Synthesis of Finite State Machines: Logic Optimization is the second in a set of two monographs devoted to the synthesis of Finite State Machines (FSMs). The first volume, Synthesis of Finite State Machines: Functional Optimization, addresses functional optimization, whereas this one addresses logic optimization. The result of functional optimization is a symbolic description of an FSM which represents a sequential function chosen from a collection of permissible candidates. Logic optimization is the body of techniques for converting a symbolic description of an FSM into a hardware implementation. The mapping of a given symbolic representation into a two-valued logic implementation is called state encoding (or state assignment) and it impacts heavily area, speed, testability and power consumption of the realized circuit. The first part of the book introduces the relevant background, presents results previously scattered in the literature on the computational complexity of encoding problems, and surveys in depth old and new approaches to encoding in logic synthesis. The second part of the book presents two main results about symbolic minimization; a new procedure to find minimal two-level symbolic covers, under face, dominance and disjunctive constraints, and a unified frame to check encodability of encoding constraints and find codes of minimum length that satisfy them. The third part of the book introduces generalized prime implicants (GPIs), which are the counterpart, in symbolic minimization of two-level logic, to prime implicants in two-valued two-level minimization. GPIs enable the design of an exact procedure for two-level symbolic minimization, based on a covering step which is complicated by the need to guarantee encodability of the final cover. A new efficient algorithm to verify encodability of a selected cover is presented. If a cover is not encodable, it is shown how to augment it minimally until an encodable superset of GPIs is determined. To handle encodability the authors have extended the frame to satisfy encoding constraints presented in the second part. The covering problems generated in the minimization of GPIs tend to be very large. Recently large covering problems have been attacked successfully by representing the covering table with binary decision diagrams (BDD). In the fourth part of the book the authors introduce such techniques and extend them to the case of the implicit minimization of GPIs, where the encodability and augmentation steps are also performed implicitly. Synthesis of Finite State Machines: Logic Optimization will be of interest to researchers and professional engineers who work in the area of computer-aided design of integrated circuits.

Synthesis of Finite State Machines: Functional Optimization is one of two monographs devoted to the synthesis of Finite State Machines (FSMs). This volume addresses functional optimization, whereas the second addresses logic optimization. By functional optimization here we mean the body of techniques that: compute all permissible sequential functions for a given topology of interconnected FSMs, and select a best' sequential function out of the permissible ones. The result is a symbolic description of the FSM representing the chosen sequential function. By logic optimization here we mean the steps that convert a symbolic description of an FSM into a hardware implementation, with the goal to optimize objectives like area, testability, performance and so on. Synthesis of Finite State Machines: Functional Optimization is divided into three parts. The first part presents some preliminary definitions, theories and techniques related to the exploration of behaviors of FSMs. The second part presents an implicit algorithm for exact state minimization of incompletely specified finite state machines (ISFSMs), and an exhaustive presentation of explicit and implicit algorithms for the binate covering problem. The third part addresses the computation of permissible behaviors at a node of a network of FSMs and the related minimization problems of non-deterministic finite state machines (NDFSMs). Key themes running through the book are the exploration of behaviors contained in a non-deterministic FSM (NDFSM), and the representation of combinatorial problems arising in FSM synthesis by means of Binary Decision Diagrams (BDDs). Synthesis of Finite State Machines: Functional Optimization will be of interest to researchers and designers in logic synthesis, CAD and design automation.

Synthesis of Finite State Machines: Logic Optimization is the second in a set of two monographs devoted to the synthesis of Finite State Machines (FSMs). The first volume, Synthesis of Finite State Machines: Functional Optimization, addresses functional optimization, whereas this one addresses logic optimization. The result of functional optimization is a symbolic description of an FSM which represents a sequential function chosen from a collection of permissible candidates. Logic optimization is the body of techniques for converting a symbolic description of an FSM into a hardware implementation. The mapping of a given symbolic representation into a two-valued logic implementation is called state encoding (or state assignment) and it impacts heavily area, speed, testability and power consumption of the realized circuit. The first part of the book introduces the relevant background, presents results previously scattered in the literature on the computational complexity of encoding problems, and surveys in depth old and new approaches to encoding in logic synthesis. The second part of the book presents two main results about symbolic minimization; a new procedure to find minimal two-level symbolic covers, under face, dominance and disjunctive constraints, and a unified frame to check encodability of encoding constraints and find codes of minimum length that satisfy them. The third part of the book introduces generalized prime implicants (GPIs), which are the counterpart, in symbolic minimization of two-level logic, to prime implicants in two-valued two-level minimization. GPIs enable the design of an exact procedure for two-level symbolic minimization, based on a covering step which is complicated by the need to guarantee encodability of the final cover. A new efficient algorithm to verify encodability of a selected cover is presented. If a cover is not encodable, it is shown how to augment it minimally until an encodable superset of GPIs is determined. To handle encodability the authors have extended the frame to satisfy encoding constraints presented in the second part. The covering problems generated in the minimization of GPIs tend to be very large. Recently large covering problems have been attacked successfully by representing the covering table with binary decision diagrams (BDD). In the fourth part of the book the authors introduce such techniques and extend them to the case of the implicit minimization of GPIs, where the encodability and augmentation steps are also performed implicitly. Synthesis of Finite State Machines: Logic Optimization will be of interest to researchers and professional engineers who work in the area of computer-aided design of integrated circuits.

Synthesis of Finite State Machines: Functional Optimization is one of two monographs devoted to the synthesis of Finite State Machines (FSMs). This volume addresses functional optimization, whereas the second addresses logic optimization. By functional optimization here we mean the body of techniques that: compute all permissible sequential functions for a given topology of interconnected FSMs, and select a `best' sequential function out of the permissible ones. The result is a symbolic description of the FSM representing the chosen sequential function. By logic optimization here we mean the steps that convert a symbolic description of an FSM into a hardware implementation, with the goal to optimize objectives like area, testability, performance and so on. Synthesis of Finite State Machines: Functional Optimization is divided into three parts. The first part presents some preliminary definitions, theories and techniques related to the exploration of behaviors of FSMs. The second part presents an implicit algorithm for exact state minimization of incompletely specified finite state machines (ISFSMs), and an exhaustive presentation of explicit and implicit algorithms for the binate covering problem. The third part addresses the computation of permissible behaviors at a node of a network of FSMs and the related minimization problems of non-deterministic finite state machines (NDFSMs). Key themes running through the book are the exploration of behaviors contained in a non-deterministic FSM (NDFSM), and the representation of combinatorial problems arising in FSM synthesis by means of Binary Decision Diagrams (BDDs). Synthesis of Finite State Machines: Functional Optimization will be of interest to researchers and designers in logic synthesis, CAD and design automation.