An efficient algorithm to search for minimal closed covers in sequential machines

The removal of redundant states in a finite state machine (FSM) is essential to reducing the complexity of a sequential circuit. An efficient algorithm for state minimization in incompletely specified state machines is presented. This algorithm employs a tight lower bound and a fail-first heuristic and generates a relatively small search space from the prime compatibles. It utilizes efficient pruning rules to further reduce the search space and finds a minimal closed cover. The technique guarantees the elimination of all the redundant states in a very short execution time. Experimental results with a large number of FSMs including the MCNC FSM benchmarks are presented. The results are compared with other work in this area. >

[1]  Fabrizio Luccio Extending the Definition of Prime Compatibility Classes of States in Incomplete Sequential Machine Reduction , 1969, IEEE Transactions on Computers.

[2]  Nripendra N. Biswas State Minimization of Incompletely Specified Sequential Machines , 1974, IEEE Transactions on Computers.

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Ben Bennetts An Improved Method of Prime C-Class Derivation in the State Reduction of Sequential Networks , 1971, IEEE Transactions on Computers.

[5]  Seymour Ginsburg A Synthesis Technique for Minimal State Sequential Machines , 1959, IRE Trans. Electron. Comput..

[6]  R. L. Grimsdale Electronic Computers , 1957, Nature.

[7]  A. Richard Newton,et al.  MUSE: a multilevel symbolic encoding algorithm for state assignment , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  Tiziano Villa,et al.  NOVA: State Assignment of Finite State Machines for Optimal Two-Level Logic Implementations , 1989, 26th ACM/IEEE Design Automation Conference.

[9]  Chao-Chih Yang Closure Partition Method for Minimizing Incomplete Sequential Machines , 1973, IEEE Transactions on Computers.

[10]  P. Pardalos,et al.  An exact algorithm for the maximum clique problem , 1990 .

[11]  Marek Perkowski,et al.  Generation of finite state machines from parallel program graphs in DIADES , 1990, IEEE International Symposium on Circuits and Systems.

[12]  William S. Meisel A Note on Internal State Minimization in Incompletely Specified Sequential Networks , 1967, IEEE Trans. Electron. Comput..

[13]  Srinivas Devadas,et al.  Irredundant interacting sequential machines via optimal logic synthesis , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[14]  Nripendra N. Biswas,et al.  Minimization of Incompletely Specified Sequential Machines , 1975, IEEE Transactions on Computers.

[15]  José Luis Huertas,et al.  A new method for the state reduction of incompletely specified finite sequential machines , 1990, Proceedings of the European Design Automation Conference, 1990., EDAC..

[16]  Robert W. House,et al.  A New Rule for Reducing CC Tables , 1970, IEEE Transactions on Computers.

[17]  Ellis Horowitz,et al.  Fundamentals of Computer Algorithms , 1978 .

[18]  Fabrizio Luccio,et al.  A Method for Minimizing the Number of Internal States in Incompletely Specified Sequential Networks , 1965, IEEE Trans. Electron. Comput..

[19]  S. C. De Sarkar,et al.  Simplification of Incompletely Specified Flow Tables with the Help of Prime Closed Sets , 1969, IEEE Transactions on Computers.

[20]  Charles P. Pfleeger,et al.  State Reduction in Incompletely Specified Finite-State Machines , 1973, IEEE Transactions on Computers.

[21]  Masaru Yamamoto A Method for Minimizing Incompletely Specified Sequential Machines , 1980, IEEE Transactions on Computers.

[22]  S. Yang,et al.  Logic Synthesis and Optimization Benchmarks User Guide Version 3.0 , 1991 .

[23]  Alberto L. Sangiovanni-Vincentelli,et al.  Irredundant sequential machines via optimal logic synthesis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[24]  Ayakannu Mathialagan,et al.  Implication trees in the minimization of incompletely specified sequential machines , 1983 .

[25]  D. Sarma,et al.  Fast heuristic algorithms for finite state machine minimization , 1991, Proceedings of the European Conference on Design Automation..

[26]  H. Allen Curtis The Further Reduction of CC-Tables , 1971, IEEE Transactions on Computers.

[27]  J. Hartmanis,et al.  Algebraic Structure Theory Of Sequential Machines , 1966 .

[28]  Azaria Paz,et al.  Theory of Machines and Computations , 1971 .

[29]  Robert M. Haralick,et al.  Increasing Tree Search Efficiency for Constraint Satisfaction Problems , 1979, Artif. Intell..

[30]  Stephen H. Unger,et al.  Minimizing the Number of States in Incompletely Specified Sequential Switching Functions , 1959, IRE Trans. Electron. Comput..

[31]  고경식 불완전하게 규제된 순서회로의 내부상태의 단위화방법 ( A Method for Minimizing the Number of Internal States in Incompletely Specified Sequential Networks ) , 1967 .