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P Systems-Based Computing Polynomials With Integer Coefficients: Design and Formal Verification.

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    This study extends membrane systems to compute polynomials with integer coefficients. The new deterministic P system efficiently captures polynomial values for natural numbers.

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    Area of Science:

    • * Natural Computing
    • * Theoretical Computer Science
    • * Membrane Computing

    Background:

    • * Automatic design of mechanical procedures for abstract problems is a significant scientific challenge.
    • * Membrane systems are a key area within Natural Computing, with prior work focusing on polynomials with natural number coefficients.
    • * Extending these systems to handle integer coefficients is a logical progression.

    Purpose of the Study:

    • * To extend deterministic membrane systems to capture values of polynomials with integer coefficients.
    • * To present a novel deterministic transition P system for this purpose.
    • * To analyze the computational resources required by the designed system.

    Main Methods:

    • * Design of a deterministic transition P system employing priorities in weak interpretation.
    • * Association of the P system with an arbitrary polynomial having integer coefficients.
    • * Encoding the unique computation's configuration using two distinguished objects representing polynomial values for natural numbers.

    Main Results:

    • * Successful extension of deterministic membrane systems to polynomials with integer coefficients.
    • * Demonstration of a unique computation within the designed P system.
    • * Analysis of the descriptive computational resources utilized by the membrane system.

    Conclusions:

    • * The presented deterministic P system effectively computes polynomials with integer coefficients.
    • * This work advances the capabilities of membrane systems in Natural Computing.
    • * The findings contribute to the understanding of computational resource requirements in such systems.