Applied Mathematics & Information Sciences

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This work is devoted to constructing a deterministic finite automaton whose states are particular types of order-preserving Boolean partial maps introduced by Bisi and Chiaselotti. The domains of such maps are subsets of a finite poset equipped with an idempotent and antitone map. These maps can be identified with certain linear systems of real inequalities and this automaton provides a computational model useful for building the global extensions of such maps.