ISSN 0032-9460, Problems of Information Transmission, 2006, Vol. 42, No. 4, pp. 340–343.
Pleiades Publishing, Inc., 2006.
Original Russian Text
V.V. Tarasov, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 4, pp. 87–90.
Construction of Virus-Free Switching Circuits
V. V. Tarasov
Ryazan State Radio Engineering Academy
Received November 29, 2004; in ﬁnal form February 28, 2006
Abstract—We consider relay switching circuits constructed from switches whose operation is
described by Boolean functions with external parameters z
and a Boolean variable x
that controls the relay coil. We construct switching circuits that are free from the inﬂuence of
external factors whose indicators are z
Boolean functions with external parameters were previously used by the author to construct cir-
cuits of functional elements that are free from the inﬂuence of external factors , as well as circuits
that realize the indicators of external factors . Now we turn to the analysis of relay switching
circuits. Traditionally, to a switch in a switching circuit there is assigned either a variable x
its negation ¯x
(accordingly, we speak about either a closing switch or a break switch), i being
the number of the relay that controls the switch; the relay coil is always in one of the two states:
= 1) or nonexcited (x
= 0); the switch is also in one of the two states: on (i.e., current
passes through the switch) or oﬀ (current does not pass). Provided that a relay coil and a switch
are synchronized properly, it is assumed that, when the relay coil is excited, a closing switch is
switched on and a break switch is switched oﬀ, and vice versa when the relay coil is nonexcited.
In fact, the relay coil is the principal external factor since it is powered independently of the input
current of the switching system. Other (nonprincipal) external factors act as if beyond the intention
of a circuit designer and aﬀect the system operation depending on the relay coil excitation level.
As external factors, we regard inﬂuence of an operator and, maybe, of a trespasser, as well as well
as changes in temperature conditions, resilience of contacts, parasitic electromagnetic ﬁelds, etc.
To switches in a circuit, we assign Boolean functions f
z) ∨ ¯xh
) are Boolean indicators of external factors. It is readily seen that the concepts
of a closing switch and a break switch become somewhat fuzzy; we shall refer to such switches as
switches with viruses, where g
z) are, respectively, the closing and break projections of
the virus of the switch f
Below we construct (two-terminal) one-relay circuits from switches with viruses according to
standard rules . Clearly, operation of such a circuit uniquely deﬁnes a realizing function f(x,
Our goal is to ﬁnd necessary and suﬃcient conditions to construct, from switches with viruses,
circuits that realize, ﬁrst of all, the functions x and ¯x (they will be referred to as an x-switch and
¯x-switch, respectively), in order to be able after that to construct a new base of (now virus-free)
, i = 1,n, and hence to realize arbitrary Boolean functions g(x
standard way, using n relays. We do not care how functions are realized, whether in the narrow
class of π-circuits or in a wider class of switching circuits, since functional capabilities of base
systems of switches in both classes of control systems obviously are the same.