Babakov R.M., Barkalov A.A.
A matrix method for detecting formal solutions of the problem of algebraic synthesis of a finite-state machine with a datapath of transitions

For a finite-state machine with a datapath of transitions, a new method for detecting formal solutions to an algebraic synthesis problem is proposed. It represents the set of finite-state machine transitions in the form of a matrix that contains information about the current state encoding. This matrix is matched to the merged matrix of operations, which contains all possible transformations of state codes using a given set of transition operations. Such an approach allows one to simultaneously compare all transition operations with each finite-state machine transition, which reduces the number of verifications of the existence of a formal solution to the problem of algebraic synthesis. The result is the reduction in the execution time of any algorithms of algebraic synthesis of a finite-state machine with a datapath of transitions based on the enumeration of ways of using the operations to implement automatic transitions. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: algebraic synthesis, datapath of transitions, finite-state machine, graph-scheme of algorithms, matrix of transitions, merged matrix of operations, Linear transformations, Algebraic synthesis, Data paths, Datapath of transition, Finite states machine, Formal solution, Graph-scheme of algorithm, matrix, Matrix of transition, Merged matrix of operation, Matrix algebra

Cite:
Babakov R.M., Barkalov A.A. (2023). A matrix method for detecting formal solutions of the problem of algebraic synthesis of a finite-state machine with a datapath of transitions. Cybernetics and Systems Analysis, 59 (2), 18–26. doi: https://doi.org/10.1007/s10559-023-00554-6 http://jnas.nbuv.gov.ua/article/UJRN-0001392154 [In Ukrainian].