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This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code, is intended...
This paper is the first step in the
solution of the problem of finite completion of comma-free codes.
We show that every finite comma-free code is included in a
finite comma-free code of particular kind, which we called, for
lack of a better term,
canonical comma-free code. Certainly, finite maximal comma-free codes
are always canonical. The final step of the solution which consists
in proving further that every canonical comma-free code is completed
to a finite
maximal comma-free code, is intended...
This paper is a sequel to an earlier paper of the present author, in which it was proved that every finite comma-free code is embedded into a so-called (finite) canonical comma-free code. In this paper, it is proved that every (finite) canonical comma-free code is embedded into a finite maximal comma-free code, which thus achieves the conclusion that every finite comma-free code has finite completions.
This paper is a sequel to an
earlier paper of the present author, in which it was proved that
every finite comma-free code is embedded into a so-called (finite)
canonical comma-free code. In this paper, it is proved that every
(finite) canonical comma-free code is embedded into a finite maximal comma-free
code, which thus achieves the conclusion that every finite comma-free
code has finite completions.
We address the problem of encoding the state variables of a finite state machine such that the BDD representing the next state function and the output function has the minimum number of nodes. We present an exact algorithm to solve this problem when only the present state variables are encoded. We provide results on MCNC benchmark circuits.
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