Search results for "ternary logic"
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Novel qutrit circuit design for multiplexer, De-multiplexer, and decoder
2022
AbstractDesigning conventional circuits present many challenges, including minimizing internal power dissipation. An approach to overcoming this problem is utilizing quantum technology, which has attracted significant attention as an alternative to Nanoscale CMOS technology. The reduction of energy dissipation makes quantum circuits an up-and-coming emerging technology. Ternary logic can potentially diminish the quantum circuit width, which is currently a limitation in quantum technologies. Using qutrit instead of qubit could play an essential role in the future of quantum computing. First, we propose two approaches for quantum ternary decoder circuit in this context. Then, we propose a qua…
A Completeness Proof for a Regular Predicate Logic with Undefined Truth Value
2023
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of "is defined" is extended to terms and formulas via a straightforward recursive algorithm. The "is defined" formulas are constructed so that they themselves are always defined. The completeness proof relies on the Henkin construction. For each formula, precisely one of the formula, its negation, and the negation of its "is defined" formula is true on the constructed model. Many other ternary logics in the literature can be reduced to ours. Partial functions …