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Algebraic interpretation of a microprogram finite-state machine with datapath of transitions. (English. Russian original) Zbl 1346.68124

Cybern. Syst. Anal. 52, No. 2, 191-198 (2016); translation from Kibern. Sist. Anal. 2016, No. 2, 22-29 (2016).
Summary: A new principle is proposed for the representation of functions of a microprogram finite state machine with datapath of transitions in the form of a set of some algebras. The principle consists of partitioning the set of tuples forming transition and output functions into subsets each of which is interpreted as a partial function from the signature of the corresponding algebra.

MSC:

68Q70 Algebraic theory of languages and automata
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
Full Text: DOI

References:

[1] V. M. Glushkov, Synthesis of Digital Automata [in Russian], Fizmatgiz, Moscow (1962). · Zbl 0104.35404
[2] S. I. Baranov, Synthesis of Microprogrammed Automata [in Russian], Energiya, Leningrad (1979).
[3] A. A. Barkalov and R. M. Babakov, “Organization of control units with operational addressing,” USiM, No. 6, 34-39 (2008).
[4] A. A. Barkalov and R. M. Babakov, “Operational formation of state codes in microprogram automata,” Cybernetics and Systems Analysis, 47, No. 2, 193-197 (2011). · doi:10.1007/s10559-011-9301-y
[5] A. A. Barkalov and R. M. Babakov, “Structural representation of the process of synthesis of control automata with datapaths of transitions,” USiM, No. 3, 47-53 (2011).
[6] M. Arbib (ed.), Algebraic Theory of Machines, Languages, and Semigroups [Russian translation], Statistika, Moscow (1975). · Zbl 0358.94001
[7] B. I. Plotkin, L. Ya. Gringlaz, and A. A. Gvaramiya, Elements of Algebraic Automata Theory: A Textbook for Higher Schools [in Russian], Vyssh. Shkola, Moscow (1994).
[8] J. Cook and G. Beyz, Computer Mathematics [Russian translation], Nauka, Moscow (1990). · Zbl 0697.68002
[9] A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970). · Zbl 0223.08001
[10] B. I. Plotkin, Universal Algebra, Algebraic Logic, and Databases [in Russian], Nauka, Moscow (1991). · Zbl 0769.68018
[11] V. M. Glushkov, G. E. Tseytlin, and E. L. Yushchenko, Algebra, Languages, and Programming [in Russian], 3rd Edition, Naukova Dumka, Kyiv (1989).
[12] S. V. Sudoplatov and E. V. Ovchinnikova, Elements of Discrete Mathematics [in Russian], INFRA-M, Moscow and Izd. NGTU, Novosibirsk (2002). · Zbl 1104.03021
[13] A. M. Bogomolov and V. N. Salii, Algebraic Foundations of the Theory of Discrete Systems [in Russian], Nauka, Moscow (1997). · Zbl 0906.68099
[14] F. A. Novikov, Discrete Mathematics for Computer Programmers [in Russian], Piter, St. Petersburg (2000).
[15] V. B. Kudryavtsev, S. V. Alyoshin, and A. S. Podkolzin, An Introduction to the Theory of Automata [in Russian], Nauka, Moscow (1985). · Zbl 0604.68058
[16] V. M. Glushkov, “The abstract theory of automata,” Uspekhi Mat. Nauk, XVI, Issue 5, 3-62 (1961).
[17] B. A. Trakhtenbrot and Ya. M. Bardzin, Finite Automata (Behavior and Synthesis) [in Russian], Nauka, Moscow (1970).
[18] Yu. A. Shikhanovich, Introduction to Modern Mathematics (Initial Concepts) [in Russian], Nauka, Moscow (1965). · Zbl 0138.24501
[19] S. I. Baranov and V. A. Sklyarov, Programmable LSI Digital Devices with Array Structure [in Russian], Radio i Svyaz’, Moscow (1986).
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