamiltonian and other supporting equations representing as many of the actual physical effects on satellites as possible.

Query transformation in heterogeneous distributed database systems

A heterogeneous Distributed Database Management system is organized as a federation of nodes with different functional capabilities and using different nodal query languages. The problem of query decomposition and translation is investigated and two approaches are identified as direct translation and a translation using an intermediate canonical language. The use of universal symbolic manipulation techniques instead of dedicated cross-translators to perform query transformation is suggested.

Towards efficient partial evaluation in logic programming

Partial evaluation is a symbolic manipulation technique used to produce efficient algorithms when part of the input to the algorithm is known. Other applications of partial evaluators such as universal compilation and compiler generation are also known to be possible. A partial evaluator receives as input a program and partially known input to that program, and outputs a residual program which should run at least as efficient as the input program with restricted input. In this paper we study the case where both the input and residual programs are logic programs, being the partial evaluator itself a logic program. Up to now, partial evaluators have failed to process large “non=toy” examples. Here we present extensions to partial evaluators whic will allow us to produce more efficient residual programs using less computing resources, during partial evaluation. First, the introduced extensions allow the processing of large examples, which is not possible with the previous techniques. This is now possible since the extensions use less CPU time and memory consumption during the partial evaluation process. Second, the extended partial evaluator produces smaller residual programs, producing important CPU time optimizing effects. With the standard techniques, a partial evaluator will most probably act as a pessimizer, not as an optimizer. Examples are given.

Symbolic manipulation of loops and lattice gauge theory in the loop representation

The symbolic manipulation techniques, necessary to push the calculation of observables in the loop representation to higher order is discussed. Z(2) gauge theory in the loop representation is used to show how this techniques can be implemented in a concrete model.

Efficiently computing communication complexity for multilevel logic synthesis

A new method for computing the communication complexity of a given partitioning whose running time is O(pq), where p is the number of implicants (cubes) in the minimum covering of the function and q is the number of different overlapping of those cubes, is presented. Two heuristics for finding a good partition which give encouraging results are presented. Together, these two techniques allow a much larger class of functions to be synthesized. Two heuristic partitioning methods have been tested for certain circuits from the MCNC benchmark set. Using either heuristic, 11 out of 14 examples actually achieve the optimal solutions. A prototype program designed using the above techniques was developed and tested for circuits from the MCNC benchmark set. The experiment shows that the new symbolic manipulation technique is several orders of magnitude faster than an old version. >

A survey of FORTRAN code generation using MACSYMA

This paper presents the underlying symbolic manipulation techniques used by the authors to produce FORTRAN code with the artificial intelligence code MACSYMA. The FORTRAN codes produced use finite difference methods to solve the governing equations for numerical grid generation, including elliptic and variational methods, and to solve the hosted equations, including fluid dynamics, heat transfer, and electro‐statics. Consideration will be given to writing the hosted equations in strong conservation form in general nonorthogonal coordinates; high order and conditional differencing schemes; colocated variables versus staggered grids; and code validation procedures.

Dual Lanczos transformation theory: Spectral and temporal properties of the Brownian harmonic oscillator embedded in the dynamically invariant subspaces for first and second moment coordinate and momentum fluctuations

The utility of dual Lanczos transformation theory in elucidating and solving time evolution and spectral density problems is demonstrated in a theoretical treatment of those spectral and temporal properties of the Brownian harmonic oscillator embedded in the dynamically invariant subspaces for first and second moment coordinate and momentum fluctuations. By coupling the mathematical apparatus of dual Lanczos transformation theory with symbolic manipulation techniques, some new results along with known results are obtained in a rather trivial fashion as compared with the methods usually adopted in classical Brownian motion theory. Aside from the theoretical treatment of the Brownian harmonic oscillator, the present work illustrates a number of important concepts and the use of the theory, including: (i) the mechanics of its implementation; (ii) the notion of dynamically invariant subspaces embedded with certain spectral and temporal properties; (iii) the investigation of generalized Langevin equations and memory function hierarchies; (iv) the use of spectral domains in the complex plane to make rigorous statements about expected temporal character, including the possible existence of separations in time scales and the role of memory effects; (v) the extraction and utilization of dynamically embedded information to determine the time evolution or spectral densities of dynamical variables and their ensemble averages, autocorrelation functions, and cross correlation functions; and (vi) the handling of time evolution and spectral density problems that are inaccessible by matrix diagonalization techniques and those that may not be given the usual continued fraction representation.

Symbolic and algebraic computation research in Italy

We like to fix the starting point of the research activities in Symbolic and Algebraic Computation (SAC) in Italy at the IFIP Working Conference on Symbol Manipulation Languages and Techniques held in Pisa in September 1966. This event in fact, stimulated early research conducted for several years by single researchers cooperating more with foreign colleagues than each other.