# Sequention

Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 101)

## Abstract

The third chapter continues a theme of the first section on a higher level. Not only separate switchings are investigated but their sequences of a certain type. These sequences are named sequentions. Sequention is a more complicated mathematical form, which includes venjunctions as minisequentions. Depending on configuration, sequentions are subdivided into the following types: simple and complicated, correct and incorrect, perfect and imperfect, elementary and composite, compatible and inconsistent. For the elements of composite sequentions, binary relations are established as being derived from relationships existing in ordered sets. The rules are developed for transformation of sequentions by means of splitting and slicing actions. General principles are formulated for performing conjunction, disjunction and venjunction operations on sequentions. On the basis of decomposition of sequentions logical expressions are obtained. These expressions represent sequential functions in conjunctive or venjunctive form. For clarity, logical behavior of sequention is assigned by a graph of special form. It is suggested to estimate logical expressions of sequential type by memory depth and volume of memory. Example of the corresponding calculation is brought forward.

## References

1. 1.
Vasyukevich, V.: Monotone sequences of binary data sets and their identification by means of venjunctive functions. ACCS Journal 32(5), 49–56 (1998)Google Scholar
2. 2.
Vasyukevich, V.: Asynchronous sequences decoding. ACCS Journal 41(2), 93–99 (2007)Google Scholar
3. 3.
Gill, A.: Introduction to the Theory of Finite-State Machines. McGraw-Hill, New York (1962)
4. 4.
Yakubaitis, E., Vasyukevich, V., et al.: Automata theory. Journal of Mathematical Sciences 7(2), 193–243 (1977)
5. 5.
McCluskey, E.: Introduction to the Theory of Switching Circuits. McGraw-Hill Book Company, New York (1965)
6. 6.
Hill, F., Peterson, G.: Introduction to Switching Theory and Logical Design. John Wiley and Sons, Chichester (1968)Google Scholar
7. 7.
Muller, D., Bartky, W.: A Theory of Asynchronous Circuits. In: Proc. Int’l Symp. Theory of Switching, Part 1, pp. 204–243 (1959)Google Scholar