On the reduction of the decision problem

Kalmár, László; Surányi, János

doi:10.2307/2267211

Cited by 12 publications

(10 citation statements)

References 2 publications

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“…Associated potential, or Lyapunov, function achieves its global minimum value at an equilibrium point of the network corresponding to the problem's solution. • Satisfiability Problem [67,45]. Values of variables of a Boolean logic formula are represented by voltage values of the root tree-like network and potential is indicated if the values can be assigned in a manner to make the Boolean formula true.…”

Section: Analog Computation On Electrical Properties Of Plant Rootsmentioning

confidence: 99%

Computers from Plants We Never Made: Speculations

Adamatzky¹,

Harding²,

Erokhin

et al. 2017

Emergence, Complexity and Computation

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Plants are highly intelligent organisms. They continuously make distributed processing of sensory information, concurrent decision making and parallel actuation. The plants are efficient green computers per se. Outside in nature, the plants are programmed and hardwired to perform a narrow range of tasks aimed to maximize the plants' ecological distribution, survival and reproduction. To 'persuade' plants to solve tasks outside their usual range of activities, we must either choose problem domains which homomorphic to the plants natural domains or modify biophysical properties of plants to make them organic electronic devices. We discuss possible designs and prototypes of computing systems that could be based on morphological development of roots, interaction of roots, and analog electrical computation with plants, and plant-derived electronic components. In morphological plant processors data are represented by initial configuration of roots and configurations of sources of attractants and repellents; results of computation are represented by topology of the roots' network. Computation is implemented by the roots following gradients of attractants and repellents, as well as interacting with each other. Problems solvable by plant roots, in principle, include shortest-path, minimum spanning tree, Voronoi diagram, α-shapes, convex subdivision of concave polygons. Electrical properties of plants can be modified by loading the plants with functional nanoparticles or coating parts of plants of conductive polymers. Thus, we are in position to make living variable resistors, capacitors, operational amplifiers, multipliers, potentiometers and fixed-function generators. The electrically modified plants can implement summation, integration with respect to time, inversion, multiplication, exponentiation, logarithm, division. Mathematical and engineering problems to be solved can be represented in plant root networks of resistive or reaction elements. Developments in plant-based computing architectures will trigger emergence of a unique community of biologists, electronic engineering and computer scientists working together to produce living electronic devices which future green computers will be made of.

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Section: Analog Computation On Electrical Properties Of Plant Rootsmentioning

confidence: 99%

Computers from Plants We Never Made: Speculations

Adamatzky¹,

Harding²,

Erokhin

et al. 2017

Emergence, Complexity and Computation

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show abstract

“…As the cognoscenti might notice, this is in fact a classic pairing/unpairing function that has been used, by Pepis, Kalmar and Robinson in some fundamental work on recursion theory, decidability and Hilbert's Tenth Problem in [Pepis 1938, Kalmar 1939, Robinson 1950]. …”

Section: Pairing/unpairing Operations Acting Directly On Bitlistsmentioning

confidence: 99%

An embedded declarative data transformation language

Tarau

2009

Proceedings of the 11th ACM SIGPLAN Conference on Principles and Practice of Declarative Programming

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We introduce a logic programming framework for data type transformations based on isomorphisms between elementary data types (natural numbers, finite functions, sets and permutations, digraphs, DAGs, hypergraphs, etc.) and automatically derived extensions to hereditarily finite universes through ranking/unranking operations.An embedded higher order combinator language provides anyto-any encodings automatically.Applications range from stream iterators on combinatorial objects and uniform generation of random instances to succinct data representations and serialization of Prolog terms.The self-contained source code of the paper, as generated from a literate Prolog program, is available at

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“…The predicates pepis pair/3 and pepis unpair/3 are derived from the function pepis J and its left and right unpairing companions pepis K and pepis L that have been used, by Pepis, Kalmar and Robinson in some fundamental work on recursion theory, decidability and Hilbert's Tenth Problem in [23,10,28]:…”

Section: The Pepis-kalmar-robinson Pairing Functionmentioning

confidence: 99%

“…Computational and Data Representation aspects of Finite Set Theory have been described in logic programming and theorem proving contexts in [6,24,22]. Pairing functions have been used work on decision problems as early as [23,10,27,29].…”

Section: Related Workmentioning

confidence: 99%

Ranking and Unranking of Hereditarily Finite Functions and Permutations

Tarau

2008

Preprint

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Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. ranking and unranking functions. Starting from a generalization of Ackerman's encoding of Hereditarily Finite Sets with Urelements and a novel tupling/untupling operation, we derive encodings for Finite Functions and use them as building blocks for an executable theory of Hereditarily Finite Functions. The more difficult problem of ranking and unranking Hereditarily Finite Permutations is then tackled using Lehmer codes and factoradics. The paper is organized as a self-contained literate Prolog program available at http://logic.csci.unt.edu/tarau/research/2008/pHFF.zip.

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On the reduction of the decision problem

Cited by 12 publications

References 2 publications

Computers from Plants We Never Made: Speculations

Computers from Plants We Never Made: Speculations

An embedded declarative data transformation language

Ranking and Unranking of Hereditarily Finite Functions and Permutations

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