Istituto di Scienza e Tecnologie dell'Informazione     
Frosini G., Gerace G. B. A simplified method for minimizing the number of internal states in pulse input asynchronous sequential circuits. Internal note IEI-B69-02, 1969.
This paper describes simplified procedurcs for minimizing the number of internal states of two important classes of incompletely specified primitive flow tables (complete primitive PA tables and incomplete primitive PA tables) for pulse input asynchronous sequential circuits (PA circuits). In a complete primitive PA table optional entries result only from the fact that in every input sequence each input state Ii is immediately followed by a special input state Io called null input state; and in an incomplete primitive PA table optional entries result from the restriction above and from the further restriction that any input state following Io is different from input state preceding Io. Properties and applications of PA circuits were described in a previous paper, where it is shown that for any pulse input synchronous circuit fully specified there exists a PA circuit, with identical input-output specifications, described by a complete PA table, and that al1y asynchronous circuit fully specified can be realized using a PA circuit described by an incomplete primitive PA table. In this paper it is shown that, for complete and incomplete primitive PA tables, the compatibility relation between internal states has some transitive properties, which allow to strongly simplify the reduction process. For complete primitive PA tables a minimal covering is obtained selecting compatibi1ity classes among the maximal ones, and for incomplete primitive PA tables the selection between compatibility classes is restricted to usefu1 c1asses. These are easily derived from the maximal classes, and the number of useful c1asses equa1s the number of the maximal ones.
Subject Pulse input asynchronous
Sequential circuits

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