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<p>A new algorithm for solving the problem of algebraic synthesis is proposed for a finite-state machine with a datapath of transitions, which allows finding formal solutions to the problem for a given set of transition operations. The algorithm is based on presenting state encoding as a transition matrix. This matrix is compared with a combined matrix of operations, which contains all possible options for the transformation of state codes using a given set of transition operations. The element-by-element comparison of matrices allows revealing the availability of a formal solution for the selected set of state codes. It is shown that the proposed algorithm finds all the possible solutions using a complete enumeration of the ways of state encoding. The speed of the proposed algorithm was evaluated when it was implemented in Python.</p>

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An Algorithm for Solving the Problem of Algebraic Synthesis of a Finite-State Machine with Datapath of Transitions Based on a Matrix Approach

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • R. M. Babakov,
  • A. A. Barkalov

摘要

A new algorithm for solving the problem of algebraic synthesis is proposed for a finite-state machine with a datapath of transitions, which allows finding formal solutions to the problem for a given set of transition operations. The algorithm is based on presenting state encoding as a transition matrix. This matrix is compared with a combined matrix of operations, which contains all possible options for the transformation of state codes using a given set of transition operations. The element-by-element comparison of matrices allows revealing the availability of a formal solution for the selected set of state codes. It is shown that the proposed algorithm finds all the possible solutions using a complete enumeration of the ways of state encoding. The speed of the proposed algorithm was evaluated when it was implemented in Python.