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An Algorithm for Algebraic Synthesis of a Finite-State Machine Based on Operation Enumeration.

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Title: An Algorithm for Algebraic Synthesis of a Finite-State Machine Based on Operation Enumeration.
Authors: Babakov, R. M., Barkalov, A. A.
Source: Cybernetics & Systems Analysis; Jan2026, Vol. 62 Issue 1, p11-19, 9p
Subject Terms: Finite state machines, Encoding, Logic design, Applied sciences, Computer software execution, Algorithms
Abstract: For a finite-state machine with a datapath of transitions, a new algorithm for algebraic synthesis is proposed that combines the enumeration of state encoding methods with the enumeration of transition operations. The algorithm is based on representing any transition operation as an arithmetic–logical operator over two operands: the code of the current machine state and a constant of the corresponding format. This representation enables automated enumeration of transition operations by enumerating the constants in the used operations within the range of state code values. The output of the algorithm is a set of solutions to the algebraic synthesis problem, where each solution contains values of the state codes and a set of values of the constants used in the operations. The joint enumeration of transition operations and state encoding methods expands the search space. It also increases the number of solutions found for the algebraic synthesis problem compared to the prototype algorithm that does not enumerate transition operations. A software implementation of the proposed algorithm has been performed, confirming its correctness and effectiveness. [ABSTRACT FROM AUTHOR]
Copyright of Cybernetics & Systems Analysis is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: An Algorithm for Algebraic Synthesis of a Finite-State Machine Based on Operation Enumeration.
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  Data: <searchLink fieldCode="AR" term="%22Babakov%2C+R%2E+M%2E%22">Babakov, R. M.</searchLink><br /><searchLink fieldCode="AR" term="%22Barkalov%2C+A%2E+A%2E%22">Barkalov, A. A.</searchLink>
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  Data: Cybernetics & Systems Analysis; Jan2026, Vol. 62 Issue 1, p11-19, 9p
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  Data: <searchLink fieldCode="DE" term="%22Finite+state+machines%22">Finite state machines</searchLink><br /><searchLink fieldCode="DE" term="%22Encoding%22">Encoding</searchLink><br /><searchLink fieldCode="DE" term="%22Logic+design%22">Logic design</searchLink><br /><searchLink fieldCode="DE" term="%22Applied+sciences%22">Applied sciences</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+software+execution%22">Computer software execution</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: For a finite-state machine with a datapath of transitions, a new algorithm for algebraic synthesis is proposed that combines the enumeration of state encoding methods with the enumeration of transition operations. The algorithm is based on representing any transition operation as an arithmetic–logical operator over two operands: the code of the current machine state and a constant of the corresponding format. This representation enables automated enumeration of transition operations by enumerating the constants in the used operations within the range of state code values. The output of the algorithm is a set of solutions to the algebraic synthesis problem, where each solution contains values of the state codes and a set of values of the constants used in the operations. The joint enumeration of transition operations and state encoding methods expands the search space. It also increases the number of solutions found for the algebraic synthesis problem compared to the prototype algorithm that does not enumerate transition operations. A software implementation of the proposed algorithm has been performed, confirming its correctness and effectiveness. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Cybernetics & Systems Analysis is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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