Algebraic Interpretation of a Microprogram Finite-State Machine with Datapath of Transitions

Abstract

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.

Using of method of replacement of input variables in microprogram finite-state machine with datapath of transitions

“…Also, the area of its effective application, expressed by a set of values or ranges of values of the parameters of the FSM, must be determined. The modern process of designing of digital devices is impossible without the use of specialized CAD systems, which leads to the problem of developing a synthesizable VHDL model oriented to a certain elemental basis (for example, FPGA) [9]. Also, using a similar model for a given FSM, the hardware amount, expressed, for example, in the number of LUT elements and used FPGA internal memory units, can be experimentally determined.…”

“…In the FSM with DT, the abstract transition function is divided into a set of partial functions, each of which implements a proper subset of FSM transitions [9]. The partitioning is performed in such manner that for each partial function, a uniform law of arithmetic-logical transformation of state codes (transition operation) can be specified, which makes it possible to realize all transitions from the corresponding subset.…”