Evolutionary Algorithm for State Assignment of Finite State Machines

Introduction A significant part of digital circuits is constituted by sequential synchronous circuits behaviour of which can be presented by a finite state machine (FSM). So nothing strange the FSM synthesis methods are continually developed (cf. the monographs [14, 19] or [17, 8]). One of the most crucial steps in FSM synthesis is the encoding of FSM states referred to as the state assignment problem (SAP). It consists in the unique assignment of bit strings to the states of sequential circuit (SC). This step of FSM synthesis is important because it affects the quality of realised SC (cost/area, maximum frequency, power consumption). Effective algorithms for the state encoding were developed, e.g. NOVA [18] for two-level implementation targeted to Programmable Logic Arrays (PLAs) or MUSTANG [10] and JEDI [15] for multilevel FSM implementation. However, state assignments generated by these methods, for FSMs implemented in modern programmable devices [1, 7] allowing efficient implementations of digital systems, are far from optimum [9]. Taking above into account, and considering other conditions (cf. [5, 12, 16]) we decided to try to cope with SAP using evolutionary algorithm (EA). Genetic and evolutionary algorithms are successfully used in VLSI CAD [11]. They were also applied to SAP [3, 4, 5]. In this paper we propose an evolutionary algorithm for SAP. We introduce the original crossover operators and next compare them with the known ones using. State assignment problem States of FSM are named but when a sequential circuit is implemented they are represented by bit strings. Therefore during FSM synthesis states have to be encoded i.e. uniquely assigned with binary strings (state codes). Assume FSM has m states from the set S = {s1, s2, ..., sm}. The minimum number of bits that must be used to encode FSM states is rmin = | log2 m], where |d] is the smallest integer not less than d. The number A of possible assignments is